Tissue refractometry using Hilbert phase microscopy.
Lue, Niyom; Bewersdorf, Joerg; Lessard, Mark D; Badizadegan, Kamran; Dasari, Ramachandra R; Feld, Michael S; Popescu, Gabriel
2007-12-15
We present, for the first time to our knowledge, quantitative phase images associated with unstained 5 mum thick tissue slices of mouse brain, spleen, and liver. The refractive properties of the tissue are retrieved in terms of the average refractive index and its spatial variation. We find that the average refractive index varies significantly with tissue type, such that the brain is characterized by the lowest value and the liver by the highest. The spatial power spectra of the phase images reveal power law behavior with different exponents for each tissue type. This approach opens a new possibility for stain-free characterization of tissues, where the diagnostic power is provided by the intrinsic refractive properties of the biological structure. We present results obtained for liver tissue affected by a lysosomal storage disease and show that our technique can quantify structural changes during this disease development.
Live cell refractometry using Hilbert phase microscopy and confocal reflectance microscopy.
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R; Feld, Michael S
2009-11-26
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ.
Live Cell Refractometry Using Hilbert Phase Microscopy and Confocal Reflectance Microscopy†
Lue, Niyom; Choi, Wonshik; Popescu, Gabriel; Yaqoob, Zahid; Badizadegan, Kamran; Dasari, Ramachandra R.; Feld, Michael S.
2010-01-01
Quantitative chemical analysis has served as a useful tool for understanding cellular metabolisms in biology. Among many physical properties used in chemical analysis, refractive index in particular has provided molecular concentration that is an important indicator for biological activities. In this report, we present a method of extracting full-field refractive index maps of live cells in their native states. We first record full-field optical thickness maps of living cells by Hilbert phase microscopy and then acquire physical thickness maps of the same cells using a custom-built confocal reflectance microscope. Full-field and axially averaged refractive index maps are acquired from the ratio of optical thickness to physical thickness. The accuracy of the axially averaged index measurement is 0.002. This approach can provide novel biological assays of label-free living cells in situ. PMID:19803506
Improved specimen reconstruction by Hilbert phase contrast tomography.
Barton, Bastian; Joos, Friederike; Schröder, Rasmus R
2008-11-01
The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
International Nuclear Information System (INIS)
Luks, A.; Perinova, V.
1993-01-01
A suitable ordering of phase exponential operators has been compared with the antinormal ordering of the annihilation and creation operators of a single mode optical field. The extended Wigner function for number and phase in the enlarged Hilbert space has been used for the derivation of the Wigner function for number and phase in the original Hilbert space. (orig.)
Phase difference estimation method based on data extension and Hilbert transform
International Nuclear Information System (INIS)
Shen, Yan-lin; Tu, Ya-qing; Chen, Lin-jun; Shen, Ting-ao
2015-01-01
To improve the precision and anti-interference performance of phase difference estimation for non-integer periods of sampling signals, a phase difference estimation method based on data extension and Hilbert transform is proposed. Estimated phase difference is obtained by means of data extension, Hilbert transform, cross-correlation, auto-correlation, and weighted phase average. Theoretical analysis shows that the proposed method suppresses the end effects of Hilbert transform effectively. The results of simulations and field experiments demonstrate that the proposed method improves the anti-interference performance of phase difference estimation and has better performance of phase difference estimation than the correlation, Hilbert transform, and data extension-based correlation methods, which contribute to improving the measurement precision of the Coriolis mass flowmeter. (paper)
Hilbert transform and optical tomography for anisotropic edge enhancement of phase objects
International Nuclear Information System (INIS)
Montes-Perez, Areli; Meneses-Fabian, Cruz; Rodriguez-Zurita, Gustavo
2011-01-01
In phase object tomography a slice reconstruction is related to distribution of refractive index. Typically, this is obtained by applying the filtered back-projection algorithm to the set of projections (sinogram) obtained experimentally, which are sequentially obtained by calculating the phase of the wave emerging from the slice of the object at different angles. In this paper, based on optical implementation of the Hilbert-transform in a 4f Fourier operator, the Hilbert transform of the projections leaving of the object are obtained numerically. When these projection data are captured for a set of viewing angles an unconventional sinogram is eventually obtained, we have called it as an Hilbert-sinogram. The reconstruction obtained by applying the filtered back-projection algorithm is proportional to the Hilbert transform of the distribution of refractive index of the slice and the obtained image shows a typical isotropic edge enhancement. In this manuscript, the theoretical analysis and the numerical implementation of the Hilbert-transform, mathematical model of the edge enhancement reconstructed are extensively detailed.
Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.
Fernández-Pousa, Carlos R; Maestre, Haroldo; Torregrosa, Adrián J; Capmany, Juan
2008-10-27
We show that the minimal phase of the temporal coherence function gamma (tau) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 microm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.
Biological applications of phase-contrast electron microscopy.
Nagayama, Kuniaki
2014-01-01
Here, I review the principles and applications of phase-contrast electron microscopy using phase plates. First, I develop the principle of phase contrast based on a minimal model of microscopy, introducing a double Fourier-transform process to mathematically formulate the image formation. Next, I explain four phase-contrast (PC) schemes, defocus PC, Zernike PC, Hilbert differential contrast, and schlieren optics, as image-filtering processes in the context of the minimal model, with particular emphases on the Zernike PC and corresponding Zernike phase plates. Finally, I review applications of Zernike PC cryo-electron microscopy to biological systems such as protein molecules, virus particles, and cells, including single-particle analysis to delineate three-dimensional (3D) structures of protein and virus particles and cryo-electron tomography to reconstruct 3D images of complex protein systems and cells.
States in the Hilbert space formulation and in the phase space formulation of quantum mechanics
International Nuclear Information System (INIS)
Tosiek, J.; Brzykcy, P.
2013-01-01
We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function
Asghari, Mohammad H; Azaña, José
2009-02-01
A simple all-fiber design for implementing an all-optical temporal Hilbert transformer is proposed and numerically demonstrated. We show that an all-optical Hilbert transformer can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile incorporating a single pi phase shift in the middle of the grating length. All-optical Hilbert transformers capable of processing arbitrary optical waveforms with bandwidths up to a few hundreds of gigahertz can be implemented using feasible FBGs.
Tensor algebra over Hilbert space: Field theory in classical phase space
International Nuclear Information System (INIS)
Matos Neto, A.; Vianna, J.D.M.
1984-01-01
It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt
DEFF Research Database (Denmark)
Israelsen, Niels Møller; Maria, Michael; Feuchter, Thomas
2018-01-01
-linearities lead together to an unknown chirp of the detected interferogram. One method to compensate for the chirp is to perform a pixel-wavenumber calibration versus phase that requires numerical extraction of the phase. Typically a Hilbert transform algorithm is employed to extract the optical phase versus...... wavenumber for calibration and dispersion compensation. In this work we demonstrate UHR-OCT at 1300 nm using a Super continuum source and highlight the resolution constraints in using the Hilbert transform algorithm when extracting the optical phase for calibration and dispersion compensation. We demonstrate...... that the constraints cannot be explained purely by the numerical errors in the data processing module utilizing the Hilbert transform but must be dictated by broadening mechanisms originating from the experimentally obtained interferograms....
Li, Xiangyu; Huang, Zhanhua; Zhu, Meng; He, Jin; Zhang, Hao
2014-12-01
Hilbert transform (HT) is widely used in temporal speckle pattern interferometry, but errors from low modulations might propagate and corrupt the calculated phase. A spatio-temporal method for phase retrieval using temporal HT and spatial phase unwrapping is presented. In time domain, the wrapped phase difference between the initial and current states is directly determined by using HT. To avoid the influence of the low modulation intensity, the phase information between the two states is ignored. As a result, the phase unwrapping is shifted from time domain to space domain. A phase unwrapping algorithm based on discrete cosine transform is adopted by taking advantage of the information in adjacent pixels. An experiment is carried out with a Michelson-type interferometer to study the out-of-plane deformation field. High quality whole-field phase distribution maps with different fringe densities are obtained. Under the experimental conditions, the maximum number of fringes resolvable in a 416×416 frame is 30, which indicates a 15λ deformation along the direction of loading.
Trusiak, Maciej; Służewski, Łukasz; Patorski, Krzysztof
2016-02-22
Hybrid single shot algorithm for accurate phase demodulation of complex fringe patterns is proposed. It employs empirical mode decomposition based adaptive fringe pattern enhancement (i.e., denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and accurate local fringe direction map calculation. Robustness to fringe pattern significant noise, uneven background and amplitude modulation as well as local fringe period and shape variations is corroborated by numerical simulations and experiments. Proposed automatic, adaptive, fast and comprehensive fringe analysis solution compares favorably with other previously reported techniques.
Directory of Open Access Journals (Sweden)
Unger Laura Anna
2015-09-01
Full Text Available This work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories. We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5 mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.
Optofluidic time-stretch quantitative phase microscopy.
Guo, Baoshan; Lei, Cheng; Wu, Yi; Kobayashi, Hirofumi; Ito, Takuro; Yalikun, Yaxiaer; Lee, Sangwook; Isozaki, Akihiro; Li, Ming; Jiang, Yiyue; Yasumoto, Atsushi; Di Carlo, Dino; Tanaka, Yo; Yatomi, Yutaka; Ozeki, Yasuyuki; Goda, Keisuke
2018-03-01
Innovations in optical microscopy have opened new windows onto scientific research, industrial quality control, and medical practice over the last few decades. One of such innovations is optofluidic time-stretch quantitative phase microscopy - an emerging method for high-throughput quantitative phase imaging that builds on the interference between temporally stretched signal and reference pulses by using dispersive properties of light in both spatial and temporal domains in an interferometric configuration on a microfluidic platform. It achieves the continuous acquisition of both intensity and phase images with a high throughput of more than 10,000 particles or cells per second by overcoming speed limitations that exist in conventional quantitative phase imaging methods. Applications enabled by such capabilities are versatile and include characterization of cancer cells and microalgal cultures. In this paper, we review the principles and applications of optofluidic time-stretch quantitative phase microscopy and discuss its future perspective. Copyright © 2017 Elsevier Inc. All rights reserved.
Computing Instantaneous Frequency by normalizing Hilbert Transform
Huang, Norden E.
2005-05-31
This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.
International Nuclear Information System (INIS)
Englman, R.
2016-01-01
The recent phase shift data of Takada et al. (Phys. Rev. Lett. 113 (2014) 126601) for a two level system are reconstructed from their current intensity curves by the method of Hilbert transform, for which the underlying Physics is the principle of causality. An introductory algebraic model illustrates pedagogically the working of the method and leads to newly derived relationships involving phenomenological parameters, in particular for the sign of the phase slope between the resonance peaks. While the parametrization of the experimental current intensity data in terms of a few model parameters shows only a qualitative agreement for the phase shift, due to the strong impact of small, detailed variations in the experimental intensity curve on the phase behavior, the numerical Hilbert transform yields a satisfactory reproduction of the phase.
Phase-Modulation Laser Interference Microscopy
DEFF Research Database (Denmark)
Brazhe, Alexey; Brazhe, Nadezda; Maximov, G. V.
2008-01-01
We describe how phase-modulation laser interference microscopy and wavelet analysis can be applied to noninvasive nonstained visualization and study of the structural and dynamical properties of living cells. We show how phase images of erythrocytes can reveal the difference between various...... erythrocyte forms and stages of hemolysis and how phase images of neurons reveal their complex intracellular structure. Temporal variations of the refractive index are analyzed to detect cellular rhythmic activity on different time scales as well as to uncover interactions between the cellular processes....
Frames in super Hilbert modules
Directory of Open Access Journals (Sweden)
Mehdi Rashidi-Kouchi
2018-01-01
Full Text Available In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.
Trusiak, Maciej; Patorski, Krzysztof
2015-02-23
Gram-Schmidt orthonormalization is a very fast and efficient method for the fringe pattern phase demodulation. It requires only two arbitrarily phase-shifted frames. Images are treated as vectors and upon orthogonal projection of one fringe vector onto another the quadrature fringe pattern pair is obtained. Orthonormalization process is very susceptible, however, to noise, uneven background and amplitude modulation fluctuations. The Hilbert-Huang transform based preprocessing is proposed to enhance fringe pattern phase demodulation by filtering out the spurious noise and background illumination and performing fringe normalization. The Gram-Schmidt orthonormalization process error analysis is provided and its filtering-expanded capabilities are corroborated analyzing DSPI fringes and performing amplitude demodulation of Bessel fringes. Synthetic and experimental fringe pattern analyses presented to validate the proposed technique show that it compares favorably with other pre-filtering schemes, i.e., Gaussian filtering and continuous wavelet transform.
International Nuclear Information System (INIS)
Khan, Tariq; Majumdar, Shantanu; Udpa, Lalita; Ramuhalli, Pradeep; Crawford, Susan; Diaz, Aaron; Anderson, Michael T.
2012-01-01
The objective of this work is to develop processing algorithms to detect and localize flaws using ultrasonic phased-array data. Data was collected on cast austenitic stainless stell (CASS) weld specimens onloan from the U.S. nuclear power industry' Pressurized Walter Reactor Owners Group (PWROG) traveling specimen set. Each specimen consists of a centrifugally cast stainless stell (CCSS) pipe section welded to a statically cst(SCSS) or wrought (WRSS) section. The paper presents a novel automated flaw detection and localization scheme using low frequency ultrasonic phased array inspection singals from the weld and heat affected zone of the based materials. The major steps of the overall scheme are preprocessing and region of interest (ROI) detection followed by the Hilbert-Huang transform (HHT) of A-scans in the detected ROIs. HHT offers time-frequency-energy distribution for each ROI. The Accumulation of energy in a particular frequency band is used as a classification feature for the particular ROI
Generalised phase contrast: microscopy, manipulation and more
DEFF Research Database (Denmark)
Palima, Darwin; Glückstad, Jesper
2010-01-01
Generalised phase contrast (GPC) not only leads to more accurate phase imaging beyond thin biological samples, but serves as an enabling framework in developing tools over a wide spectrum of contemporary applications in optics and photonics, including optical trapping and micromanipulation, optic...
Quantitative phase microscopy using deep neural networks
Li, Shuai; Sinha, Ayan; Lee, Justin; Barbastathis, George
2018-02-01
Deep learning has been proven to achieve ground-breaking accuracy in various tasks. In this paper, we implemented a deep neural network (DNN) to achieve phase retrieval in a wide-field microscope. Our DNN utilized the residual neural network (ResNet) architecture and was trained using the data generated by a phase SLM. The results showed that our DNN was able to reconstruct the profile of the phase target qualitatively. In the meantime, large error still existed, which indicated that our approach still need to be improved.
2013-01-01
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.
Drive frequency dependent phase imaging in piezoresponse force microscopy
International Nuclear Information System (INIS)
Bo Huifeng; Kan Yi; Lu Xiaomei; Liu Yunfei; Peng Song; Wang Xiaofei; Cai Wei; Xue Ruoshi; Zhu Jinsong
2010-01-01
The drive frequency dependent piezoresponse (PR) phase signal in near-stoichiometric lithium niobate crystals is studied by piezoresponse force microscopy. It is clearly shown that the local and nonlocal electrostatic forces have a great contribution to the PR phase signal. The significant PR phase difference of the antiparallel domains are observed at the contact resonances, which is related to the electrostatic dominated electromechanical interactions of the cantilever and tip-sample system. Moreover, the modulation voltage induced frequency shift at higher eigenmodes could be attributed to the change of indention force depending on the modulation amplitude with a piezoelectric origin. The PR phase of the silicon wafer is also measured for comparison. It is certificated that the electrostatic interactions are universal in voltage modulated scanning probe microscopy and could be extended to other phase imaging techniques.
Transverse entanglement migration in Hilbert space
International Nuclear Information System (INIS)
Chan, K. W.; Torres, J. P.; Eberly, J. H.
2007-01-01
We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down-conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the biphoton state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the full entanglement
Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John
2015-10-16
In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.
Phase modulation mode of scanning ion conductance microscopy
Energy Technology Data Exchange (ETDEWEB)
Li, Peng; Zhang, Changlin [State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Liu, Lianqing, E-mail: lqliu@sia.cn, E-mail: gli@engr.pitt.edu; Wang, Yuechao; Yang, Yang [State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016 (China); Li, Guangyong, E-mail: lqliu@sia.cn, E-mail: gli@engr.pitt.edu [Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261 (United States)
2014-08-04
This Letter reports a phase modulation (PM) mode of scanning ion conductance microscopy. In this mode, an AC current is directly generated by an AC voltage between the electrodes. The portion of the AC current in phase with the AC voltage, which is the current through the resistance path, is modulated by the tip-sample distance. It can be used as the input of feedback control to drive the scanner in Z direction. The PM mode, taking the advantages of both DC mode and traditional AC mode, is less prone to electronic noise and DC drift but maintains high scanning speed. The effectiveness of the PM mode has been proven by experiments.
Single beam Fourier transform digital holographic quantitative phase microscopy
Energy Technology Data Exchange (ETDEWEB)
Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Quantitative phase imaging with scanning holographic microscopy: an experimental assesment
Directory of Open Access Journals (Sweden)
Tada Yoshitaka
2006-11-01
Full Text Available Abstract This paper demonstrates experimentally how quantitative phase information can be obtained in scanning holographic microscopy. Scanning holography can operate in both coherent and incoherent modes, simultaneously if desired, with different detector geometries. A spatially integrating detector provides an incoherent hologram of the object's intensity distribution (absorption and/or fluorescence, for example, while a point detector in a conjugate plane of the pupil provides a coherent hologram of the object's complex amplitude, from which a quantitative measure of its phase distribution can be extracted. The possibility of capturing simultaneously holograms of three-dimensional specimens, leading to three-dimensional reconstructions with absorption contrast, reflectance contrast, fluorescence contrast, as was previously demonstrated, and quantitative phase contrast, as shown here for the first time, opens up new avenues for multimodal imaging in biological studies.
Diffraction phase microscopy realized with an automatic digital pinhole
Zheng, Cheng; Zhou, Renjie; Kuang, Cuifang; Zhao, Guangyuan; Zhang, Zhimin; Liu, Xu
2017-12-01
We report a novel approach to diffraction phase microscopy (DPM) with automatic pinhole alignment. The pinhole, which serves as a spatial low-pass filter to generate a uniform reference beam, is made out of a liquid crystal display (LCD) device that allows for electrical control. We have made DPM more accessible to users, while maintaining high phase measurement sensitivity and accuracy, through exploring low cost optical components and replacing the tedious pinhole alignment process with an automatic pinhole optical alignment procedure. Due to its flexibility in modifying the size and shape, this LCD device serves as a universal filter, requiring no future replacement. Moreover, a graphic user interface for real-time phase imaging has been also developed by using a USB CMOS camera. Experimental results of height maps of beads sample and live red blood cells (RBCs) dynamics are also presented, making this system ready for broad adaption to biological imaging and material metrology.
Plymen, Roger; Robinson, Paul
1995-01-01
Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.
Hilbert-type inequalities for Hilbert space operators | Krnic ...
African Journals Online (AJOL)
In this paper we establish a general form of the Hilbert inequality for positive invertible operators on a Hilbert space. Special emphasis is given to such inequalities with homogeneous kernels. In some general cases the best possible constant factors are also derived. Finally, we obtain the improvement of previously deduced ...
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert A ⊗ B -module E ⊗ F , and we get more results. For Hilbert ...
Efficient Phase Unwrapping Architecture for Digital Holographic Microscopy
Directory of Open Access Journals (Sweden)
Wen-Jyi Hwang
2011-09-01
Full Text Available This paper presents a novel phase unwrapping architecture for accelerating the computational speed of digital holographic microscopy (DHM. A fast Fourier transform (FFT based phase unwrapping algorithm providing a minimum squared error solution is adopted for hardware implementation because of its simplicity and robustness to noise. The proposed architecture is realized in a pipeline fashion to maximize through put of thecomputation. Moreover, the number of hardware multipliers and dividers are minimized to reduce the hardware costs. The proposed architecture is used as a custom user logic in a system on programmable chip (SOPC for physical performance measurement. Experimental results reveal that the proposed architecture is effective for expediting the computational speed while consuming low hardware resources for designing an embedded DHM system.
Digital holographic microscopy of phase separation in multicomponent lipid membranes
Farzam Rad, Vahideh; Moradi, Ali-Reza; Darudi, Ahmad; Tayebi, Lobat
2016-12-01
Lateral in-homogeneities in lipid compositions cause microdomains formation and change in the physical properties of biological membranes. With the presence of cholesterol and mixed species of lipids, phospholipid membranes segregate into lateral domains of liquid-ordered and liquid-disordered phases. Coupling of two-dimensional intralayer phase separations and interlayer liquid-crystalline ordering in multicomponent membranes has been previously demonstrated. By the use of digital holographic microscopy (DHMicroscopy), we quantitatively analyzed the volumetric dynamical behavior of such membranes. The specimens are lipid mixtures composed of sphingomyelin, cholesterol, and unsaturated phospholipid, 1,2-dioleoyl-sn-glycero-3-phosphocholine. DHMicroscopy in a transmission mode is an effective tool for quantitative visualization of phase objects. By deriving the associated phase changes, three-dimensional information on the morphology variation of lipid stacks at arbitrary time scales is obtained. Moreover, the thickness distribution of the object at demanded axial planes can be obtained by numerical focusing. Our results show that the volume evolution of lipid domains follows approximately the same universal growth law of previously reported area evolution. However, the thickness of the domains does not alter significantly by time; therefore, the volume evolution is mostly attributed to the changes in area dynamics. These results might be useful in the field of membrane-based functional materials.
Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.
Chen, Hsi-Hsun; Lin, Yu-Zi; Luo, Yuan
2018-05-16
Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC.
Directory of Open Access Journals (Sweden)
Zachary F Phillips
Full Text Available We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification-an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC, is a single-shot variant of Differential Phase Contrast (DPC, which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps for various in vitro cell samples and c. elegans in a micro-fluidic channel.
Effects of phase change on reflection in phase-measuring interference microscopy
Dubois , Arnaud
2004-01-01
International audience; We show by analytical and numerical calculations that the phase change on reflection that occurs in interference microscopy is almost independent of the numerical aperture of the objective. The shift of the microscope interferogram response due to the phase change on reflection, however, increases with the numerical aperture. Measurements of the interferogram shift are made with a Linnik interference microscope equipped with various numerical-aperture objectives and ar...
Coherent states on Hilbert modules
International Nuclear Information System (INIS)
Ali, S Twareque; Bhattacharyya, T; Roy, S S
2011-01-01
We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.
Energy Technology Data Exchange (ETDEWEB)
Ramírez-Salgado, J. [Instituto Mexicano del Petróleo, Dirección de Investigación y Posgrado, Eje Central Norte Lázaro Cárdenas, No. 152, 07730 D.F., México (Mexico); Domínguez-Aguilar, M.A., E-mail: madoming@imp.mx [Instituto Mexicano del Petróleo, Dirección de Investigación y Posgrado, Eje Central Norte Lázaro Cárdenas, No. 152, 07730 D.F., México (Mexico); Castro-Domínguez, B. [University of Tokyo, Department of Chemical System Engineering, Faculty of Engineering Bldg. 5, 7F 722, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113–8656 (Japan); Hernández-Hernández, P. [Instituto Mexicano del Petróleo, Dirección de Investigación y Posgrado, Eje Central Norte Lázaro Cárdenas, No. 152, 07730 D.F., México (Mexico); Newman, R.C. [University of Toronto, Department of Chemical Engineering and Applied Chemistry, 200 College Street, Toronto M5S 3E5 (Canada)
2013-12-15
The secondary phase transformations in a commercial super duplex stainless steel were investigated by micro-chemical analyses and high resolution scanning probe microscopy. Energy dispersive X-ray and electron probe detected ferrite and austenite as well as secondary phases in unetched aged duplex stainless steel type 25Cr-7Ni-3Mo. Volta potential indicated that nitride and sigma appeared more active than ferrite, while secondary austenite and austenite presented a nobler potential. Reversal order in nobility is thought to be attributable to the potential ranking provided by oxide nature diversity as a result of secondary phase surface compositions on steel. After eutectoid transformation, secondary austenite was detected by electron probe microanalysis, whereas atomic force microscopy distinguished this phase from former austenite by image contrast. Magnetic force microscopy revealed a “ghosted” effect on the latter microstructure probably derived from metal memory reminiscence of mechanical polishing at passivity and long range magnetic forces of ferrite phase. - Highlights: • Nobility detection of secondary phases by SKPFM in DSS particles is not a straightforward procedure. • As Volta potential and contrast are not always consistent SKPFM surface oxides is thought played an important role in detection. • AFM distinguished secondary austenite from former austenite by image contrast though SEM required EPMA.
Noise properties of Hilbert transform evaluation
International Nuclear Information System (INIS)
Pavliček, Pavel; Svak, Vojtěch
2015-01-01
The Hilbert transform is a standard method for the calculation of the envelope and phase of a modulated signal in optical measurement methods. Usually, the intensity of light is converted into an electric signal at a detector. Therefore the actual spatially or temporally sampled signal is always affected by noise. Because the noise values of individual samples are independent, the noise can be considered as white. If the envelope and phase are calculated from the noised signal, they will also be affected by the noise. We calculate the variance and spectral density of both the envelope noise and the phase noise. We determine which parameters influence the variance and spectral density of both the envelope noise and the phase noise. Finally, we determine the influence of the noise on the measurement uncertainty in white-light interferometry and fringe-pattern analysis. (paper)
Topological freeness for Hilbert bimodules
DEFF Research Database (Denmark)
Kwasniewski, Bartosz
2014-01-01
It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description...
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1980-01-01
A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives
Teleportation schemes in infinite dimensional Hilbert spaces
International Nuclear Information System (INIS)
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-01-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples
Patricia A. Moss; Les Groom
2001-01-01
Microscopy is the study and interpretation of images produced by a microscope. "Interpretation" is the keyword, because the microscope enables one to see structures that are too small or too close together to be resolved by the unaided eye. (The human eye cannot separate two points or lines that are closer together than 0.1 mm.) it is important to...
Newly designed, simple relief phase contrast for microscopy of microorganisms
Czech Academy of Sciences Publication Activity Database
Žižka, Zdeněk
2010-01-01
Roč. 55, č. 6 (2010), s. 662-665 ISSN 0015-5632 R&D Projects: GA MŠk LC06066 Institutional research plan: CEZ:AV0Z50200510 Keywords : optical microscopy * Zeiss NG 10/1 * microphotography Subject RIV: EE - Microbiology, Virology Impact factor: 0.977, year: 2010
Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.
Ashrafi, Reza; Azaña, José
2012-07-01
A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.
Theoretical study of ferroelectric nanoparticles using phase reconstructed electron microscopy
Phatak, C.; Petford-Long, A. K.; Beleggia, M.; De Graef, M.
2014-06-01
Ferroelectric nanostructures are important for a variety of applications in electronic and electro-optical devices, including nonvolatile memories and thin-film capacitors. These applications involve stability and switching of polarization using external stimuli, such as electric fields. We present a theoretical model describing how the shape of a nanoparticle affects its polarization in the absence of screening charges, and quantify the electron-optical phase shift for detecting ferroelectric signals with phase-sensitive techniques in a transmission electron microscope. We provide an example phase shift computation for a uniformly polarized prolate ellipsoid with varying aspect ratio in the absence of screening charges.
Liquid identification by Hilbert spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Lyatti, M; Divin, Y; Poppe, U; Urban, K, E-mail: M.Lyatti@fz-juelich.d, E-mail: Y.Divin@fz-juelich.d [Forschungszentrum Juelich, 52425 Juelich (Germany)
2009-11-15
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T{sub c} Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Liquid identification by Hilbert spectroscopy
Lyatti, M.; Divin, Y.; Poppe, U.; Urban, K.
2009-11-01
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- Tc Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Liquid identification by Hilbert spectroscopy
International Nuclear Information System (INIS)
Lyatti, M; Divin, Y; Poppe, U; Urban, K
2009-01-01
Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- T c Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.
Weaving Hilbert space fusion frames
Neyshaburi, Fahimeh Arabyani; Arefijamaal, Ali Akbar
2018-01-01
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas especially for wireless sensor networks. In this paper, we survey the notion of weaving Hilbert space fusion frames. This concept can be had potential applications in wireless sensor networks which require distributed processing using different fusion frames...
Czech Academy of Sciences Publication Activity Database
Žižka, Zdeněk; Gabriel, Jiří
2015-01-01
Roč. 60, č. 6 (2015), s. 545-550 ISSN 0015-5632 Institutional support: RVO:61388971 Keywords : polarization microscopy * microbial cells * positive phase contrast Subject RIV: EE - Microbiology, Virology Impact factor: 1.335, year: 2015
International Nuclear Information System (INIS)
Talaikova, N A; Ryabukho, V P
2016-01-01
We consider a simplified and compact scheme of interference phase microscopy using a diffraction grating and spatial filtering of the diffracted field, i.e., diffraction phase microscopy. The scheme and the parameters of the device with the possibility of using the optical system of a smartphone and its software are analysed. The results of experimental determination of the spatial structure parameters of erythrocytes are presented. (paper)
Lewin, M.; Hauer, B.; Bornhöfft, M.; Jung, L.; Benke, J.; Michel, A.-K. U.; Mayer, J.; Wuttig, M.; Taubner, T.
2015-10-01
Phase Change Materials (PCM) show two stable states in the solid phase with significantly different optical and electronic properties. They can be switched reversibly between those two states and are promising candidates for future non-volatile memory applications. The development of phase change devices demands characterization tools, yielding information about the switching process at high spatial resolution. Scattering-type Scanning Near-field Optical Microscopy (s-SNOM) allows for spectroscopic analyses of the different optical properties of the PCMs on the nm-scale. By correlating the optical s-SNOM images with transmission electron microscopy images of the same sample, we unambiguously demonstrate the correlation of the infrared optical contrast with the structural state of the phase change material. The investigated sample consists of sandwiched amorphous and crystalline regions of Ag 4 In 3 Sb 67 Te 26 below a 100 nm thick ( ZnS ) 80 - ( SiO2 ) 20 capping layer. Our results demonstrate the sensitivity of s-SNOM to small dielectric near-field contrasts even below a comparably thick capping layer ( 100 nm ).
Multiplexed phase-space imaging for 3D fluorescence microscopy.
Liu, Hsiou-Yuan; Zhong, Jingshan; Waller, Laura
2017-06-26
Optical phase-space functions describe spatial and angular information simultaneously; examples of optical phase-space functions include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration removal and 3D reconstruction. High-resolution capture of 4D phase-space datasets is, however, challenging. Previous scanning approaches are slow, light inefficient and do not achieve diffraction-limited resolution. Here, we propose a multiplexed method that solves these problems. We use a spatial light modulator (SLM) in the pupil plane of a microscope in order to sequentially pattern multiplexed coded apertures while capturing images in real space. Then, we reconstruct the 3D fluorescence distribution of our sample by solving an inverse problem via regularized least squares with a proximal accelerated gradient descent solver. We experimentally reconstruct a 101 Megavoxel 3D volume (1010×510×500µm with NA 0.4), demonstrating improved acquisition time, light throughput and resolution compared to scanning aperture methods. Our flexible patterning scheme further allows sparsity in the sample to be exploited for reduced data capture.
Enlightening intracellular complexity of living cells with quantitative phase microscopy
Martinez Torres, C.; Laperrousaz, B.; Berguiga, L.; Boyer Provera, E.; Elezgaray, J.; Nicolini, F. E.; Maguer-Satta, V.; Arneodo, A.; Argoul, F.
2016-03-01
The internal distribution of refractive indices (RIs) of a living cell is much more complex than usually admitted in multi-shell models. The reconstruction of RI maps from single phase images has rarely been achieved for several reasons: (i) we still have very little knowledge of the impact of internal macromolecular complexes on the local RI and (ii) phase changes produced by light propagation through the sample are mixed with diffraction effects by internal cell bodies. We propose the implementation a 2D wavelet-based contour chain detection method to distinguish internal boundaries thanks to their greatest optical path difference gradients. These contour chains correspond to the highest image phase contrast and follow the local RI inhomogeneities linked to the intracellular structural intricacy. Their statistics and spatial distribution are morphological indicators for distinguishing cells of different origins and to follow their transformation in pathologic situations. We use this method to compare non adherent blood cells from primary and laboratory culture origins, in healthy and pathological situations (chronic myelogenous leukaemia). In a second part of this presentation, we concentrate on the temporal dynamics of the phase contour chains and we discuss the spectral decomposition of their dynamics in both health and disease.
Exponential Hilbert series of equivariant embeddings
Johnson, Wayne A.
2018-01-01
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities inv...
International Nuclear Information System (INIS)
Marciano Junior, E.; Cunha Munhoz, F.A. da; Splettstoser Junior, J.; Placido, W.F.
1989-01-01
The identification and quantitative determination of phases in calcium aluminate clinker is of great importance to the producer, as it enables a better understanding of the cement and concrete properties, specially those concerning setting time and compressive strenght. Polished sections of three electrofused clinkers, one experimental and two industrial, were used to select the most suitable etchings in order to identify by microscopy the main phases (Ca, CA 2 , C 2 AS, C 12 A 7 , α-Al 2 O 3 ). Quantitative phases determinations by reflected light microscopy showed good results when compared to X-ray diffractometry measurements [pt
Means of Hilbert space operators
Hiai, Fumio
2003-01-01
The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
Structure of Hilbert space operators
Jiang, Chunlan
2006-01-01
This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K -theory, complex geometry and operator algebra tools. Sample Chapter(s). Chapter 1: Background (153 KB). Contents: Jordan Standard Theorem and K 0 -Group; Approximate Jordan Theorem of Opera
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
Rigged Hilbert spaces for chaotic dynamical systems
International Nuclear Information System (INIS)
Suchanecki, Z.; Antoniou, I.; Bandtlow, O.F.
1996-01-01
We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. copyright 1996 American Institute of Physics
Direct imaging of phase objects enables conventional deconvolution in bright field light microscopy.
Directory of Open Access Journals (Sweden)
Carmen Noemí Hernández Candia
Full Text Available In transmitted optical microscopy, absorption structure and phase structure of the specimen determine the three-dimensional intensity distribution of the image. The elementary impulse responses of the bright field microscope therefore consist of separate absorptive and phase components, precluding general application of linear, conventional deconvolution processing methods to improve image contrast and resolution. However, conventional deconvolution can be applied in the case of pure phase (or pure absorptive objects if the corresponding phase (or absorptive impulse responses of the microscope are known. In this work, we present direct measurements of the phase point- and line-spread functions of a high-aperture microscope operating in transmitted bright field. Polystyrene nanoparticles and microtubules (biological polymer filaments serve as the pure phase point and line objects, respectively, that are imaged with high contrast and low noise using standard microscopy plus digital image processing. Our experimental results agree with a proposed model for the response functions, and confirm previous theoretical predictions. Finally, we use the measured phase point-spread function to apply conventional deconvolution on the bright field images of living, unstained bacteria, resulting in improved definition of cell boundaries and sub-cellular features. These developments demonstrate practical application of standard restoration methods to improve imaging of phase objects such as cells in transmitted light microscopy.
Quantum theory in complex Hilbert space
International Nuclear Information System (INIS)
Sharma, C.S.
1988-01-01
The theory of complexification of a real Hilbert space as developed by the author is scrutinized with the aim of explaining why quantum theory should be done in a complex Hilbert space in preference to real Hilbert space. It is suggested that, in order to describe periodic motions in stationary states of a quantum system, the mathematical object modelling a state of a system should have enough points in it to be able to describe explicit time dependence of a periodic motion without affecting the probability distributions of observables. Heuristic evidence for such an assumption comes from Dirac's theory of interaction between radiation and matter. If the assumption is adopted as a requirement on the mathematical model for a quantum system, then a real Hilbert space is ruled out in favour of a complex Hilbert space for a possible model for such a system
Single particle analysis based on Zernike phase contrast transmission electron microscopy.
Danev, Radostin; Nagayama, Kuniaki
2008-02-01
We present the first application of Zernike phase-contrast transmission electron microscopy to single-particle 3D reconstruction of a protein, using GroEL chaperonin as the test specimen. We evaluated the performance of the technique by comparing 3D models derived from Zernike phase contrast imaging, with models from conventional underfocus phase contrast imaging. The same resolution, about 12A, was achieved by both imaging methods. The reconstruction based on Zernike phase contrast data required about 30% fewer particles. The advantages and prospects of each technique are discussed.
Holography microscopy as an artifact-free alternative to phase-contrast
Czech Academy of Sciences Publication Activity Database
Pastorek, Lukáš; Venit, Tomáš; Hozák, Pavel
2018-01-01
Roč. 149, č. 2 (2018), s. 179-186 ISSN 0948-6143 R&D Projects: GA MŠk(CZ) LM2015062 Institutional support: RVO:68378050 Keywords : Holography microscopy * Phase-contrast * Halo effect Subject RIV: EB - Genetics ; Molecular Biology OBOR OECD: Cell biology Impact factor: 2.553, year: 2016
Kooi, B.J.; Palasantzas, G.; de Hosson, J.T.M.
2006-01-01
Magnesium nanoparticles with size above 10 nm, prepared by gas-phase syntheses, were investigated by high-resolution transmission electron microscopy. The dominant particle shape is a hexagonal prism terminated by Mg(0002) and Mg{1010} facets. Oxidation of Mg yields a MgO shell (similar to 3 nm
Proposals for the solution of the phase problem in electron microscopy
International Nuclear Information System (INIS)
Toorn, P. van.
1979-01-01
This thesis discusses the phase problem in electron microscopy, i.e. the determination of the unknown complex wave function in the image plane or in the exit pupil from the measured intensity distributions in both planes. The calculation of the wave function is the first problem to be solved for the determination of the object structure from electron micrographs. (Auth.)
Power Spectral Density and Hilbert Transform
2016-12-01
there is 1.3 W of power. How much bandwidth does a pure sine wave require? The bandwidth of an ideal sine wave is 0 Hz. How do you represent a 1-W...the Hilbert transform. 2.3 Hilbert Transform The Hilbert transform is a math function used to convert a real function into an analytic signal...The math operation minus 2 means to move 2 steps back on the number line. For minus –2, we move 2 steps backwards from –2, which is the same as
Czyrska-Filemonowicz, A; Buffat, P A
2009-01-01
Surface processing of a Ti-6Al-4V alloy led to a complex multilayered microstructure containing several phases of the Ni-Ti-P-Al-O system, which improves the mechanical and tribological surface properties. The microstructure, chemical and phase compositions of the hard layer formed on the surface were investigated by LM, XRD, SEM as well as analytical/high-resolution TEM, STEM, EDS, electron diffraction and FIB. Phase identification based on electron diffraction, HRTEM and EDS microanalysis revealed the presence of several binary and ternary phases in the system Ti-Ni-P, sometimes with partial substitution of Ti by Al. However some phases, mainly nanoparticles, still remain not identified satisfactorily. Electron microscopy techniques used for identification of phases present in surface multilayers and some practical limits to their routine application are reminded here.
Time-resolved imaging refractometry of microbicidal films using quantitative phase microscopy.
Rinehart, Matthew T; Drake, Tyler K; Robles, Francisco E; Rohan, Lisa C; Katz, David; Wax, Adam
2011-12-01
Quantitative phase microscopy is applied to image temporal changes in the refractive index (RI) distributions of solutions created by microbicidal films undergoing hydration. We present a novel method of using an engineered polydimethylsiloxane structure as a static phase reference to facilitate calibration of the absolute RI across the entire field. We present a study of dynamic structural changes in microbicidal films during hydration and subsequent dissolution. With assumptions about the smoothness of the phase changes induced by these films, we calculate absolute changes in the percentage of film in regions across the field of view.
Quantitative tracking of tumor cells in phase-contrast microscopy exploiting halo artifact pattern
Kang, Mi-Sun; Song, Soo-Min; Lee, Hana; Kim, Myoung-Hee
2012-03-01
Tumor cell morphology is closely related to its invasiveness characteristics and migratory behaviors. An invasive tumor cell has a highly irregular shape, whereas a spherical cell is non-metastatic. Thus, quantitative analysis of cell features is crucial to determine tumor malignancy or to test the efficacy of anticancer treatment. We use phase-contrast microscopy to analyze single cell morphology and to monitor its change because it enables observation of long-term activity of living cells without photobleaching and phototoxicity, which is common in other fluorescence-labeled microscopy. Despite this advantage, there are image-level drawbacks to phase-contrast microscopy, such as local light effect and contrast interference ring, among others. Thus, we first applied a local filter to compensate for non-uniform illumination. Then, we used intensity distribution information to detect the cell boundary. In phase-contrast microscopy images, the cell normally appears as a dark region surrounded by a bright halo. As the halo artifact around the cell body is minimal and has an asymmetric diffusion pattern, we calculated the cross-sectional plane that intersected the center of each cell and was orthogonal to the first principal axis. Then, we extracted the dark cell region by level set. However, a dense population of cultured cells still rendered single-cell analysis difficult. Finally, we measured roundness and size to classify tumor cells into malignant and benign groups. We validated segmentation accuracy by comparing our findings with manually obtained results.
A constructive presentation of rigged Hilbert spaces
International Nuclear Information System (INIS)
Celeghini, Enrico
2015-01-01
We construct a rigged Hilbert space for the square integrable functions on the line L2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io(2). L 2 (R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators defined on the rigged Hilbert spaces L 2 (R) or R are shown to belong to the universal enveloping algebra of io(2). The procedure can be extended to orthogonal and pseudo-orthogonal spaces of arbitrary dimension by tensorialization.Circumventing all formal problems the paper proposes a kind of toy model, well defined from a mathematical point of view, of rigged Hilbert spaces where, in contrast with the Hilbert spaces, operators with different cardinality are allowed. (paper)
Hilbert space methods in partial differential equations
Showalter, Ralph E
1994-01-01
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Theory of linear operators in Hilbert space
Akhiezer, N I
1993-01-01
This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
LORENTZ PHASE IMAGING AND IN-SITU LORENTZ MICROSCOPY OF PATTERNED CO-ARRAYS
International Nuclear Information System (INIS)
VOLKOV, V.V.; ZHU, Y.
2003-01-01
Understanding magnetic structures and properties of patterned and ordinary magnetic films at nanometer length-scale is the area of immense technological and fundamental scientific importance. The key feature to such success is the ability to achieve visual quantitative information on domain configurations with a maximum ''magnetic'' resolution. Several methods have been developed to meet these demands (Kerr and Faraday effects, differential phase contrast microscopy, magnetic force microscopy, SEMPA etc.). In particular, the modern off-axis electron holography allows retrieval of the electron-wave phase shifts down to 2π/N (with typical N = 10-20, approaching in the limit N ∼ 100) in TEM equipped with field emission gun, which is already successfully employed for studies of magnetic materials at nanometer scale. However, it remains technically demanding, sensitive to noise and needs highly coherent electron sources. As possible alternative we developed a new method of Lorentz phase microscopy [1,2] based on the Fourier solution [3] of magnetic transport-of-intensity (MTIE) equation. This approach has certain advantages, since it is less sensitive to noise and does not need high coherence of the source required by the holography. In addition, it can be realized in any TEM without basic hardware changes. Our approach considers the electron-wave refraction in magnetic materials (magnetic refraction) and became possible due to general progress in understanding of noninterferometric phase retrieval [4-6] dealing with optical refraction. This approach can also be treated as further development of Fresnel microscopy, used so far for imaging of in-situ magnetization process in magnetic materials studied by TEM. Figs. 1-3 show some examples of what kind information can be retrieved from the conventional Fresnel images using the new approach. Most of these results can be compared with electron-holographic data. Using this approach we can shed more light on fine details of
Electron microscopy and phase analysis of fly ash from pressurized fluidized bed combustion
International Nuclear Information System (INIS)
Maenami, Hiroki; Isu, Norifumi; Ishida, Emile H.; Mitsuda, Takeshi
2004-01-01
The characterization of the typical fly ashes from pressurized fluidized bed combustion system (PFBC) in Japan and Europe was carried out by electron microscopy and phase analysis using energy-dispersive X-ray spectroscopy (EDX). The purity of limestone as in-bed sulfur removal sorbent influences the desulfurization reaction. The high-purity limestone yielded both hydroxyl ellestadite and anhydrite in Japanese PFBC ashes, while dolomite-rich limestone yielded anhydrite in European PFBC ashes. When the high-purity limestone was used, hydroxyl ellestadite particles were observed as the independent particles or the rim around limestone particles. The Al 2 O 3 content in the glassy phase was inversely proportional to the CaO content in the glassy phase, suggesting that the glassy phases were formed from metakaoline and calcite as end members. Since hydroxyl ellestadite, glassy phase and metakaoline are reactive under hydrothermal conditions, PFBC ashes are expected to be used as raw materials for autoclaved products
Flipping interferometry and its application for quantitative phase microscopy in a micro-channel.
Roitshtain, Darina; Turko, Nir A; Javidi, Bahram; Shaked, Natan T
2016-05-15
We present a portable, off-axis interferometric module for quantitative phase microscopy of live cells, positioned at the exit port of a coherently illuminated inverted microscope. The module creates on the digital camera an interference pattern between the image of the sample and its flipped version. The proposed simplified module is based on a retro-reflector modification in an external Michelson interferometer. The module does not contain any lenses, pinholes, or gratings and its alignment is straightforward. Still, it allows full control of the off-axis angle and does not suffer from ghost images. As experimentally demonstrated, the module is useful for quantitative phase microscopy of live cells rapidly flowing in a micro-channel.
Holography microscopy as an artifact-free alternative to phase-contrast.
Pastorek, Lukáš; Venit, Tomáš; Hozák, Pavel
2018-02-01
Artifact-free microscopic images represent a key requirement of multi-parametric image analysis in modern biomedical research. Holography microscopy (HM) is one of the quantitative phase imaging techniques, which has been finding new applications in life science, especially in morphological screening, cell migration, and cancer research. Rather than the classical imaging of absorbing (typically stained) specimens by bright-field microscopy, the information about the light-wave's phase shifts induced by the biological sample is employed for final image reconstruction. In this comparative study, we investigated the usability and the reported advantage of the holography imaging. The claimed halo-free imaging was analyzed compared to the widely used Zernike phase-contrast microscopy. The intensity and phase cross-membrane profiles at the periphery of the cell were quantified. The intensity profile for cells in the phase-contrast images suffers from the significant increase in intensity values around the cell border. On the contrary, no distorted profile is present outside the cell membrane in holography images. The gradual increase in phase shift values is present in the internal part of the cell body projection in holography image. This increase may be related to the increase in the cell internal material according to the dry mass theory. Our experimental data proved the halo-free nature of the holography imaging, which is an important prerequisite of the correct thresholding and cell segmentation, nowadays frequently required in high-content screening and other image-based analysis. Consequently, HM is a method of choice whenever the image analysis relies on the accurate data on cell boundaries.
New generation quantitative x-ray microscopy encompassing phase-contrast
International Nuclear Information System (INIS)
Wilkins, S.W.; Mayo, S.C.; Gureyev, T.E.; Miller, P.R.; Pogany, A.; Stevenson, A.W.; Gao, D.; Davis, T.J.; Parry, D.J.; Paganin, D.
2000-01-01
Full text: We briefly outline a new approach to X-ray ultramicroscopy using projection imaging in a scanning electron microscope (SEM). Compared to earlier approaches, the new approach offers spatial resolution of ≤0.1 micron and includes novel features such as: i) phase contrast to give additional sample information over a wide energy range, rapid phase/amplitude extraction algorithms to enable new real-time modes of microscopic imaging widespread applications are envisaged to fields such as materials science, biomedical research, and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to X-ray projection microscopy using synchrotron sources
Transmission electron microscopy studies on nanometer-sized ω phase produced in Gum Metal
International Nuclear Information System (INIS)
Yano, Takaaki; Murakami, Yasukazu; Shindo, Daisuke; Hayasaka, Yuichiro; Kuramoto, Shigeru
2010-01-01
The morphology, numerical density and average spacing of the ω phase formed in Gum Metal, a Ti-based alloy showing unique mechanical properties, were studied by transmission electron microscopy. Based on dark-field image observations and precise thickness measurements using a thin-foil specimen, the average spacing of the nanometer-sized ω phase was determined to be 6 nm. This spacing appeared to be sufficiently small for trapping dislocations. The results are discussed in conjunction with the dislocation-free deformation mechanism proposed for Gum Metal.
International Nuclear Information System (INIS)
Jung, Mi; Choi, Jeong-Woo
2010-01-01
The discrimination of the heterogeneity of different materials on nanostructured surfaces has attracted a great deal of interest in biotechnology as well as nanotechnology. Phase imaging through tapping mode of atomic force microscopy (TMAFM) can be used to distinguish the heterogeneity on a nanostructured surface. Nanostructures were fabricated using anodic aluminum oxide (AAO). An 11-mercaptoundecanoic acid (11-MUA) layer adsorbed onto the Au nanodots through self-assembly to improve the bio-compatibility. The Au nanostructures that were modified with 11-MUA and the concave surfaces were investigated using the TMAFM phase images to compare the heterogeneous and homogeneous nanostructured surfaces. Although the topography and phase images were taken simultaneously, the images were different. Therefore, the contrast in the TMAFM phase images revealed the different compositional materials on the heterogeneous nanostructure surface.
Bouchal, Petr; Chmelík, Radim; Bouchal, Zdeněk
2018-02-01
A new concept of dual-polarization spatial light interference microscopy (DPSLIM) is proposed and demonstrated experimentally. The method works with two orthogonally polarized modes in which signal and reference waves are combined to realize the polarization-sensitive phase-shifting, thus allowing advanced reconstruction of the phase associated with the image field. The image phase is reconstructed directly from four polarization encoded interference records by a single step processing. This is a progress compared with common methods, in which the phase of the image field is reconstructed using the optical path difference and the amplitudes of interfering waves, which are calculated in multiple-step processing of the records. The DPSLIM is implemented in a common-path configuration using a spatial light modulator, which is connected to a commercial microscope Nikon E200. The optical performance of the method is demonstrated in experiments using both polystyrene microspheres and live LW13K2 cells.
Frames and bases in tensor products of Hilbert spaces and Hilbert C ...
Indian Academy of Sciences (India)
[14] Heil C E and Walnut D F, Continuous and discrete wavelet transforms, SIAM Review 31. (1989) 628–666. [15] Khosravi A and Asgari M S, Frames and bases in tensor product of Hilbert spaces, Int. J. Math. 4(6) (2003) 527–538. [16] Lance E C, Hilbert C. ∗. -modules – a toolkit for operator algebraists, London Math. Soc.
A phase-field and electron microscopy study of phase separation in Fe-Cr alloys
Energy Technology Data Exchange (ETDEWEB)
Hedstroem, Peter, E-mail: pheds@kth.se [Materials Science and Engineering, KTH (Royal Institute of Technology), SE-100 44 Stockholm (Sweden); Baghsheikhi, Saeed [Materials Science and Engineering, KTH (Royal Institute of Technology), SE-100 44 Stockholm (Sweden); Liu, Ping [Sandvik Materials Technology, R and D Centre, SE-81181 Sandviken (Sweden); Odqvist, Joakim [Materials Science and Engineering, KTH (Royal Institute of Technology), SE-100 44 Stockholm (Sweden); Sandvik Materials Technology, R and D Centre, SE-81181 Sandviken (Sweden)
2012-02-01
Highlights: Black-Right-Pointing-Pointer Experimental characterization and Phase-field modeling of phase separation in Fe-Cr. Black-Right-Pointing-Pointer Transition from particle-like to spinodal-like structure observed. Black-Right-Pointing-Pointer Structural evolution generates increased hardness. Black-Right-Pointing-Pointer Results in agreement with recent thermodynamic description. Black-Right-Pointing-Pointer Quantitative kinetic modeling must include thermal noise and improved kinetic data. - Abstract: Phase separation in the binary Fe-Cr system, the basis for the entire stainless steel family, is considered responsible for the low temperature embrittlement in ferritic, martensitic and duplex stainless steels. These steels are often used in load-bearing applications with considerable service time at elevated temperature. Thus, understanding the effect of microstructure on mechanical properties and predicting dynamics of phase separation are key issues. In the present work, experimental evaluation of structure and mechanical properties in binary Fe-Cr alloys as well as phase-field modeling, using a new thermodynamic description of Fe-Cr, is conducted. A significant hardening evolution with time is found for alloys aged between 400 and 550 Degree-Sign C, and it can be attributed to phase separation. The decomposed structure changed with increasing Cr content at 500 Degree-Sign C, with a more particle-like structure at 25 wt% Cr and a more spinodal-like structure at 30 wt% Cr. The observed transition of structure agrees with the thermodynamically predicted spinodal, although the transition is expected to be gradual. The phase-field simulations qualitatively agree with experiments. However, to enable accurate quantitative predictions, the diffusional mobilities must be evaluated further and thermal fluctuations as well as 3D diffusion fields must be properly accounted for.
High resolution electron microscopy of the triply incommensurate phase of 2H-TaSe2
Onozuka, Takashi; Otsuka, Nobuo; Sato, Hiroshi
1986-09-01
The triply incommensurate phase of 2H-TaSe2 obtained by cooling from the normal phase was investigated by transmission electron microscopy between 87 and 113 K with the resolution of 3 Å, one order of magnitude better than earlier experiments. Moirélike patterns observed in this phase were confirmed to be interference fringes due to the first- and second-order diffraction beams (with small separation and possibly with higher-order diffraction beams) from the incommensurate structure and were not due to the dark-field diffraction contrast of domains of the commensurate structure as interpreted earlier. Lattice fringes (~9 Å) of this modulated phase do not show any discontinuity across the boundaries of regions of different contrasts of the moirélike fringes which is expected from domain boundaries. Instead, a periodic change in the spacing of the lattice fringes (phase-slip region) expected from the superposition of split superlattice spots in forming the lattice image is observed. This is what is believed to be the first direct observation of the existence of the phase-slip region which is also expected from the discommensuration theory. A series of observations presented here thus shows that the triply incommensurate phase is intrinsically incommensurate and suggests the need for a modification of interpretations of this phase in terms of the double honeycomb discommensuration model.
Liu, Yang; Uttam, Shikhar; Pham, Hoa V.; Hartman, Douglas J.
2017-02-01
Pathology remains the gold standard for cancer diagnosis and in some cases prognosis, in which trained pathologists examine abnormality in tissue architecture and cell morphology characteristic of cancer cells with a bright-field microscope. The limited resolution of conventional microscope can result in intra-observer variation, missed early-stage cancers, and indeterminate cases that often result in unnecessary invasive procedures in the absence of cancer. Assessment of nanoscale structural characteristics via quantitative phase represents a promising strategy for identifying pre-cancerous or cancerous cells, due to its nanoscale sensitivity to optical path length, simple sample preparation (i.e., label-free) and low cost. I will present the development of quantitative phase microscopy system in transmission and reflection configuration to detect the structural changes in nuclear architecture, not be easily identifiable by conventional pathology. Specifically, we will present the use of transmission-mode quantitative phase imaging to improve diagnostic accuracy of urine cytology and the nuclear dry mass is progressively correlate with negative, atypical, suspicious and positive cytological diagnosis. In a second application, we will present the use of reflection-mode quantitative phase microscopy for depth-resolved nanoscale nuclear architecture mapping (nanoNAM) of clinically prepared formalin-fixed, paraffin-embedded tissue sections. We demonstrated that the quantitative phase microscopy system detects a gradual increase in the density alteration of nuclear architecture during malignant transformation in animal models of colon carcinogenesis and in human patients with ulcerative colitis, even in tissue that appears histologically normal according to pathologists. We evaluated the ability of nanoNAM to predict "future" cancer progression in patients with ulcerative colitis.
Practical aspects of Boersch phase contrast electron microscopy of biological specimens
Energy Technology Data Exchange (ETDEWEB)
Walter, Andreas [Max-Planck-Institute of Biophysics, Department of Structural Biology, Max-von-Laue-Str. 3, D-60439 Frankfurt (Germany); Muzik, Heiko; Vieker, Henning; Turchanin, Andrey; Beyer, Andre; Goelzhaeuser, Armin [University of Bielefeld, Physics of Supramolecular Systems and Surfaces, Universitaetsstr. 25, D-33615 Bielefeld (Germany); Lacher, Manfred; Steltenkamp, Siegfried; Schmitz, Sam; Holik, Peter [Caesar Research Center, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany); Kuehlbrandt, Werner [Max-Planck-Institute of Biophysics, Department of Structural Biology, Max-von-Laue-Str. 3, D-60439 Frankfurt (Germany); Rhinow, Daniel, E-mail: daniel.rhinow@biophys.mpg.de [Max-Planck-Institute of Biophysics, Department of Structural Biology, Max-von-Laue-Str. 3, D-60439 Frankfurt (Germany)
2012-05-15
Implementation of physical phase plates into transmission electron microscopes to achieve in-focus contrast for ice-embedded biological specimens poses several technological challenges. During the last decade several phase plates designs have been introduced and tested for electron cryo-microscopy (cryoEM), including thin film (Zernike) phase plates and electrostatic devices. Boersch phase plates (BPPs) are electrostatic einzel lenses shifting the phase of the unscattered beam by an arbitrary angle. Adjusting the phase shift to 90 Degree-Sign achieves the maximum contrast transfer for phase objects such as biomolecules. Recently, we reported the implementation of a BPP into a dedicated phase contrast aberration-corrected electron microscope (PACEM) and demonstrated its use to generate in-focus contrast of frozen-hydrated specimens. However, a number of obstacles need to be overcome before BPPs can be used routinely, mostly related to the phase plate devices themselves. CryoEM with a physical phase plate is affected by electrostatic charging, obliteration of low spatial frequencies, and mechanical drift. Furthermore, BPPs introduce single sideband contrast (SSB), due to the obstruction of Friedel mates in the diffraction pattern. In this study we address the technical obstacles in detail and show how they may be overcome. We use X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) to identify contaminants responsible for electrostatic charging, which occurs with most phase plates. We demonstrate that obstruction of low-resolution features is significantly reduced by lowering the acceleration voltage of the microscope. Finally, we present computational approaches to correct BPP images for SSB contrast and to compensate for mechanical drift of the BPP. -- Highlights: Black-Right-Pointing-Pointer Various obstacles need to be overcome before Boersch phase plates can be used routinely. Black-Right-Pointing-Pointer Technical problems include
Practical aspects of Boersch phase contrast electron microscopy of biological specimens
International Nuclear Information System (INIS)
Walter, Andreas; Muzik, Heiko; Vieker, Henning; Turchanin, Andrey; Beyer, André; Gölzhäuser, Armin; Lacher, Manfred; Steltenkamp, Siegfried; Schmitz, Sam; Holik, Peter; Kühlbrandt, Werner; Rhinow, Daniel
2012-01-01
Implementation of physical phase plates into transmission electron microscopes to achieve in-focus contrast for ice-embedded biological specimens poses several technological challenges. During the last decade several phase plates designs have been introduced and tested for electron cryo-microscopy (cryoEM), including thin film (Zernike) phase plates and electrostatic devices. Boersch phase plates (BPPs) are electrostatic einzel lenses shifting the phase of the unscattered beam by an arbitrary angle. Adjusting the phase shift to 90° achieves the maximum contrast transfer for phase objects such as biomolecules. Recently, we reported the implementation of a BPP into a dedicated phase contrast aberration-corrected electron microscope (PACEM) and demonstrated its use to generate in-focus contrast of frozen–hydrated specimens. However, a number of obstacles need to be overcome before BPPs can be used routinely, mostly related to the phase plate devices themselves. CryoEM with a physical phase plate is affected by electrostatic charging, obliteration of low spatial frequencies, and mechanical drift. Furthermore, BPPs introduce single sideband contrast (SSB), due to the obstruction of Friedel mates in the diffraction pattern. In this study we address the technical obstacles in detail and show how they may be overcome. We use X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) to identify contaminants responsible for electrostatic charging, which occurs with most phase plates. We demonstrate that obstruction of low-resolution features is significantly reduced by lowering the acceleration voltage of the microscope. Finally, we present computational approaches to correct BPP images for SSB contrast and to compensate for mechanical drift of the BPP. -- Highlights: ► Various obstacles need to be overcome before Boersch phase plates can be used routinely. ► Technical problems include electrostatic charging, mechanical drift, and image artefacts.
Invited Review Article: Methods for imaging weak-phase objects in electron microscopy
International Nuclear Information System (INIS)
Glaeser, Robert M.
2013-01-01
Contrast has traditionally been produced in electron-microscopy of weak phase objects by simply defocusing the objective lens. There now is renewed interest, however, in using devices that apply a uniform quarter-wave phase shift to the scattered electrons relative to the unscattered beam, or that generate in-focus image contrast in some other way. Renewed activity in making an electron-optical equivalent of the familiar “phase-contrast” light microscope is based in part on the improved possibilities that are now available for device microfabrication. There is also a better understanding that it is important to take full advantage of contrast that can be had at low spatial frequency when imaging large, macromolecular objects. In addition, a number of conceptually new phase-plate designs have been proposed, thus increasing the number of options that are available for development. The advantages, disadvantages, and current status of each of these options is now compared and contrasted. Experimental results that are, indeed, superior to what can be accomplished with defocus-based phase contrast have been obtained recently with two different designs of phase-contrast aperture. Nevertheless, extensive work also has shown that fabrication of such devices is inconsistent, and that their working lifetime is short. The main limitation, in fact, appears to be electrostatic charging of any device that is placed into the electron diffraction pattern. The challenge in fabricating phase plates that are practical to use for routine work in electron microscopy thus may be more in the area of materials science than in the area of electron optics
International Nuclear Information System (INIS)
Fan Yihui; Zhang Xiaohong; Bai Jing; Mao Renfang; Zhang Chunyu; Lei Qingquan; Fu Songbin
2007-01-01
In this study, we used calyculin A to induce premature condensed chromosomes (PCC). S-phase PCC is as 'pulverized' appearance when viewed by light microscopy. Then, we applied atomic force microscopy (AFM) to investigate the ultrastructual organization of S-phase PCC. S-phase PCC shows ridges and grooves as observed by AFM. After trypsin treatment, chromosome surface roughness is increased and chromosome thickness is decreased. At high magnification, the ridges are composed of densely packed 30 nm chromatin fibers which form chromosome axis. Around the ridges, many 30 nm chromatin fibers radiate from center. Some of the 30 nm chromatin fibers are free ends. The grooves are not real 'gap', but several 30 nm chromatin fibers which connect two ridges and form 'grid' structure. There are four chromatin fibers detached from chromosome: two free straight 30 nm chromatin fibers, one loop chromatin fiber and one straight combining with loop chromatin fiber. These results suggested that the S-phase PCC was high-order organization of 30 nm chromatin fibers and the 30 nm chromatin fibers could exist as loops and free ends
Digital Holographic Microscopy: Quantitative Phase Imaging and Applications in Live Cell Analysis
Kemper, Björn; Langehanenberg, Patrik; Kosmeier, Sebastian; Schlichthaber, Frank; Remmersmann, Christian; von Bally, Gert; Rommel, Christina; Dierker, Christian; Schnekenburger, Jürgen
The analysis of complex processes in living cells creates a high demand for fast and label-free methods for online monitoring. Widely used fluorescence methods require specific labeling and are often restricted to chemically fixated samples. Thus, methods that offer label-free and minimally invasive detection of live cell processes and cell state alterations are of particular interest. In combination with light microscopy, digital holography provides label-free, multi-focus quantitative phase imaging of living cells. In overview, several methods for digital holographic microscopy (DHM) are presented. First, different experimental setups for the recording of digital holograms and the modular integration of DHM into common microscopes are described. Then the numerical processing of digitally captured holograms is explained. This includes the description of spatial and temporal phase shifting techniques, spatial filtering based reconstruction, holographic autofocusing, and the evaluation of self-interference holograms. Furthermore, the usage of partial coherent light and multi-wavelength approaches is discussed. Finally, potentials of digital holographic microscopy for quantitative cell imaging are illustrated by results from selected applications. It is shown that DHM can be used for automated tracking of migrating cells and cell thickness monitoring as well as for refractive index determination of cells and particles. Moreover, the use of DHM for label-free analysis in fluidics and micro-injection monitoring is demonstrated. The results show that DHM is a highly relevant method that allows novel insights in dynamic cell biology, with applications in cancer research and for drugs and toxicity testing.
Photon-counting-based diffraction phase microscopy combined with single-pixel imaging
Shibuya, Kyuki; Araki, Hiroyuki; Iwata, Tetsuo
2018-04-01
We propose a photon-counting (PC)-based quantitative-phase imaging (QPI) method for use in diffraction phase microscopy (DPM) that is combined with a single-pixel imaging (SPI) scheme (PC-SPI-DPM). This combination of DPM with the SPI scheme overcomes a low optical throughput problem that has occasionally prevented us from obtaining quantitative-phase images in DPM through use of a high-sensitivity single-channel photodetector such as a photomultiplier tube (PMT). The introduction of a PMT allowed us to perform PC with ease and thus solved a dynamic range problem that was inherent to SPI. As a proof-of-principle experiment, we performed a comparison study of analogue-based SPI-DPM and PC-SPI-DPM for a 125-nm-thick indium tin oxide (ITO) layer coated on a silica glass substrate. We discuss the basic performance of the method and potential future modifications of the proposed system.
Phase microscopy using light-field reconstruction method for cell observation.
Xiu, Peng; Zhou, Xin; Kuang, Cuifang; Xu, Yingke; Liu, Xu
2015-08-01
The refractive index (RI) distribution can serve as a natural label for undyed cell imaging. However, the majority of images obtained through quantitative phase microscopy is integrated along the illumination angle and cannot reflect additional information about the refractive map on a certain plane. Herein, a light-field reconstruction method to image the RI map within a depth of 0.2 μm is proposed. It records quantitative phase-delay images using a four-step phase shifting method in different directions and then reconstructs a similar scattered light field for the refractive sample on the focus plane. It can image the RI of samples, transparent cell samples in particular, in a manner similar to the observation of scattering characteristics. The light-field reconstruction method is therefore a powerful tool for use in cytobiology studies. Copyright © 2015 Elsevier Ltd. All rights reserved.
Phase-shifting Real-time Holographic Microscopy applied in micro-structures surface analysis
International Nuclear Information System (INIS)
Brito, I V; Gesualdi, M R R; Muramatsu, M; Ricardo, J
2011-01-01
The microscopic real-time analysis of micro structured materials is of great importance in various domains of science and technology. For other hand, the holographic interferometry comprises a group of powerful optical methods for non-destructive testing in surface analysis. The holographic microscopy uses the holographic interferometric techniques to obtain quantitative intensity and phase information of the optical waves by microscopic systems. With the development of CCD cameras, computers (hardware and software), and new materials for holographic recording, these techniques can be used to replace the classical form of registration and became promising tools in surface analysis. In this work, we developed a prototype of Photorefractive and Digital Holographic Microscope for real-time analysis of micro-structured systems based on the phase-shifting real-time holographic interferometry techniques. Using this apparatus, we are made analysis of shapes and surfaces to obtain the phase maps and the 3D profiles of some samples.
Correction of phase-shifting error in wavelength scanning digital holographic microscopy
Zhang, Xiaolei; Wang, Jie; Zhang, Xiangchao; Xu, Min; Zhang, Hao; Jiang, Xiangqian
2018-05-01
Digital holographic microscopy is a promising method for measuring complex micro-structures with high slopes. A quasi-common path interferometric apparatus is adopted to overcome environmental disturbances, and an acousto-optic tunable filter is used to obtain multi-wavelength holograms. However, the phase shifting error caused by the acousto-optic tunable filter reduces the measurement accuracy and, in turn, the reconstructed topographies are erroneous. In this paper, an accurate reconstruction approach is proposed. It corrects the phase-shifting errors by minimizing the difference between the ideal interferograms and the recorded ones. The restriction on the step number and uniformity of the phase shifting is relaxed in the interferometry, and the measurement accuracy for complex surfaces can also be improved. The universality and superiority of the proposed method are demonstrated by practical experiments and comparison to other measurement methods.
The role of the rigged Hilbert space in quantum mechanics
International Nuclear Information System (INIS)
Madrid, Rafael de la
2005-01-01
There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's braket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space
Time average vibration fringe analysis using Hilbert transformation
International Nuclear Information System (INIS)
Kumar, Upputuri Paul; Mohan, Nandigana Krishna; Kothiyal, Mahendra Prasad
2010-01-01
Quantitative phase information from a single interferogram can be obtained using the Hilbert transform (HT). We have applied the HT method for quantitative evaluation of Bessel fringes obtained in time average TV holography. The method requires only one fringe pattern for the extraction of vibration amplitude and reduces the complexity in quantifying the data experienced in the time average reference bias modulation method, which uses multiple fringe frames. The technique is demonstrated for the measurement of out-of-plane vibration amplitude on a small scale specimen using a time average microscopic TV holography system.
Spectral Theory of Operators on Hilbert Spaces
Kubrusly, Carlos S
2012-01-01
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathemat
Hilbert schemes of points and Heisenberg algebras
International Nuclear Information System (INIS)
Ellingsrud, G.; Goettsche, L.
2000-01-01
Let X [n] be the Hilbert scheme of n points on a smooth projective surface X over the complex numbers. In these lectures we describe the action of the Heisenberg algebra on the direct sum of the cohomologies of all the X [n] , which has been constructed by Nakajima. In the second half of the lectures we study the relation of the Heisenberg algebra action and the ring structures of the cohomologies of the X [n] , following recent work of Lehn. In particular we study the Chern and Segre classes of tautological vector bundles on the Hilbert schemes X [n] . (author)
Advantages of intermediate X-ray energies in Zernike phase contrast X-ray microscopy.
Wang, Zhili; Gao, Kun; Chen, Jian; Hong, Youli; Ge, Xin; Wang, Dajiang; Pan, Zhiyun; Zhu, Peiping; Yun, Wenbing; Jacobsen, Chris; Wu, Ziyu
2013-01-01
Understanding the hierarchical organizations of molecules and organelles within the interior of large eukaryotic cells is a challenge of fundamental interest in cell biology. Light microscopy is a powerful tool for observations of the dynamics of live cells, its resolution attainable is limited and insufficient. While electron microscopy can produce images with astonishing resolution and clarity of ultra-thin (3D images of cryo-preserved cells. The relatively low X-ray energy (3D imaging (e.g., ~1 μm DoF for 20 nm resolution). An X-ray microscope operating at intermediate energy around 2.5 keV using Zernike phase contrast can overcome the above limitations and reduces radiation dose to the specimen. Using a hydrated model cell with an average chemical composition reported in literature, we calculated the image contrast and the radiation dose for absorption and Zernike phase contrast, respectively. The results show that an X-ray microscope operating at ~2.5 keV using Zernike phase contrast offers substantial advantages in terms of specimen size, radiation dose and depth-of-focus. Copyright © 2012 Elsevier Inc. All rights reserved.
Electron microscopy analyses and electrical properties of the layered Bi2WO6 phase
International Nuclear Information System (INIS)
Taoufyq, A.; Ait Ahsaine, H.; Patout, L.; Benlhachemi, A.; Ezahri, M.
2013-01-01
The bismuth tungstate Bi 2 WO 6 was synthesized using a classical coprecipitation method followed by a calcination process at different temperatures. The samples were characterized by X-ray diffraction, simultaneous thermogravimetry and differential thermal analysis (TGA/DTA), scanning and transmission electron microscopy (SEM, TEM) analyses. The Rietveld analysis and electron diffraction clearly confirmed the Pca2 1 non centrosymmetric space group previously proposed for this phase. The layers Bi 2 O 2 2+ and WO 4 2− have been directly evidenced from the HRTEM images. The electrical properties of Bi 2 WO 6 compacted pellets systems were determined from electrical impedance spectrometry (EIS) and direct current (DC) analyses, under air and argon, between 350 and 700 °C. The direct current analyses showed that the conduction observed from EIS analyses was mainly ionic in this temperature range, with a small electronic contribution. Electrical change above the transition temperature of 660 °C is observed under air and argon atmospheres. The strong conductivity increase observed under argon is interpreted in terms of formation of additional oxygen vacancies coupled with electron conduction. - Graphical abstract: High resolution transmission electron microscopy: inverse fast Fourier transform giving the layered structure of the Bi 2 WO 6 phase, with a representation of the cell dimensions (b and c vectors). The Bi 2 O 2 2+ and WO 4 2− sandwiches are visible in the IFFT image. - Highlights: • Using transmission electron microscopy, we visualize the layered structure of Bi 2 WO 6 . • Electrical analyses under argon gas show some increase in conductivity. • The phase transition at 660 °C is evidenced from electrical modification
Jesse, Stephen; Kalinin, Sergei V; Nikiforov, Maxim P
2013-07-09
An approach for the thermomechanical characterization of phase transitions in polymeric materials (polyethyleneterephthalate) by band excitation acoustic force microscopy is developed. This methodology allows the independent measurement of resonance frequency, Q factor, and oscillation amplitude of a tip-surface contact area as a function of tip temperature, from which the thermal evolution of tip-surface spring constant and mechanical dissipation can be extracted. A heating protocol maintained a constant tip-surface contact area and constant contact force, thereby allowing for reproducible measurements and quantitative extraction of material properties including temperature dependence of indentation-based elastic and loss moduli.
Wang, Pin; Bista, Rajan K.; Khalbuss, Walid E.; Qiu, Wei; Staton, Kevin D.; Zhang, Lin; Brentnall, Teresa A.; Brand, Randall E.; Liu, Yang
2011-03-01
Alterations in nuclear architecture are the hallmark diagnostic characteristic of cancer cells. In this work, we show that the nuclear architectural characteristics quantified by spatial-domain low-coherence quantitative phase microscopy (SL-QPM), is more sensitive for the identification of cancer cells than conventional cytopathology. We demonstrated the importance of nuclear architectural characteristics in both an animal model of intestinal carcinogenesis - APC/Min mouse model and human cytology specimens with colorectal cancer by identifying cancer from cytologically noncancerous appearing cells. The determination of nanoscale nuclear architecture using this simple and practical optical instrument is a significant advance towards cancer diagnosis.
International Nuclear Information System (INIS)
Kooi, B. J.; Palasantzas, G.; De Hosson, J. Th. M.
2006-01-01
Magnesium nanoparticles with size above 10 nm, prepared by gas-phase syntheses, were investigated by high-resolution transmission electron microscopy. The dominant particle shape is a hexagonal prism terminated by Mg(0002) and Mg(1010) facets. Oxidation of Mg yields a MgO shell (∼3 nm thick), which has an orientation relation with the Mg. Inhomogeneous facet oxidation influences their growth kinetics resulting in a relatively broad size and shape distribution. Faceted voids between Mg and MgO shells indicate a fast outward diffusion of Mg and vacancy rearrangement into voids. The faceting of polar (220) planes is assisted by electron irradiation
Interference electron microscopy of one-dimensional electron-optical phase objects
International Nuclear Information System (INIS)
Fazzini, P.F.; Ortolani, L.; Pozzi, G.; Ubaldi, F.
2006-01-01
The application of interference electron microscopy to the investigation of electron optical one-dimensional phase objects like reverse biased p-n junctions and ferromagnetic domain walls is considered. In particular the influence of diffraction from the biprism edges on the interference images is analyzed and the range of applicability of the geometric optical equation for the interpretation of the interference fringe shifts assessed by comparing geometric optical images with full wave-optical simulations. Finally, the inclusion of partial spatial coherence effects are discussed
Yaqoob, Zahid; Choi, Wonshik; Oh, Seungeun; Lue, Niyom; Park, Yongkeun; Fang-Yen, Christopher; Dasari, Ramachandra R.; Badizadegan, Kamran; Feld, Michael S.
2010-01-01
We report a quantitative phase microscope based on spectral domain optical coherence tomography and line-field illumination. The line illumination allows self phase-referencing method to reject common-mode phase noise. The quantitative phase microscope also features a separate reference arm, permitting the use of high numerical aperture (NA > 1) microscope objectives for high resolution phase measurement at multiple points along the line of illumination. We demonstrate that the path-length sensitivity of the instrument can be as good as 41 pm/Hz, which makes it suitable for nanometer scale study of cell motility. We present the detection of natural motions of cell surface and two-dimensional surface profiling of a HeLa cell. PMID:19550464
Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy.
Grah, Joana Sarah; Harrington, Jennifer Alison; Koh, Siang Boon; Pike, Jeremy Andrew; Schreiner, Alexander; Burger, Martin; Schönlieb, Carola-Bibiane; Reichelt, Stefanie
2017-02-15
In this paper we propose a workflow to detect and track mitotic cells in time-lapse microscopy image sequences. In order to avoid the requirement for cell lines expressing fluorescent markers and the associated phototoxicity, phase contrast microscopy is often preferred over fluorescence microscopy in live-cell imaging. However, common specific image characteristics complicate image processing and impede use of standard methods. Nevertheless, automated analysis is desirable due to manual analysis being subjective, biased and extremely time-consuming for large data sets. Here, we present the following workflow based on mathematical imaging methods. In the first step, mitosis detection is performed by means of the circular Hough transform. The obtained circular contour subsequently serves as an initialisation for the tracking algorithm based on variational methods. It is sub-divided into two parts: in order to determine the beginning of the whole mitosis cycle, a backwards tracking procedure is performed. After that, the cell is tracked forwards in time until the end of mitosis. As a result, the average of mitosis duration and ratios of different cell fates (cell death, no division, division into two or more daughter cells) can be measured and statistics on cell morphologies can be obtained. All of the tools are featured in the user-friendly MATLAB®Graphical User Interface MitosisAnalyser. Copyright © 2017. Published by Elsevier Inc.
Pohl, L.; Kaiser, M.; Ketelhut, S.; Pereira, S.; Goycoolea, F.; Kemper, Björn
2016-03-01
Digital holographic microscopy (DHM) enables high resolution non-destructive inspection of technical surfaces and minimally-invasive label-free live cell imaging. However, the analysis of confluent cell layers represents a challenge as quantitative DHM phase images in this case do not provide sufficient information for image segmentation, determination of the cellular dry mass or calculation of the cell thickness. We present novel strategies for the analysis of confluent cell layers with quantitative DHM phase contrast utilizing a histogram based-evaluation procedure. The applicability of our approach is illustrated by quantification of drug induced cell morphology changes and it is shown that the method is capable to quantify reliable global morphology changes of confluent cell layers.
Energy Technology Data Exchange (ETDEWEB)
Li, Jing Ze, E-mail: Lijinge@uestc.edu.cn [State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Microelectronic and Solid-state Electronic, University of Electronic Science and Technology of China, Chengdu 610054 (China); State Key Laboratory of Polymer Materials Engineering (Sichuan University), Chengdu 610054 (China); Xinjiang Key Laboratory of Electronic Information Materials and Devices, Urumuqi 830011 (China); Wang, Ying; Hong Wang, Zhi; Mei, Di; Zou, Wei [State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Microelectronic and Solid-state Electronic, University of Electronic Science and Technology of China, Chengdu 610054 (China); Min Chang, Ai [State Key Laboratory of Polymer Materials Engineering (Sichuan University), Chengdu 610054 (China); Wang, Qi [Xinjiang Key Laboratory of Electronic Information Materials and Devices, Urumuqi 830011 (China); Komura, Motonori; Ito, Kaori [Division of Integrated Molecular Engineering, Chemical Resources Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Iyoda, Tomokazu, E-mail: Iyoda.t.aa@m.titech.ac.jp [Division of Integrated Molecular Engineering, Chemical Resources Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan)
2010-09-15
Three metal salts, i.e., AgNO{sub 3}, HAuCl{sub 4}, and KCl, were proposed as novel staining reagents instead of traditional RuO{sub 4} and OsO{sub 4} labeled with expensive price and extreme toxicity for scanning electron microscopy (SEM) imaging of microphase separated block copolymer film. A simple and costless aqueous solution immersion procedure could ensure selective staining of the metal slat in specific phase of the nanostructured copolymer film, leading to a clear phase contrasted SEM image. The heavy metal salt has better staining effect, demonstrating stable and high signal-to-noise SEM image even at an acceleration voltage as high as 30 kV and magnification up to 250,000 times.
Transmission electron microscopy investigation of interfaces in a two-phase TiAl alloy
Mahon, G. J.; Howe, J. M.
1990-06-01
The atomic structures of the γ/α2 and γ/γT interfaces in a TiAl alloy were investigated using conventional and high-resolution transmission electron microscopy (TEM) in order to understand the growth mechanisms and deformation behavior of the two-phase alloy. The results show that the α2 plates grow from the γ phase by the migration of a/6 partial dislocation ledges across the faces and that the γ/α2 interface usually contains closely spaced arrays of interfacial dislocations. Deformation twins cut through both γ twin boundaries and α2 plates during deformation, although slip of twinning c slocations through α2 appears to be a difficult process. Both the γ/α2 and γ/γT interfaces can be imaged and modeled at the atomic level, although slight crystal and/or beam tilt can complicate image interpretation.
Cardenas, Nelson; Mohanty, Samarendra K.
2012-03-01
RBC has been shown to possess shape memory subsequent to shear-induced shape transformation. However, this property of RBC may not be generalized to all kinds of stresses. Here, we report our observation on the action of radiation pressure forces on RBC's shape memory using optical manipulation and quantitative phase microscopy (OMQPM). QPM, based on Mach-Zehnder interferrometry, allowed measurement of dynamic changes of shape of RBC in optical tweezers at different trapping laser powers. In high power near-infrared optical tweezers (>200mW), the RBC was found to deform significantly due to optical forces. Upon removal of the tweezers, hysteresis in recovering its original resting shape was observed. In very high power tweezers or long-term stretching events, shape memory was almost erased. This irreversibility of the deformation may be due to temperature rise or stress-induced phase transformation of lipids in RBC membrane.
Chen, Yu; Fingler, Jeff; Trinh, Le A.; Fraser, Scott E.
2016-03-01
A phase variance optical coherence microscope (pvOCM) has been created to visualize blood flow in the vasculature of zebrafish embryos, without using exogenous labels. The pvOCM imaging system has axial and lateral resolutions of 2 μm in tissue, and imaging depth of more than 100 μm. Imaging of 2-5 days post-fertilization zebrafish embryos identified the detailed structures of somites, spinal cord, gut and notochord based on intensity contrast. Visualization of the blood flow in the aorta, veins and intersegmental vessels was achieved with phase variance contrast. The pvOCM vasculature images were confirmed with corresponding fluorescence microscopy of a zebrafish transgene that labels the vasculature with green fluorescent protein. The pvOCM images also revealed functional information of the blood flow activities that is crucial for the study of vascular development.
Energy Technology Data Exchange (ETDEWEB)
Sun Fei [Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061 (China); Zhang Jianxin, E-mail: jianxin@sdu.edu.cn [Key Laboratory of Liquid Structure and Heredity of Materials, Ministry of Education, Shandong University, Jinan 250061 (China); Liu Pan [Institute of Microstructure and Property of Advanced Materials, Beijing University of Technology, Beijing 100124 (China); Feng Qiang [National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083 (China); State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083 (China); Han Xiaodong; Mao Shengcheng [Institute of Microstructure and Property of Advanced Materials, Beijing University of Technology, Beijing 100124 (China)
2012-09-25
Graphical abstract: (a) TEM micrograph of {sigma} phase; (b) HRTEM image of {sigma}/{gamma} interface corresponding to the area of the white frame in (a); (c) an enlarged image of area from the white frame in (b). The combination of {sigma}/{gamma} interface appears very well, and a two-atomic-layer step is shown on the {sigma}/{gamma} interface. In addition, {sigma} phase has the orientation relationship of [0 0 1]{sub {gamma}}//[1 1 2{sup Macron }]{sub {sigma}}, (2{sup Macron} 2 0){sub {gamma}}//(1{sup Macron} 1 0){sub {sigma}}, (2{sup Macron }2{sup Macron} 0){sub {gamma}}//(1 1 1){sub {sigma}}; [0 1 1]{sub {gamma}}//[1 1 0]{sub {sigma}}, (1 1{sup Macron} 1){sub {gamma}}//(0 0 1{sup Macron }){sub {sigma}} with the {gamma} phase. Highlights: Black-Right-Pointing-Pointer Elemental characteristic of {sigma} phase is studied by HAADF techniques and EDS analysis. Black-Right-Pointing-Pointer Interfacial characteristics of {sigma}/{gamma} interface are revealed by HRTEM. Black-Right-Pointing-Pointer An atomic structural {sigma}/{gamma} interface with a two-atomic-layer step has been proposed. - Abstract: By means of high resolution transmission electron microscopy (HRTEM) and high-angle annular dark-field image technique (HAADF), morphological of plate-shaped {sigma} phase and interfacial characteristics between plate-shaped {sigma} phase and {gamma} phase in Ni-based single crystal superalloys have been studied. On the basis of HRTEM observations, an atomic structural interface between {sigma} phase and {gamma} phase with a step has been proposed. {sigma} Phase has the relationship of [0 0 1]{sub {gamma}}//[1 1 2{sup Macron }]{sub {sigma}}, (2{sup Macron} 2 0){sub {gamma}}//(1{sup Macron} 1 0){sub {sigma},} (2{sup Macron }2{sup Macron} 0){sub {gamma}}//(1 1 1){sub {sigma}}; [0 1 1]{sub {gamma}}//[1 1 0]{sub {sigma}}, (1 1{sup Macron} 1){sub {gamma}}//(0 0 1{sup Macron }){sub {sigma}} with the {gamma} phase. The compositional characteristics of the {sigma} phase which
Quantum Hilbert matrices and orthogonal polynomials
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...
Hilbert's Grand Hotel with a series twist
Wijeratne, Chanakya; Mamolo, Ami; Zazkis, Rina
2014-08-01
This paper presents a new twist on a familiar paradox, linking seemingly disparate ideas under one roof. Hilbert's Grand Hotel, a paradox which addresses infinite set comparisons is adapted and extended to incorporate ideas from calculus - namely infinite series. We present and resolve several variations, and invite the reader to explore his or her own variations.
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
Invariant Hilbert spaces of holomorphic functions
Faraut, J; Thomas, EGF
1999-01-01
A Hilbert space of holomorphic functions on a complex manifold Z, which is invariant under a group G of holomorphic automorphisms of Z, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on Z and G which implies that this decomposition is multiplicity
κ-Minkowski representations on Hilbert spaces
International Nuclear Information System (INIS)
Agostini, Alessandra
2007-01-01
The algebra of functions on κ-Minkowski noncommutative space-time is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski space-time in terms of the usual trace of operators
Hilbert space theory of classical electrodynamics
Indian Academy of Sciences (India)
Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.
Vertical integration from the large Hilbert space
Erler, Theodore; Konopka, Sebastian
2017-12-01
We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.
Notes on Hilbert and Cauchy Matrices
Czech Academy of Sciences Publication Activity Database
Fiedler, Miroslav
2010-01-01
Roč. 432, č. 1 (2010), s. 351-356 ISSN 0024-3795 Institutional research plan: CEZ:AV0Z10300504 Keywords : Hilbert matrix * Cauchy matrix * combined matrix * AT-property Subject RIV: BA - General Mathematics Impact factor: 1.005, year: 2010
Noise properties of Hilbert transform evaluation
Czech Academy of Sciences Publication Activity Database
Pavlíček, Pavel; Svak, V.
2015-01-01
Roč. 26, č. 8 (2015), s. 085207 ISSN 0957-0233 R&D Projects: GA ČR GA13-12301S Institutional support: RVO:68378271 Keywords : Hilbert transform * noise * measurement uncertainty * white -light interferometry * fringe-pattern analysis Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.492, year: 2015
A relative Hilbert-Mumford criterion
DEFF Research Database (Denmark)
Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus
2015-01-01
We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noetherian k-algebra A. We also extend the classical...
Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu
2016-08-01
Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.
Stampanoni, M.; Reichold, J.; Weber, B.; Haberthür, D.; Schittny, J.; Eller, J.; Büchi, F. N.; Marone, F.
2010-09-01
Nowadays, thanks to the high brilliance available at modern, third generation synchrotron facilities and recent developments in detector technology, it is possible to record volumetric information at the micrometer scale within few minutes. High signal-to-noise ratio, quantitative information on very complex structures like the brain micro vessel architecture, lung airways or fuel cells can be obtained thanks to the combination of dedicated sample preparation protocols, in-situ acquisition schemes and cutting-edge imaging analysis instruments. In this work we report on recent experiments carried out at the TOMCAT beamline of the Swiss Light Source [1] where synchrotron-based tomographic microscopy has been successfully used to obtain fundamental information on preliminary models for cerebral fluid flow [2], to provide an accurate mesh for 3D finite-element simulation of the alveolar structure of the pulmonary acinus [3] and to investigate the complex functional mechanism of fuel cells [4]. Further, we introduce preliminary results on the combination of absorption and phase contrast microscopy for the visualization of high-Z nanoparticles in soft tissues, a fundamental information when designing modern drug delivery systems [5]. As an outlook we briefly discuss the new possibilities offered by high sensitivity, high resolution grating interferomtery as well as Zernike Phase contrast nanotomography [6].
Convexity Of Inversion For Positive Operators On A Hilbert Space
International Nuclear Information System (INIS)
Sangadji
2001-01-01
This paper discusses and proves three theorems for positive invertible operators on a Hilbert space. The first theorem gives a comparison of the generalized arithmetic mean, generalized geometric mean, and generalized harmonic mean for positive invertible operators on a Hilbert space. For the second and third theorems each gives three inequalities for positive invertible operators on a Hilbert space that are mutually equivalent
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Nguyen, Thanh; Bui, Vy; Lam, Van; Raub, Christopher B; Chang, Lin-Ching; Nehmetallah, George
2017-06-26
We propose a fully automatic technique to obtain aberration free quantitative phase imaging in digital holographic microscopy (DHM) based on deep learning. The traditional DHM solves the phase aberration compensation problem by manually detecting the background for quantitative measurement. This would be a drawback in real time implementation and for dynamic processes such as cell migration phenomena. A recent automatic aberration compensation approach using principle component analysis (PCA) in DHM avoids human intervention regardless of the cells' motion. However, it corrects spherical/elliptical aberration only and disregards the higher order aberrations. Traditional image segmentation techniques can be employed to spatially detect cell locations. Ideally, automatic image segmentation techniques make real time measurement possible. However, existing automatic unsupervised segmentation techniques have poor performance when applied to DHM phase images because of aberrations and speckle noise. In this paper, we propose a novel method that combines a supervised deep learning technique with convolutional neural network (CNN) and Zernike polynomial fitting (ZPF). The deep learning CNN is implemented to perform automatic background region detection that allows for ZPF to compute the self-conjugated phase to compensate for most aberrations.
Sparsity-based multi-height phase recovery in holographic microscopy
Rivenson, Yair; Wu, Yichen; Wang, Hongda; Zhang, Yibo; Feizi, Alborz; Ozcan, Aydogan
2016-11-01
High-resolution imaging of densely connected samples such as pathology slides using digital in-line holographic microscopy requires the acquisition of several holograms, e.g., at >6-8 different sample-to-sensor distances, to achieve robust phase recovery and coherent imaging of specimen. Reducing the number of these holographic measurements would normally result in reconstruction artifacts and loss of image quality, which would be detrimental especially for biomedical and diagnostics-related applications. Inspired by the fact that most natural images are sparse in some domain, here we introduce a sparsity-based phase reconstruction technique implemented in wavelet domain to achieve at least 2-fold reduction in the number of holographic measurements for coherent imaging of densely connected samples with minimal impact on the reconstructed image quality, quantified using a structural similarity index. We demonstrated the success of this approach by imaging Papanicolaou smears and breast cancer tissue slides over a large field-of-view of ~20 mm2 using 2 in-line holograms that are acquired at different sample-to-sensor distances and processed using sparsity-based multi-height phase recovery. This new phase recovery approach that makes use of sparsity can also be extended to other coherent imaging schemes, involving e.g., multiple illumination angles or wavelengths to increase the throughput and speed of coherent imaging.
Sparsity-based multi-height phase recovery in holographic microscopy
Rivenson, Yair
2016-11-30
High-resolution imaging of densely connected samples such as pathology slides using digital in-line holographic microscopy requires the acquisition of several holograms, e.g., at >6–8 different sample-to-sensor distances, to achieve robust phase recovery and coherent imaging of specimen. Reducing the number of these holographic measurements would normally result in reconstruction artifacts and loss of image quality, which would be detrimental especially for biomedical and diagnostics-related applications. Inspired by the fact that most natural images are sparse in some domain, here we introduce a sparsity-based phase reconstruction technique implemented in wavelet domain to achieve at least 2-fold reduction in the number of holographic measurements for coherent imaging of densely connected samples with minimal impact on the reconstructed image quality, quantified using a structural similarity index. We demonstrated the success of this approach by imaging Papanicolaou smears and breast cancer tissue slides over a large field-of-view of ~20 mm2 using 2 in-line holograms that are acquired at different sample-to-sensor distances and processed using sparsity-based multi-height phase recovery. This new phase recovery approach that makes use of sparsity can also be extended to other coherent imaging schemes, involving e.g., multiple illumination angles or wavelengths to increase the throughput and speed of coherent imaging.
Methods for detection and characterization of signals in noisy data with the Hilbert-Huang transform
International Nuclear Information System (INIS)
Stroeer, Alexander; Cannizzo, John K.; Camp, Jordan B.; Gagarin, Nicolas
2009-01-01
The Hilbert-Huang transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of nonstationary signals with high time-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the Hilbert-Huang transform with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal-to-noise ratios.
Towards non-invasive 3D hepatotoxicity assays with optical coherence phase microscopy
Nelson, Leonard J.; Koulovasilopoulos, Andreas; Treskes, Philipp; Hayes, Peter C.; Plevris, John N.; Bagnaninchi, Pierre O.
2015-03-01
Three-dimensional tissue-engineered models are increasingly recognised as more physiologically-relevant than standard 2D cell culture for pre-clinical drug toxicity testing. However, many types of conventional toxicity assays are incompatible with dense 3D tissues. This study investigated the use of optical coherence phase microscopy (OCPM) as a novel approach to assess cell death in 3D tissue culture. For 3D micro-spheroid formation Human hepatic C3A cells were encapsulated in hyaluronic acid gels and cultured in 100μl MEME/10%FBS in 96-well plates. After spheroid formation the 3D liver constructs were exposed to acetaminophen on culture day 8. Acetaminophen hepatotoxicity in 3D cultures was evaluated using standard biochemical assays. An inverted OCPM in common path configuration was developed with a Callisto OCT engine (Thorlabs), centred at 930nm and a custom scanning head. Intensity data were used to perform in-depth microstructural imaging. In addition, phase fluctuations were measured by collecting several successive B scans at the same location, and statistics on the first time derivative of the phase, i.e. time fluctuations, were analysed over the acquisition time interval to retrieve overall cell viability. OCPM intensity (cell cluster size) and phase fluctuation statistics were directly compared with biochemical assays. In this study, we investigated optical coherence phase tomography to assess cell death in a 3d liver model after exposure to a prototypical hepatotoxin, acetaminophen. We showed that OCPM has the potential to assess noninvasively and label-free drug toxicity in 3D tissue models.
A four-phase strategy for the implementation of reflectance confocal microscopy in dermatology.
Hoogedoorn, L; Gerritsen, M J P; Wolberink, E A W; Peppelman, M; van de Kerkhof, P C M; van Erp, P E J
2016-08-01
Reflectance confocal microscopy (RCM) is gradually implemented in dermatology. Strategies for further implementation and practical 'hands on' guidelines are lacking. The primary outcome was to conduct a general strategy for further implementation of RCM. The secondary outcome was the diagnosis of psoriasis and differentiation of stable from unstable psoriatic plaques by means of the 'hands on' protocol, derived from the strategy. We used a four-phased model; an exploring phase, a systematic literature search, a clinical approach and, finally, an integration phase to develop a clinical guideline for RCM in psoriasis. Receiver operating characteristic curve statistics was applied to define the accuracy for the diagnosis of unstable psoriasis. A general strategy for further implementation of RCM and practical approach was developed to examine psoriasis by RCM and to distinguish stable from unstable psoriasis. Unstable psoriasis was diagnosed by epidermal inflammatory cell counts with a sensitivity and specificity of 91.7% and 98.3%, respectively, and with an accuracy of 0.92 (area under the curve). In addition, a monitoring model was proposed. This is the first study that shows a method for implementation of RCM in dermatology. The strategy and hands on protocol for psoriasis may serve as a model for other dermatological entities and additionally may lead to specialized ready-to-use RCM protocols for clinical dermatological practice. © 2016 European Academy of Dermatology and Venereology.
Compact Hilbert Curve Index Algorithm Based on Gray Code
Directory of Open Access Journals (Sweden)
CAO Xuefeng
2016-12-01
Full Text Available Hilbert curve has best clustering in various kinds of space filling curves, and has been used as an important tools in discrete global grid spatial index design field. But there are lots of redundancies in the standard Hilbert curve index when the data set has large differences between dimensions. In this paper, the construction features of Hilbert curve is analyzed based on Gray code, and then the compact Hilbert curve index algorithm is put forward, in which the redundancy problem has been avoided while Hilbert curve clustering preserved. Finally, experiment results shows that the compact Hilbert curve index outperforms the standard Hilbert index, their 1 computational complexity is nearly equivalent, but the real data set test shows the coding time and storage space decrease 40%, the speedup ratio of sorting speed is nearly 4.3.
Depth-variant blind restoration with pupil-phase constraints for 3D confocal microscopy
International Nuclear Information System (INIS)
Hadj, Saima Ben; Blanc-Féraud, Laure; Engler, Gilbert
2013-01-01
Three-dimensional images of confocal laser scanning microscopy suffer from a depth-variant blur, due to refractive index mismatch between the different mediums composing the system as well as the specimen, leading to optical aberrations. Our goal is to develop an image restoration method for 3D confocal microscopy taking into account the blur variation with depth. The difficulty is that optical aberrations depend on the refractive index of the biological specimen. The depth-variant blur function or the Point Spread Function (PSF) is thus different for each observation. A blind or semi-blind restoration method needs to be developed for this system. For that purpose, we use a previously developed algorithm for the joint estimation of the specimen function (original image) and the 3D PSF, the continuously depth-variant PSF is approximated by a convex combination of a set of space-invariant PSFs taken at different depths. We propose to add to that algorithm a pupil-phase constraint for the PSF estimation, given by the the optical instrument geometry. We thus define a blind estimation algorithm by minimizing a regularized criterion in which we integrate the Gerchberg-Saxton algorithm allowing to include these physical constraints. We show the efficiency of this method relying on some numerical tests
Abrahamsson, Sara; Ilic, Rob; Wisniewski, Jan; Mehl, Brian; Yu, Liya; Chen, Lei; Davanco, Marcelo; Oudjedi, Laura; Fiche, Jean-Bernard; Hajj, Bassam; Jin, Xin; Pulupa, Joan; Cho, Christine; Mir, Mustafa; El Beheiry, Mohamed; Darzacq, Xavier; Nollmann, Marcelo; Dahan, Maxime; Wu, Carl; Lionnet, Timothée; Liddle, J Alexander; Bargmann, Cornelia I
2016-03-01
Multifocus microscopy (MFM) allows high-resolution instantaneous three-dimensional (3D) imaging and has been applied to study biological specimens ranging from single molecules inside cells nuclei to entire embryos. We here describe pattern designs and nanofabrication methods for diffractive optics that optimize the light-efficiency of the central optical component of MFM: the diffractive multifocus grating (MFG). We also implement a "precise color" MFM layout with MFGs tailored to individual fluorophores in separate optical arms. The reported advancements enable faster and brighter volumetric time-lapse imaging of biological samples. In live microscopy applications, photon budget is a critical parameter and light-efficiency must be optimized to obtain the fastest possible frame rate while minimizing photodamage. We provide comprehensive descriptions and code for designing diffractive optical devices, and a detailed methods description for nanofabrication of devices. Theoretical efficiencies of reported designs is ≈90% and we have obtained efficiencies of > 80% in MFGs of our own manufacture. We demonstrate the performance of a multi-phase MFG in 3D functional neuronal imaging in living C. elegans.
Pang, Jincheng; Özkucur, Nurdan; Ren, Michael; Kaplan, David L; Levin, Michael; Miller, Eric L
2015-11-01
Phase Contrast Microscopy (PCM) is an important tool for the long term study of living cells. Unlike fluorescence methods which suffer from photobleaching of fluorophore or dye molecules, PCM image contrast is generated by the natural variations in optical index of refraction. Unfortunately, the same physical principles which allow for these studies give rise to complex artifacts in the raw PCM imagery. Of particular interest in this paper are neuron images where these image imperfections manifest in very different ways for the two structures of specific interest: cell bodies (somas) and dendrites. To address these challenges, we introduce a novel parametric image model using the level set framework and an associated variational approach which simultaneously restores and segments this class of images. Using this technique as the basis for an automated image analysis pipeline, results for both the synthetic and real images validate and demonstrate the advantages of our approach.
International Nuclear Information System (INIS)
Shiina, Tatsuo; Suzuki, Tsuyoshi; Honda, Toshio; Ito, Atsushi; Kinjo, Yasuhito; Yoshimura, Hideyuki; Yada, Keiji; Shinohara, Kunio
2009-01-01
In soft X-ray projection microscopy, it is easy to alter the magnification by changing the distance between the pinhole and the specimen, while the image is blurred because the soft X-rays are diffracted through the propagation from specimen to CCD detector. We corrected the blurred image by the iteration procedure of Fresnel to inverse Fresnel transformation taking phase distribution of the specimen into account. The experiments were conducted at the BL-11A of the Photon Factory, KEK, Japan for the specimens such as glass-capillaries, latex-particles, dried mammalian cells and human chromosomes. Many of those blurred images were corrected adequately by the iteration procedure, though some images such as those which have high-contrast or are overlapped by small cells still remain to be improved.
Meister, Stefan
2011-04-26
Phase-change memory (PCM) has been researched extensively as a promising alternative to flash memory. Important studies have focused on its scalability, switching speed, endurance, and new materials. Still, reliability issues and inconsistent switching in PCM devices motivate the need to further study its fundamental properties. However, many investigations treat PCM cells as black boxes; nanostructural changes inside the devices remain hidden. Here, using in situ transmission electron microscopy, we observe real-time nanostructural changes in lateral Ge2Sb2Te5 (GST) PCM bridges during switching. We find that PCM devices with similar resistances can exhibit distinct threshold switching behaviors due to the different initial distribution of nanocrystalline and amorphous domains, explaining variability of switching behaviors of PCM cells in the literature. Our findings show a direct correlation between nanostructure and switching behavior, providing important guidelines in the design and operation of future PCM devices with improved endurance and lower variability. © 2011 American Chemical Society.
Phasing of the Triatoma virus diffraction data using a cryo-electron microscopy reconstruction
International Nuclear Information System (INIS)
Estrozi, L.F.; Neumann, E.; Squires, G.; Rozas-Dennis, G.; Costabel, M.; Rey, F.A.; Guerin, D.M.A.; Navaza, J.
2008-01-01
The blood-sucking reduviid bug Triatoma infestans, one of the most important vector of American human trypanosomiasis (Chagas disease) is infected by the Triatoma virus (TrV). TrV has been classified as a member of the Cripavirus genus (type cricket paralysis virus) in the Dicistroviridae family. This work presents the three-dimensional cryo-electron microscopy (cryo-EM) reconstruction of the TrV capsid at about 25 A resolution and its use as a template for phasing the available crystallographic data by the molecular replacement method. The main structural differences between the cryo-EM reconstruction of TrV and other two viruses, one from the same family, the cricket paralysis virus (CrPV) and the human rhinovirus 16 from the Picornaviridae family are presented and discussed
Semiclassical propagation: Hilbert space vs. Wigner representation
Gottwald, Fabian; Ivanov, Sergei D.
2018-03-01
A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.
Elements of Hilbert spaces and operator theory
Vasudeva, Harkrishan Lal
2017-01-01
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...
Resonances, scattering theory and rigged Hilbert spaces
International Nuclear Information System (INIS)
Parravicini, G.; Gorini, V.; Sudarshan, E.C.G.
1979-01-01
The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references
Energy Technology Data Exchange (ETDEWEB)
Aslam, I., E-mail: ia31@msstate.edu [Center for Advanced Vehicular Systems, Mississippi State University, MS 39759 (United States); Department of Mechanical Engineering, Mississippi State University, MS 39762 (United States); Li, B. [Center for Advanced Vehicular Systems, Mississippi State University, MS 39759 (United States); Department of Chemical and Materials Engineering, University of Nevada, Reno, NV 89557 (United States); Martens, R.L.; Goodwin, J.R. [Central Analytical Facility, the University of Alabama, Tuscaloosa, AL 35487 (United States); Rhee, H.J. [Center for Advanced Vehicular Systems, Mississippi State University, MS 39759 (United States); Department of Mechanical Engineering, Mississippi State University, MS 39762 (United States); Goodwin, F. [International Zinc Association, Durham, NC 27713 (United States)
2016-10-15
Site-specific studies were carried out to characterize the interface of a galvanized dual-phase (DP) steel. Focused ion beam (FIB) was used to prepare specimens in the interface region (~ 100 nm thick) between the coating and the substrate. Transmission electron microscopy (TEM), scanning TEM (STEM), and high resolution TEM (HRTEM) were performed to resolve the phases and the structures at the interface between the zinc (Zn) coating and the steel substrate. The STEM and TEM results showed that a continuous manganese oxide (MnO) film with a thickness of ~ 20 nm was present on the surface of the substrate while no silicon (Si) oxides were resolved. Internal oxide particles were observed as well in the sub-surface region. Despite the presence of the continuous oxide film, a well-developed inhibition layer was observed right on top of the oxide film. The inhibition layer has a thickness of ~ 100 nm. Possible mechanisms for the growth of the inhibition layer were discussed. - Highlights: •Site-specific examinations were performed on the Zn/steel interface. •Continuous external MnO oxides (20 nm) were observed at the interface. •No Si oxides were observed at the interface. •Internal oxide particles were distributed in the subsurface. •A continuous inhibition layer grew on top of the external oxides.
Solid-phase characterization in flammable-gas-tank sludges by electron microscopy
International Nuclear Information System (INIS)
Liu, J.; Pederson, L.R.; Qang, L.Q.
1995-09-01
The crystallinity, morphology, chemical composition, and crystalline phases of several Tank 241-SY-101 (hereinafter referred to as SY-101) and Tank 241-SY-103 (hereinafter referred to as SY-103) solid samples were studied by transmission electron microscopy (TEM), electron energy dispersive spectroscopy (EDS), and electron diffraction. The main focus is on the identification of aluminum hydroxide thought to be present in these tank samples. Aluminum hydroxide was found in SY-103, but not in SY-101. This difference can be explained by the different OH/Al ratios found in the two tank samples: a high OH/Al ratio in SY-101 favors the formation of sodium aluminate, but a low OH/Al ratio in SY-103 favors aluminum hydroxide. These results were confirmed by a magnetic resonance study on SY-101 and SY-103 simulant. The transition from aluminum hydroxide to sodium aluminate occurs at an OH/Al molar ratio of 3.6. It is believed that the study of Al(OH) 3 was not affected by sample preparation because all Al(OH) 3 is in the solid form according to the NMR experiments. There is no Al(OH) 3 in the liquid. It is, therefore, most likely that the observation of Al(OH) 3 is representative of the real sludge sample, and is not affected by drying. Similar conclusions also apply to other insoluble phases such as iron and chromium
Full-angle tomographic phase microscopy of flowing quasi-spherical cells.
Villone, Massimiliano M; Memmolo, Pasquale; Merola, Francesco; Mugnano, Martina; Miccio, Lisa; Maffettone, Pier Luca; Ferraro, Pietro
2017-12-19
We report a reliable full-angle tomographic phase microscopy (FA-TPM) method for flowing quasi-spherical cells along microfluidic channels. This method lies in a completely passive optical system, i.e. mechanical scanning or multi-direction probing of the sample is avoided. It exploits the engineered rolling of cells while they are flowing along a microfluidic channel. Here we demonstrate significant progress with respect to the state of the art of in-flow TPM by showing a general extension to cells having almost spherical shapes while they are flowing in suspension. In fact, the adopted strategy allows the accurate retrieval of rotation angles through a theoretical model of the cells' rotation in a dynamic microfluidic flow by matching it with phase-contrast images resulting from holographic reconstructions. So far, the proposed method is the first and the only one that permits to get in-flow TPM by probing the cells with full-angle, achieving accurate 3D refractive index mapping and the simplest optical setup, simultaneously. Proof of concept experiments were performed successfully on human breast adenocarcinoma MCF-7 cells, opening the way for the full characterization of circulating tumor cells (CTCs) in the new paradigm of liquid biopsy.
Analyzer-based x-ray phase-contrast microscopy combining channel-cut and asymmetrically cut crystals
International Nuclear Information System (INIS)
Hoennicke, M. G.; Cusatis, C.
2007-01-01
An analyzer-based x-ray phase-contrast microscopy (ABM) setup combining a standard analyzer-based x-ray phase-contrast imaging (ABI) setup [nondispersive 4-crystal setup (Bonse-Hart setup)] and diffraction by asymmetrically cut crystals is presented here. An attenuation-contrast microscopy setup with conventional x-ray source and asymmetrically cut crystals is first analyzed. Edge-enhanced effects attributed to phase jumps or refraction/total external reflection on the fiber borders were detected. However, the long exposure times and the possibility to achieve high contrast microscopies by using extremely low attenuation-contrast samples motivated us to assemble the ABM setup using a synchrotron source. This setup was found to be useful for low contrast attenuation samples due to the low exposure time, high contrast, and spatial resolution found. Moreover, thanks to the combination with the nondispersive ABI setup, the diffraction-enhanced x-ray imaging algorithm could be applied
Herzing, Andrew A; Ro, Hyun Wook; Soles, Christopher L; DeLongchamp, Dean M
2013-09-24
The morphology of the active layer in an organic photovoltaic bulk-heterojunction device is controlled by the extent and nature of phase separation during processing. We have studied the effects of fullerene crystallinity during heat treatment in model structures consisting of a layer of poly(3-hexylthiophene) (P3HT) sandwiched between two layers of [6,6]-phenyl-C61-butyric acid methyl ester (PCBM). Utilizing a combination of focused ion-beam milling and energy-filtered transmission electron microscopy, we monitored the local changes in phase distribution as a function of annealing time at 140 °C. In both cases, dissolution of PCBM within the surrounding P3HT was directly visualized and quantitatively described. In the absence of crystalline PCBM, the overall phase distribution remained stable after intermediate annealing times up to 60 s, whereas microscale PCBM aggregates were observed after annealing for 300 s. Aggregate growth proceeded vertically from the substrate interface via uptake of PCBM from the surrounding region, resulting in a large PCBM-depleted region in their vicinity. When precrystallized PCBM was present, amorphous PCBM was observed to segregate from the intermediate P3HT layer and ripen the crystalline PCBM underneath, owing to the far lower solubility of crystalline PCBM within P3HT. This process occurred rapidly, with segregation already evident after annealing for 10 s and with uptake of nearly all of the amorphous PCBM by the crystalline layer after 60 s. No microscale aggregates were observed in the precrystallized system, even after annealing for 300 s.
Context based mixture model for cell phase identification in automated fluorescence microscopy
Directory of Open Access Journals (Sweden)
Zhou Xiaobo
2007-01-01
Full Text Available Abstract Background Automated identification of cell cycle phases of individual live cells in a large population captured via automated fluorescence microscopy technique is important for cancer drug discovery and cell cycle studies. Time-lapse fluorescence microscopy images provide an important method to study the cell cycle process under different conditions of perturbation. Existing methods are limited in dealing with such time-lapse data sets while manual analysis is not feasible. This paper presents statistical data analysis and statistical pattern recognition to perform this task. Results The data is generated from Hela H2B GFP cells imaged during a 2-day period with images acquired 15 minutes apart using an automated time-lapse fluorescence microscopy. The patterns are described with four kinds of features, including twelve general features, Haralick texture features, Zernike moment features, and wavelet features. To generate a new set of features with more discriminate power, the commonly used feature reduction techniques are used, which include Principle Component Analysis (PCA, Linear Discriminant Analysis (LDA, Maximum Margin Criterion (MMC, Stepwise Discriminate Analysis based Feature Selection (SDAFS, and Genetic Algorithm based Feature Selection (GAFS. Then, we propose a Context Based Mixture Model (CBMM for dealing with the time-series cell sequence information and compare it to other traditional classifiers: Support Vector Machine (SVM, Neural Network (NN, and K-Nearest Neighbor (KNN. Being a standard practice in machine learning, we systematically compare the performance of a number of common feature reduction techniques and classifiers to select an optimal combination of a feature reduction technique and a classifier. A cellular database containing 100 manually labelled subsequence is built for evaluating the performance of the classifiers. The generalization error is estimated using the cross validation technique. The
Zikmund, T; Kvasnica, L; Týč, M; Křížová, A; Colláková, J; Chmelík, R
2014-11-01
Transmitted light holographic microscopy is particularly used for quantitative phase imaging of transparent microscopic objects such as living cells. The study of the cell is based on extraction of the dynamic data on cell behaviour from the time-lapse sequence of the phase images. However, the phase images are affected by the phase aberrations that make the analysis particularly difficult. This is because the phase deformation is prone to change during long-term experiments. Here, we present a novel algorithm for sequential processing of living cells phase images in a time-lapse sequence. The algorithm compensates for the deformation of a phase image using weighted least-squares surface fitting. Moreover, it identifies and segments the individual cells in the phase image. All these procedures are performed automatically and applied immediately after obtaining every single phase image. This property of the algorithm is important for real-time cell quantitative phase imaging and instantaneous control of the course of the experiment by playback of the recorded sequence up to actual time. Such operator's intervention is a forerunner of process automation derived from image analysis. The efficiency of the propounded algorithm is demonstrated on images of rat fibrosarcoma cells using an off-axis holographic microscope. © 2014 The Authors Journal of Microscopy © 2014 Royal Microscopical Society.
Open superstring field theory on the restricted Hilbert space
International Nuclear Information System (INIS)
Konopka, Sebastian; Sachs, Ivo
2016-01-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture −3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
Marquet, P.
2016-05-03
Quantitative phase microscopy (QPM) has recently emerged as a powerful label-free technique in the field of living cell imaging allowing to non-invasively measure with a nanometric axial sensitivity cell structure and dynamics. Since the phase retardation of a light wave when transmitted through the observed cells, namely the quantitative phase signal (QPS), is sensitive to both cellular thickness and intracellular refractive index related to the cellular content, its accurate analysis allows to derive various cell parameters and monitor specific cell processes, which are very likely to identify new cell biomarkers. Specifically, quantitative phase-digital holographic microscopy (QP-DHM), thanks to its numerical flexibility facilitating parallelization and automation processes, represents an appealing imaging modality to both identify original cellular biomarkers of diseases as well to explore the underlying pathophysiological processes.
Hard-x-ray phase-difference microscopy with a low-brilliance laboratory x-ray source
International Nuclear Information System (INIS)
Kuwabara, Hiroaki; Yashiro, Wataru; Harasse, Sebastien; Momose, Atsushi; Mizutani, Haruo
2011-01-01
We have developed a hard-X-ray phase-imaging microscopy method using a low-brilliance X-ray source. The microscope consists of a sample, a Fresnel zone plate, a transmission grating, and a source grating creating an array of mutually incoherent X-ray sources. The microscope generates an image exhibiting twin features of the sample with opposite signs separated by a distance, which is processed to generate a phase image. The method is quantitative even for non-weak-phase objects that are difficult to be quantitatively examined by the widely used Zernike phase-contrast microscopy, and it has potentially broad applications in the material and biological science fields. (author)
Energy Technology Data Exchange (ETDEWEB)
Sanchez, Jacqueline; Badia, Antonella
2003-09-01
Atomic force microscopy imaging of dipalmitoylphosphatidylcholine (DPPC)/dilauroylphosphatidylcholine (DLPC) monolayers deposited onto alkanethiol modified-gold surfaces by the Langmuir-Schaefer technique was used to investigate domain formation in a binary system where phase separation arises from a difference in the alkyl chain lengths of the lipids. We have established how the condensed domain structure (shape and size) in DPPC/DLPC monolayers depends on the surface pressure and lipid composition. The mixed monolayers exhibit a positive deviation from an ideal mixing behavior at surface pressures of {<=}32 mN/m. Lateral compression to pressures greater than the liquid-expanded-to-liquid-condensed (LE-to-LC) phase transition pressure of the mixed monolayer ({approx}8-16 mN/m) induces extensive separation into condensed DPPC-rich domains and a fluid DLPC matrix. The condensed structures observed at a few milliNeutons per meter above the LE-to-LC transition pressure resemble those reported for pure DPPC monolayers in the LE/LC co-existence region. At a bilayer equivalence pressure of 32 mN/m and 20 deg. C, condensed domains exist between x{sub DPPC} {approx}0.25 and {approx}0.80, analogous to aqueous DPPC/DLPC dispersions. Compression from 32 to 40 mN/m results in either a striking distortion of the DPPC domain shape or a break-up of the microscopic DPPC domains into a network of nanoscopic islands (at higher DPPC mol fractions), possibly reflecting a critical mixing behavior. The results of this study provide a fundamental framework for understanding and controlling the formation of lateral domain structures in mixed phospholipid monolayers.
Nested Hilbert schemes on surfaces: Virtual fundamental class
DEFF Research Database (Denmark)
Gholampour, Amin; Sheshmani, Artan; Yau, Shing-Tung
We construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of Durr-Kabanov-Okonek and the stable pair invariants of Kool......-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial...
Eigenfunction expansions and scattering theory in rigged Hilbert spaces
Energy Technology Data Exchange (ETDEWEB)
Gomez-Cubillo, F [Dpt. de Analisis Matematico, Universidad de Valladolid. Facultad de Ciencias, 47011 Valladolid (Spain)], E-mail: fgcubill@am.uva.es
2008-08-15
The work reviews some mathematical aspects of spectral properties, eigenfunction expansions and scattering theory in rigged Hilbert spaces, laying emphasis on Lippmann-Schwinger equations and Schroedinger operators.
Unstable quantum states and rigged Hilbert spaces
International Nuclear Information System (INIS)
Gorini, V.; Parravicini, G.
1978-10-01
Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references
Hilbert W*-modules and coherent states
International Nuclear Information System (INIS)
Bhattacharyya, T; Roy, S Shyam
2012-01-01
Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Concerning the Hilbert 16th problem
Ilyashenko, Yu; Il'yashenko, Yu
1995-01-01
This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualit
Directory of Open Access Journals (Sweden)
Juan Manuel Pardal
2010-09-01
Full Text Available Deleterious phases precipitation in superduplex stainless steels is the main concern in fabrication by welding and hot forming of this class of material. Sigma, chi and secondary austenite phases are considered deleterious phases because they produce negative effects on corrosion resistance. Besides, sigma and chi phases also promote strong decrease of toughness. In the present work, the precipitations of sigma, chi and secondary austenite under aging in the 800-950 °C interval were studied in two UNS S32750 steels with different grain sizes. The deleterious phases could be quantified by light optical microscopy, with no distinction between them. Scanning electron microscopy was used to distinguish the individual phases in various aging conditions. The results elucidate the influence of the aging temperature and grain size on the kinetics precipitation and morphology of deleterious phases. The kinetics of deleterious phases is higher in the fine grained material in the initial stage of aging, but the maximum amount of deleterious phases is higher in the coarse grained steel.
Sasaki, Hirokazu; Otomo, Shinya; Minato, Ryuichiro; Yamamoto, Kazuo; Hirayama, Tsukasa
2014-06-01
Phase-shifting electron holography and Lorentz microscopy were used to map dopant distributions in GaAs compound semiconductors with step-like dopant concentration. Transmission electron microscope specimens were prepared using a triple beam focused ion beam (FIB) system, which combines a Ga ion beam, a scanning electron microscope, and an Ar ion beam to remove the FIB damaged layers. The p-n junctions were clearly observed in both under-focused and over-focused Lorentz microscopy images. A phase image was obtained by using a phase-shifting reconstruction method to simultaneously achieve high sensitivity and high spatial resolution. Differences in dopant concentrations between 1 × 10(19) cm(-3) and 1 × 10(18) cm(-3) regions were clearly observed by using phase-shifting electron holography. We also interpreted phase profiles quantitatively by considering inactive layers induced by ion implantation during the FIB process. The thickness of an inactive layer at different dopant concentration area can be measured from the phase image. © The Author 2014. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Zhu, Yi; Cai, Zhonghou; Chen, Pice; Zhang, Qingteng; Highland, Matthew J.; Jung, Il Woong; Walko, Donald A.; Dufresne, Eric M.; Jeong, Jaewoo; Samant, Mahesh G.; Parkin, Stuart S. P.; Freeland, John W.; Evans, Paul G.; Wen, Haidan
2016-02-01
Dynamical phase separation during a solid-solid phase transition poses a challenge for understanding the fundamental processes in correlated materials. Critical information underlying a phase transition, such as localized phase competition, is difficult to reveal by measurements that are spatially averaged over many phase separated regions. The ability to simultaneously track the spatial and temporal evolution of such systems is essential to understanding mesoscopic processes during a phase transition. Using state-of-the-art time-resolved hard x-ray diffraction microscopy, we directly visualize the structural phase progression in a VO2 film upon photoexcitation. Following a homogenous in-plane optical excitation, the phase transformation is initiated at discrete sites and completed by the growth of one lattice structure into the other, instead of a simultaneous isotropic lattice symmetry change. The time-dependent x-ray diffraction spatial maps show that the in-plane phase progression in laser-superheated VO2 is via a displacive lattice transformation as a result of relaxation from an excited monoclinic phase into a rutile phase. The speed of the phase front progression is quantitatively measured, and is faster than the process driven by in-plane thermal diffusion but slower than the sound speed in VO2. The direct visualization of localized structural changes in the time domain opens a new avenue to study mesoscopic processes in driven systems.
Energy Technology Data Exchange (ETDEWEB)
Chen Jie; Li Wenjie; Tian Jinping; Liu Longhua; Xiong Ying; Liu Gang; Wu Ziyu; Tian Yangchao [National Synchrotron Radiation Laboratory (China); Liu Yijin [School of Physics (China); Yue Zhengbo; Yu Hanqing [Laboratory of Environmental Engineering, School of Chemistry, University of Science and Technology of China, Hefei Anhui 230029 (China); Wang Chunru, E-mail: ychtian@ustc.edu.c [Institute of Chemistry, Chinese Academy of Sciences, Beijing 10060 (China)
2009-09-01
A transmission X-ray microscope using Fresnel zone-plates (FZPs) has been installed at U7A beamline of National Synchrotron Radiation Laboratory (NSRL). The objective FZP with 45 nm outermost zone width delivers a sub-50 nm resolution. A gold phase ring with 2.5 {mu}m thickness and 4 {mu}m width was placed at the focal plane of the objective FZP at 8 keV to produce a negative Zernike phase contrast. A series of samples were used to test the performance of the Zernike phase contrast X-ray microscopy.
International Nuclear Information System (INIS)
Chen Jie; Li Wenjie; Tian Jinping; Liu Longhua; Xiong Ying; Liu Gang; Wu Ziyu; Tian Yangchao; Liu Yijin; Yue Zhengbo; Yu Hanqing; Wang Chunru
2009-01-01
A transmission X-ray microscope using Fresnel zone-plates (FZPs) has been installed at U7A beamline of National Synchrotron Radiation Laboratory (NSRL). The objective FZP with 45 nm outermost zone width delivers a sub-50 nm resolution. A gold phase ring with 2.5 μm thickness and 4 μm width was placed at the focal plane of the objective FZP at 8 keV to produce a negative Zernike phase contrast. A series of samples were used to test the performance of the Zernike phase contrast X-ray microscopy.
Hussain, Samana; Grandy, David B; Reading, Mike; Craig, Duncan Q M
2004-07-01
Despite the widespread use of drug-loaded polymeric systems, there is still considerable uncertainty with regard to the nature of the distribution of the drug within the polymer matrix. The aim of this investigation was to develop thermal and microscopic techniques whereby the miscibility and spatial distribution of a model peptide, cyclosporin A (CyA), in hydroxypropyl methylcellulose (HPMC) films may be studied. The new technique of T(zero)-modulated temperature differential scanning calorimetry (T(zero) MTDSC), scanning electron microscopy (SEM), and pulse force mode atomic force microscopy (PFM-AFM) were used in conjunction to study films prepared using a solvent evaporation process, with a solvent extraction study performed to elucidate the nature of the observed phases. T(zero) MTDSC studies showed glass transitions for both the HPMC and CycA, with the T(g) for the HPMC and CycA seen for the mixed systems. SEM showed two spherical phases of differing electron density. PFM-AFM also showed spheres of differing adhesion that increased in size on addition of drug. Pixel intensity analysis indicated that the smaller spheres corresponded to CycA. Exposure of the films to dichloromethane, in which CycA is soluble but HPMC is not, resulted in the presence of voids that corresponded well to the spheres suggested to correspond to the drug. It was concluded that the system had undergone extensive or complete phase separation, and that the thermal and microscopic techniques outlined above are an effective means by which this issue may be studied. Copyright 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:1672-1681, 2004
A note on tensor fields in Hilbert spaces
Directory of Open Access Journals (Sweden)
LEONARDO BILIOTTI
2002-06-01
Full Text Available We discuss and extend to infinite dimensional Hilbert spaces a well-known tensoriality criterion for linear endomorphisms of the space of smooth vector fields in n.Discutimos e estendemos para espaços de Hilbert um critério de tensorialidade para endomorfismos do espaço dos campos vetoriais em Rpot(n.
ON STRONG AND WEAK CONVERGENCE IN n-HILBERT SPACES
Directory of Open Access Journals (Sweden)
Agus L. Soenjaya
2014-03-01
Full Text Available We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.
Hilbert schemes of points and infinite dimensional Lie algebras
Qin, Zhenbo
2018-01-01
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...
Czech Academy of Sciences Publication Activity Database
Žižka, Zdeněk; Gabriel, Jiří
2014-01-01
Roč. 60, č. 6 (2014), s. 545-550 ISSN 0015-5632 Institutional support: RVO:61388971 Keywords : microbial cells * microscopy * microorganism Subject RIV: EE - Microbiology, Virology Impact factor: 1.000, year: 2014
A four-phase strategy for the implementation of reflectance confocal microscopy in dermatology
Hoogedoorn, L.; Gerritsen, M.J.P.; Wolberink, E.A.W.; Peppelman, M.; Kerkhof, P.C.M. van de; Erp, P.E.J. van
2016-01-01
BACKGROUND: Reflectance confocal microscopy (RCM) is gradually implemented in dermatology. Strategies for further implementation and practical 'hands on' guidelines are lacking. OBJECTIVE: The primary outcome was to conduct a general strategy for further implementation of RCM. The secondary outcome
National Aeronautics and Space Administration — The proposed "Observation platform for dynamic biomedical and biotechnology experiments using the ISS Light Microscopy Module" consists of a platen sized to fit the...
Quantum holonomy theory and Hilbert space representations
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)
2016-11-15
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Matter tensor from the Hilbert variational principle
International Nuclear Information System (INIS)
Pandres, D. Jr.
1976-01-01
We consider the Hilbert variational principle which is conventionally used to derive Einstein's equations for the source-free gravitational field. We show that at least one version of the equivalence principle suggests an alternative way of performing the variation, resulting in a different set of Einstein equations with sources automatically present. This illustrates a technique which may be applied to any theory that is derived from a variational principle and that admits a gauge group. The essential point is that, if one first imposes a gauge condition and then performs the variation, one obtains field equations with source terms which do not appear if one first performs the variation and then imposes the gauge condition. A second illustration is provided by the variational principle conventionally used to derive Maxwell's equations for the source-free electromagnetic field. If one first imposes the Lorentz gauge condition and then performs the variation, one obtains Maxwell's equations with sources present
Multipliers for continuous frames in Hilbert spaces
International Nuclear Information System (INIS)
Balazs, P; Bayer, D; Rahimi, A
2012-01-01
In this paper, we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include anti-Wick operators, STFT multipliers or Calderón–Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten-class properties. Furthermore, the concepts of controlled and weighted frames are transferred to the continuous setting. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Laser Light-field Fusion for Wide-field Lensfree On-chip Phase Contrast Microscopy of Nanoparticles
Kazemzadeh, Farnoud; Wong, Alexander
2016-12-01
Wide-field lensfree on-chip microscopy, which leverages holography principles to capture interferometric light-field encodings without lenses, is an emerging imaging modality with widespread interest given the large field-of-view compared to lens-based techniques. In this study, we introduce the idea of laser light-field fusion for lensfree on-chip phase contrast microscopy for detecting nanoparticles, where interferometric laser light-field encodings acquired using a lensfree, on-chip setup with laser pulsations at different wavelengths are fused to produce marker-free phase contrast images of particles at the nanometer scale. As a proof of concept, we demonstrate, for the first time, a wide-field lensfree on-chip instrument successfully detecting 300 nm particles across a large field-of-view of ~30 mm2 without any specialized or intricate sample preparation, or the use of synthetic aperture- or shift-based techniques.
Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating
International Nuclear Information System (INIS)
Yashiro, Wataru; Harasse, Sebastien; Momose, Atsushi; Takeuchi, Akihisa; Suzuki, Yoshio
2010-01-01
We report on a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating. After the theoretical framework of self-imaging phenomenon by the grating in the system is presented, equations for the electric field on the image plane are derived for ideal and real lenses and an equation for the intensity on the image plane for partially coherent illumination is derived. The equations are simple and similar to those applying to a projection microscope consisting of a transmission grating except that there is no defocusing effect, regardless of whether the grating is in front of or behind the lens. This means that x-ray phase-imaging microscopy can be done without the defocusing effect. It is also shown that, by resolving the self-image on the image plane, high-sensitive x-ray phase-imaging microscopy can be attained without degradation in the spatial resolution due to diffraction by the grating. Experimental results obtained using partially coherent illumination from a synchrotron x-ray source confirm that hard-x-ray phase-imaging microscopy can be quantitatively performed with high sensitivity and without the spatial resolution degradation.
Braaf, Boy; de Boer, Johannes F
2017-03-20
Three-dimensional confocal fluorescence imaging of in vivo tissues is challenging due to sample motion and limited imaging speeds. In this paper a novel method is therefore presented for scanning confocal epi-fluorescence microscopy with instantaneous depth-sensing based on self-interference fluorescence microscopy (SIFM). A tabletop epi-fluorescence SIFM setup was constructed with an annular phase plate in the emission path to create a spectral self-interference signal that is phase-dependent on the axial position of a fluorescent sample. A Mach-Zehnder interferometer based on a 3 × 3 fiber-coupler was developed for a sensitive phase analysis of the SIFM signal with three photon-counter detectors instead of a spectrometer. The Mach-Zehnder interferometer created three intensity signals that alternately oscillated as a function of the SIFM spectral phase and therefore encoded directly for the axial sample position. Controlled axial translation of fluorescent microsphere layers showed a linear dependence of the SIFM spectral phase with sample depth over axial image ranges of 500 µm and 80 µm (3.9 × Rayleigh range) for 4 × and 10 × microscope objectives respectively. In addition, SIFM was in good agreement with optical coherence tomography depth measurements on a sample with indocyanine green dye filled capillaries placed at multiple depths. High-resolution SIFM imaging applications are demonstrated for fluorescence angiography on a dye-filled capillary blood vessel phantom and for autofluorescence imaging on an ex vivo fly eye.
International Nuclear Information System (INIS)
Bae, Byeong-Ju; Hong, Sung-Hoon; Hwang, Seon-Yong; Hwang, Jae-Yeon; Yang, Ki-Yeon; Lee, Heon
2009-01-01
The electrical characteristic of phase change material was studied in nano-scale using nanoimprint lithography and a conducting atomic force microscopy measurement system. Nanoimprint lithography was used to fabricate the nano-scale phase change material pattern. A Pt-coated AFM tip was used as a top electrode to measure the electrical characteristics of the GST nano-pillar. The GST nano-pillar, which is 200 nm in diameter, was amorphized by 2 V and 5 ns reset pulse and was then brought back to the crystalline phase by applying 1.3 V and 150 ns set pulse. Using this measurement system, the GST nano-pillar was switched between the amorphous and crystalline phases more than five times. The results of the reset and the set current measurement with the GST nano-pillar sizes show that the reset and the set currents also decreased with the decrease of the GST pillar size
Min, Junwei; Yao, Baoli; Ketelhut, Steffi; Kemper, Björn
2017-02-01
The modular combination of optical microscopes with digital holographic microscopy (DHM) has been proven to be a powerful tool for quantitative live cell imaging. The introduction of condenser and different microscope objectives (MO) simplifies the usage of the technique and makes it easier to measure different kinds of specimens with different magnifications. However, the high flexibility of illumination and imaging also causes variable phase aberrations that need to be eliminated for high resolution quantitative phase imaging. The existent phase aberrations compensation methods either require add additional elements into the reference arm or need specimen free reference areas or separate reference holograms to build up suitable digital phase masks. These inherent requirements make them unpractical for usage with highly variable illumination and imaging systems and prevent on-line monitoring of living cells. In this paper, we present a simple numerical method for phase aberration compensation based on the analysis of holograms in spatial frequency domain with capabilities for on-line quantitative phase imaging. From a single shot off-axis hologram, the whole phase aberration can be eliminated automatically without numerical fitting or pre-knowledge of the setup. The capabilities and robustness for quantitative phase imaging of living cancer cells are demonstrated.
Eypert-Blaison, Céline; Romero-Hariot, Anita; Clerc, Frédéric; Vincent, Raymond
2018-03-01
From November 2009 to October 2010, the French general directorate for labor organized a large field-study using analytical transmission electron microscopy (ATEM) to characterize occupational exposure to asbestos fibers during work on asbestos containing materials (ACM). The primary objective of this study was to establish a method and to validate the feasibility of using ATEM for the analysis of airborne asbestos of individual filters sampled in various occupational environments. For each sampling event, ATEM data were compared to those obtained by phase-contrast optical microscopy (PCOM), the WHO-recommended reference technique. A total of 265 results were obtained from 29 construction sites where workers were in contact with ACM. Data were sorted depending on the combination of the ACM type and the removal technique. For each "ACM-removal technique" combination, ATEM data were used to compute statistical indicators on short, fine and WHO asbestos fibers. Moreover, exposure was assessed taking into account the use of respiratory protective devices (RPD). As in previous studies, no simple relationship was found between results by PCOM and ATEM counting methods. Some ACM, such as asbestos-containing plasters, generated very high dust levels, and some techniques generated considerable levels of dust whatever the ACM treated. On the basis of these observations, recommendations were made to measure and control the occupational exposure limit. General prevention measures to be taken during work with ACM are also suggested. Finally, it is necessary to continue acquiring knowledge, in particular regarding RPD and the dust levels measured by ATEM for the activities not evaluated during this study.
Hilbert schemes of points on some classes surface singularities
Gyenge, Ádám
2016-01-01
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...
In-focus electron microscopy of frozen-hydrated biological samples with a Boersch phase plate
Energy Technology Data Exchange (ETDEWEB)
Barton, B.; Rhinow, D.; Walter, A.; Schroeder, R. [Max Planck Institute of Biophysics, Max-von-Laue Str. 3, 60438 Frankfurt am Main (Germany); Benner, G.; Majorovits, E.; Matijevic, M.; Niebel, H. [Carl Zeiss NTS GmbH, D-73447 Oberkochen (Germany); Mueller, H.; Haider, M. [CEOS GmbH, Englerstr. 26, 69126 Heidleberg (Germany); Lacher, M.; Schmitz, S.; Holik, P. [Caesar Research Center, Ludwig-Erhard-Allee 2, D-53175 Bonn (Germany); Kuehlbrandt, W., E-mail: werner.kuehlbrandt@mpibp-frankfurt.mpg.de [Max Planck Institute of Biophysics, Max-von-Laue Str. 3, 60438 Frankfurt am Main (Germany)
2011-12-15
We report the implementation of an electrostatic Einzel lens (Boersch) phase plate in a prototype transmission electron microscope dedicated to aberration-corrected cryo-EM. The combination of phase plate, C{sub s} corrector and Diffraction Magnification Unit (DMU) as a new electron-optical element ensures minimal information loss due to obstruction by the phase plate and enables in-focus phase contrast imaging of large macromolecular assemblies. As no defocussing is necessary and the spherical aberration is corrected, maximal, non-oscillating phase contrast transfer can be achieved up to the information limit of the instrument. A microchip produced by a scalable micro-fabrication process has 10 phase plates, which are positioned in a conjugate, magnified diffraction plane generated by the DMU. Phase plates remained fully functional for weeks or months. The large distance between phase plate and the cryo sample permits the use of an effective anti-contaminator, resulting in ice contamination rates of <0.6 nm/h at the specimen. Maximal in-focus phase contrast was obtained by applying voltages between 80 and 700 mV to the phase plate electrode. The phase plate allows for in-focus imaging of biological objects with a signal-to-noise of 5-10 at a resolution of 2-3 nm, as demonstrated for frozen-hydrated virus particles and purple membrane at liquid-nitrogen temperature. -- Highlights: Black-Right-Pointing-Pointer We implement an electrostatic Boersch phase plate into a dedicated prototypical TEM. Black-Right-Pointing-Pointer Phase contrast aberration-corrected electron microscope (PACEM) includes a diffraction magnification unit (DMU). Black-Right-Pointing-Pointer DMU minimizes obstruction of low spatial frequencies by the phase plate. Black-Right-Pointing-Pointer In-focus phase contrast generation is demonstrated for frozen-hydrated biological specimens.
Comparison of mounting methods for the evaluation of fibers by phase contrast microscopy.
Lee, Eun Gyung; Pang, Thomas W S; Nelson, John; Andrew, Mike; Harper, Martin
2011-07-01
The objectives of this study were to evaluate mounting methods for fiber examination of air sample filters by phase contrast microscopy (PCM) and to evaluate differences in fiber counts that might be due to fiber movement. Acetone/triacetin (AT) with various amounts of triacetin and acetone/Euparal (AE) where the mounting medium was placed between the cleared filter wedge and the coverslip were tested as a function of time. Field sample slides collected from a taconite iron-ore processing mill, a tremolitic talc-ore processing mill, and from around a crusher in a meta-basalt stone quarry were prepared with relocatable coverslips to revisit the same field areas on the slides. For each slide, three or four field areas were randomly selected and pictures were taken every 2 weeks to determine any sign of fiber movement over time. For 11 AT slides (named as AT-3.5) prepared with 3.5 μl of the mounting medium according to the NIOSH 7400 method, no fiber movements were detected over 59 weeks. On the other hand, AT slides prepared with larger quantities (10, 15, and 20 μl) of the mounting medium (named as AT-10) and AE slides prepared with ∼10 μl mounting medium showed fiber movement from the eighth day at the earliest. Fiber movement began earlier for the slides mounted with excess triacetin than for those mounted with Euparal. The sample slide storage method, either vertically or horizontally, did not seem to accelerate fiber movement. Additionally, two other modified methods, dimethylformamide solution/Euparal (mDE) and dimethylformamide solution/triacetin (mDT), were also prepared where the mounting medium was placed between the cleared filter wedge and the glass slide. The findings of fiber movements were similar; when 3.5 μl of triacetin was used for the mDT slides, fiber movements were not detected, while fibers on slides prepared with 10 μl triacetin (mDT-10) moved around. No fiber movements were observed for the mDE slides at any time during 59 weeks. Once
International Nuclear Information System (INIS)
Biwer, B.M.; Bates, J.K.; Abrajano, T.A. Jr.; Bradley, J.P.
1989-01-01
Test samples of 131 type glass that have been reacted for extended time periods in water vapor atmospheres of different relative humidities and in static leaching solution have been examined to characterize the reaction products. Analytical electron microscopy (AEM) was used to characterize the leached samples, and a complicated layer structure was revealed, consisting of phases that precipitate from solution and also form within the residual glass layer. The precipitated phases include birnes-site, saponite, and an iron species, while the intralayer phases include the U-Ti containing phase brannerite distributed within a matrix consisting of bands of an Fe rich montmorillonite clay. Comparison is made between samples leached at 40 degrees C for 4 years with those leached at 90 degrees C for 3-1/2 years. The samples reacted in water vapor were examined with scanning electron microscopy and show increasing reaction as both the relative humidity and time of reaction increases. These samples also contain a layered structure with reaction products on the glass surface. 15 refs., 5 figs
Descloux, A.; Grußmayer, K. S.; Bostan, E.; Lukes, T.; Bouwens, A.; Sharipov, A.; Geissbuehler, S.; Mahul-Mellier, A.-L.; Lashuel, H. A.; Leutenegger, M.; Lasser, T.
2018-03-01
Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. However, going `beyond the diffraction barrier' comes at a price, since most far-field super-resolution imaging techniques trade temporal for spatial super-resolution. We propose the combination of a novel label-free white light quantitative phase imaging with fluorescence to provide high-speed imaging and spatial super-resolution. The non-iterative phase retrieval relies on the acquisition of single images at each z-location and thus enables straightforward 3D phase imaging using a classical microscope. We realized multi-plane imaging using a customized prism for the simultaneous acquisition of eight planes. This allowed us to not only image live cells in 3D at up to 200 Hz, but also to integrate fluorescence super-resolution optical fluctuation imaging within the same optical instrument. The 4D microscope platform unifies the sensitivity and high temporal resolution of phase imaging with the specificity and high spatial resolution of fluorescence microscopy.
Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris
2012-11-19
We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S21 response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.
Hilbert space, Poincare dodecahedron and golden mean transfiniteness
International Nuclear Information System (INIS)
El Naschie, M.S.
2007-01-01
A rather direct connection between Hilbert space and E-infinity theory is established via an irrational-transfinite golden mean topological probability. Subsequently the ramifications for Kleinian modular spaces and the cosmological Poincare Dodecahedron proposals are considered
Introduction to Hilbert space and the theory of spectral multiplicity
Halmos, Paul R
2017-01-01
Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.
Lectures on Hilbert schemes of points on surfaces
Nakajima, Hiraku
1999-01-01
This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book. --Mathematical Reviews The Hilbert scheme of a surface X describes collections of n (not necessarily distinct) points on X. More precisely, it is the moduli space for 0-dimensional subschemes of X of length n. Recently it was realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory--even theoretical physics. The discussion in the book reflects this feature of Hilbert schemes. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field...
Energy Technology Data Exchange (ETDEWEB)
Kohn, Amit, E-mail: akohn@post.tau.ac.il [Department of Materials Science and Engineering, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv (Israel); Habibi, Avihay; Mayo, Martin [Department of Materials Engineering, Ben-Gurion University of the Negev, 84105 Beer Sheva (Israel)
2016-01-15
The ‘transport-of-intensity’ equation (TIE) is a general phase reconstruction methodology that can be applied to Lorentz transmission electron microscopy (TEM) through the use of Fresnel-contrast (defocused) images. We present an experimental study to test the application of the TIE for quantitative magnetic mapping in Lorentz TEM without aberration correction by examining sub-micrometer sized Ni{sub 80}Fe{sub 20} (Permalloy) elements. For a JEOL JEM 2100F adapted for Lorentz microscopy, we find that quantitative magnetic phase reconstructions are possible for defoci distances ranging between approximately 200 μm and 800 μm. The lower limit originates from competing sources of image intensity variations in Fresnel-contrast images, namely structural defects and diffraction contrast. The upper defocus limit is due to a numerical error in the estimation of the intensity derivative based on three images. For magnetic domains, we show quantitative reconstructions of the product of the magnetic induction vector and thickness in element sizes down to approximately 100 nm in lateral size and 5 nm thick resulting in a minimal detection of 5 T nm. Three types of magnetic structures are tested in terms of phase reconstruction: vortex cores, domain walls, and element edges. We quantify vortex core structures at a diameter of 12 nm while the structures of domain walls and element edges are characterized qualitatively. Finally, we show by image simulations that the conclusions of this experimental study are relevant to other Lorentz TEM in which spherical aberration and defocus are dominant aberrations. - Highlights: • Testing TIE for quantitative magnetic phase reconstruction in Lorentz TEM. • Quantitative magnetic phase reconstructions for defoci distances in 200–800 μm range. • Minimal detection of the product of the magnetic induction and thickness is 5 T nm. • Quantitative phase reconstruction for vortex core structures at 12 nm diameter. • Observations
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Directory of Open Access Journals (Sweden)
Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
Integrated reconfigurable photonic filters based on interferometric fractional Hilbert transforms.
Sima, C; Cai, B; Liu, B; Gao, Y; Yu, Y; Gates, J C; Zervas, M N; Smith, P G R; Liu, D
2017-10-01
In this paper, we present integrated reconfigurable photonic filters using fractional Hilbert transformers (FrHTs) and optical phase tuning structure within the silica-on-silicon platform. The proposed structure, including grating-based FrHTs, an X-coupler, and a pair of thermal tuning filaments, is fabricated through the direct UV grating writing technique. The thermal tuning effect is realized by the controllable microheaters located on the two arms of the X-coupler. We investigate the 200 GHz maximum bandwidth photonic FrHTs based on apodized planar Bragg gratings, and analyze the reflection spectrum responses. Through device integration and thermal modulation, the device could operate as photonic notch filters with 5 GHz linewidth and controllable single sideband suppression filters with measured 12 dB suppression ratio. A 50 GHz instantaneous frequency measuring system using this device is also schematically proposed and analyzed with potential 3 dB measurement improvement. The device could be configured with these multiple functions according to need. The reconfigurable structure has great potential in ultrafast all-optical signal processing fields.
Electron microscopy analyses and electrical properties of the layered Bi{sub 2}WO{sub 6} phase
Energy Technology Data Exchange (ETDEWEB)
Taoufyq, A. [Institut Matériaux Microélectronique et Nanosciences de Provence, IM2NP, UMR CNRS 7334, Université du Sud Toulon-Var, BP 20132, 83957, La Garde Cedex (France); Laboratoire Matériaux et Environnement LME, Faculté des Sciences, Université Ibn Zohr, BP 8106, Cité Dakhla, Agadir, Maroc (Morocco); Département d‘Études des Réacteurs, Laboratoire Dosimétrie Capteurs Instrumentation, CEA Cadarache (France); Société CESIGMA—Signals and Systems, 1576 Chemin de La Planquette, F 83 130 LA GARDE (France); Ait Ahsaine, H. [Laboratoire Matériaux et Environnement LME, Faculté des Sciences, Université Ibn Zohr, BP 8106, Cité Dakhla, Agadir, Maroc (Morocco); Patout, L. [Institut Matériaux Microélectronique et Nanosciences de Provence, IM2NP, UMR CNRS 7334, Université du Sud Toulon-Var, BP 20132, 83957, La Garde Cedex (France); Benlhachemi, A.; Ezahri, M. [Laboratoire Matériaux et Environnement LME, Faculté des Sciences, Université Ibn Zohr, BP 8106, Cité Dakhla, Agadir, Maroc (Morocco); and others
2013-07-15
The bismuth tungstate Bi{sub 2}WO{sub 6} was synthesized using a classical coprecipitation method followed by a calcination process at different temperatures. The samples were characterized by X-ray diffraction, simultaneous thermogravimetry and differential thermal analysis (TGA/DTA), scanning and transmission electron microscopy (SEM, TEM) analyses. The Rietveld analysis and electron diffraction clearly confirmed the Pca2{sub 1} non centrosymmetric space group previously proposed for this phase. The layers Bi{sub 2}O{sub 2}{sup 2+} and WO{sub 4}{sup 2−} have been directly evidenced from the HRTEM images. The electrical properties of Bi{sub 2}WO{sub 6} compacted pellets systems were determined from electrical impedance spectrometry (EIS) and direct current (DC) analyses, under air and argon, between 350 and 700 °C. The direct current analyses showed that the conduction observed from EIS analyses was mainly ionic in this temperature range, with a small electronic contribution. Electrical change above the transition temperature of 660 °C is observed under air and argon atmospheres. The strong conductivity increase observed under argon is interpreted in terms of formation of additional oxygen vacancies coupled with electron conduction. - Graphical abstract: High resolution transmission electron microscopy: inverse fast Fourier transform giving the layered structure of the Bi{sub 2}WO{sub 6} phase, with a representation of the cell dimensions (b and c vectors). The Bi{sub 2}O{sub 2}{sup 2+} and WO{sub 4}{sup 2−} sandwiches are visible in the IFFT image. - Highlights: • Using transmission electron microscopy, we visualize the layered structure of Bi{sub 2}WO{sub 6}. • Electrical analyses under argon gas show some increase in conductivity. • The phase transition at 660 °C is evidenced from electrical modification.
Yücelen, Emrah; Lazić, Ivan; Bosch, Eric G T
2018-02-08
Using state of the art scanning transmission electron microscopy (STEM) it is nowadays possible to directly image single atomic columns at sub-Å resolution. In standard (high angle) annular dark field STEM ((HA)ADF-STEM), however, light elements are usually invisible when imaged together with heavier elements in one image. Here we demonstrate the capability of the recently introduced Integrated Differential Phase Contrast STEM (iDPC-STEM) technique to image both light and heavy atoms in a thin sample at sub-Å resolution. We use the technique to resolve both the Gallium and Nitrogen dumbbells in a GaN crystal in [[Formula: see text
Energy Technology Data Exchange (ETDEWEB)
Varlakov, V.P.; Fialkov, A.S.; Smirnov, B.N.
1981-01-01
The structure of channel black, DG-100, in the initial and graphitized states has been studied by phase-contrasting electron microscopy with a direct resolution of the carbon layers. An individual carbon layer is the main structural element of carbon black. The structure of channel black in the graphitized state looks like a hollow closed polyhedron made up of bundles of continuous carbon layers which can bend and become deformed to a great extent, testifying to the polymeric nature of the structure of channel black. The authors give an interpretation of the roentgen values of the 'dimensions of crystallites' in channel black.
Treatment of electrochemical noise data by the Hilbert-Huang transform
International Nuclear Information System (INIS)
Rahier, A.
2009-01-01
Most of the classical approaches for treating electro-chemical noise (ECN) data suffer from the non-linear and non steady-state character of the delivered signal. Very often, the link between time and the local corrosion events supposedly responsible for ECN data signatures is lost during treatment, as is obvious when using the classical Fourier Transform (FT), followed by an analysis of the response in the frequency domain. In this particular case, the information directly related to the corrosion events is distributed into the full spectra, thereby preventing the operator to derive clear and precise conclusions. In 2005, we suggested an alternative data treatment based on the Hilbert-Huang transform (HHT). The latter keeps track of the time variable and copes with non-linear and non steady-state behaviours of the system under examination. In 2006, we demonstrated the applicability of the newly proposed data treatment in the case of ECN data collected under BWR (Boiling Water Reactor) conditions. In 2007, we collected additional ECN data and started a preliminary investigation of two mathematical restrictions that are susceptible to impair the interpretation of the results. We discovered a possible modification of the Hilbert transform allowing generating controlled phase shifts that are different from pi/2 as is always the case for the Hilbert transform
Meister, Stefan; Kim, SangBum; Cha, Judy J.; Wong, H.-S. Philip; Cui, Yi
2011-01-01
Phase-change memory (PCM) has been researched extensively as a promising alternative to flash memory. Important studies have focused on its scalability, switching speed, endurance, and new materials. Still, reliability issues and inconsistent
Lauer, Milena H; Gehlen, Marcelo H; de Jesus, Karen; Berlinck, Roberto G S
2014-05-01
The emission spectra, quantum yields and fluorescence lifetimes of citrinin in organic solvents and hydrogel films have been determined. Citrinin shows complex fluorescence decays due to the presence of two tautomers in solution and interconversion from excited-state double proton transfer (ESDPT) process. The fluorescence decay times associated with the two tautomers have values near 1 and 5 ns depending on the medium. In hydrogel films of agarose and alginate, fluorescence imaging showed that citrinin is not homogeneously dispersed and highly emissive micrometer spots may be formed. Fluorescence spectrum and decay analysis are used to recognize the presence of citrinin in hydrogel films using confocal fluorescence microscopy and spectroscopy.
Marquet, Pierre; Depeursinge, Christian; Magistretti, Pierre J.
2014-01-01
Quantitative phase microscopy (QPM) has recently emerged as a new powerful quantitative imaging technique well suited to noninvasively explore a transparent specimen with a nanometric axial sensitivity. In this review, we expose the recent
Li, Huiqin; Sun, Limin; Shen, Guangxia; Liang, Qi
2012-02-01
In this work, we investigated the bulk phase distinguishing of the poly(ɛ-caprolactone)-polybutadiene-poly(ɛ-caprolactone) (PCL-PB-PCL) triblock copolymer blended in epoxy resin by tapping mode atomic force microscopy (TM-AFM). We found that at a set-point amplitude ratio ( r sp) less than or equal to 0.85, a clear phase contrast could be obtained using a probe with a force constant of 40 N/m. When r sp was decreased to 0.1 or less, the measured size of the PB-rich domain relatively shrank; however, the height images of the PB-rich domain would take reverse (translating from the original light to dark) at r sp = 0.85. Force-probe measurements were carried out on the phase-separated regions by TM-AFM. According to the phase shift angle vs. r sp curve, it could be concluded that the different force exerting on the epoxy matrix or on the PB-rich domain might result in the height and phase image reversion. Furthermore, the indentation depth vs. r sp plot showed that with large tapping force (lower r sp), the indentation depth for the PB-rich domain was nearly identical for the epoxy resin matrix.
International Nuclear Information System (INIS)
Rodenburg, C.; Viswanathan, P.; Jepson, M.A.E.; Liu, X.; Battaglia, G.
2014-01-01
Due to their wide range of applications, porous polymers obtained from high internal phase emulsions have been widely studied using scanning electron microscopy. However, due to their lack of electrical conductivity, quantitative information of wall thicknesses and surface roughness, which are of particular interest to tissue engineering, has not been obtained. Here, Helium Ion Microscopy is used to examine uncoated polymer foams and some very strong but unexpected contrast is observed, the origin of which is established here. Based on this analysis, a method for the measurement of wall thickness variations and wall roughness measurements has been developed, based on the modeling of Helium ion transmission. The results presented here indicate that within the walls of the void structure there exist small features with height variations of ∼30 nm and wall thickness variations from ∼100 nm to larger 340 nm in regions surrounding interconnecting windows within the structure. The suggested imaging method is applicable to other porous carbon based structures with wall thicknesses in the range of 40–340 nm. - Highlights: • The first helium ion microscopy image of uncoated structures formed from HIPEs is presented. • Unusually high contrast features that change with accelerating voltage are observed. • The origin of the observed contrast is determined to be mass thickness contrast. • A new method for quantitative wall thickness variation/roughness measurements is demonstrated
Energy Technology Data Exchange (ETDEWEB)
Rodenburg, C., E-mail: c.rodenburg@sheffield.ac.uk [Department of Materials Science and Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (United Kingdom); Viswanathan, P. [Department of Biomedical Sciences, University of Sheffield, Firth Court, Western Bank Sheffield, Sheffield S10 2 TN (United Kingdom); Jepson, M.A.E. [Department of Materials, Loughborough University, Loughborough, Leicestershire LE11 3TU (United Kingdom); Liu, X. [Carl Zeiss Microscopy GmbH, Carl-Zeiss-Strasse 22, 73447 Oberkochen (Germany); Battaglia, G. [Department of Chemistry University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom); The MRC/UCL Centre for Medical Molecular Virology, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom)
2014-04-01
Due to their wide range of applications, porous polymers obtained from high internal phase emulsions have been widely studied using scanning electron microscopy. However, due to their lack of electrical conductivity, quantitative information of wall thicknesses and surface roughness, which are of particular interest to tissue engineering, has not been obtained. Here, Helium Ion Microscopy is used to examine uncoated polymer foams and some very strong but unexpected contrast is observed, the origin of which is established here. Based on this analysis, a method for the measurement of wall thickness variations and wall roughness measurements has been developed, based on the modeling of Helium ion transmission. The results presented here indicate that within the walls of the void structure there exist small features with height variations of ∼30 nm and wall thickness variations from ∼100 nm to larger 340 nm in regions surrounding interconnecting windows within the structure. The suggested imaging method is applicable to other porous carbon based structures with wall thicknesses in the range of 40–340 nm. - Highlights: • The first helium ion microscopy image of uncoated structures formed from HIPEs is presented. • Unusually high contrast features that change with accelerating voltage are observed. • The origin of the observed contrast is determined to be mass thickness contrast. • A new method for quantitative wall thickness variation/roughness measurements is demonstrated.
Jaccard, Nicolas; Griffin, Lewis D; Keser, Ana; Macown, Rhys J; Super, Alexandre; Veraitch, Farlan S; Szita, Nicolas
2014-01-01
The quantitative determination of key adherent cell culture characteristics such as confluency, morphology, and cell density is necessary for the evaluation of experimental outcomes and to provide a suitable basis for the establishment of robust cell culture protocols. Automated processing of images acquired using phase contrast microscopy (PCM), an imaging modality widely used for the visual inspection of adherent cell cultures, could enable the non-invasive determination of these characteristics. We present an image-processing approach that accurately detects cellular objects in PCM images through a combination of local contrast thresholding and post hoc correction of halo artifacts. The method was thoroughly validated using a variety of cell lines, microscope models and imaging conditions, demonstrating consistently high segmentation performance in all cases and very short processing times (image). Based on the high segmentation performance, it was possible to precisely determine culture confluency, cell density, and the morphology of cellular objects, demonstrating the wide applicability of our algorithm for typical microscopy image processing pipelines. Furthermore, PCM image segmentation was used to facilitate the interpretation and analysis of fluorescence microscopy data, enabling the determination of temporal and spatial expression patterns of a fluorescent reporter. We created a software toolbox (PHANTAST) that bundles all the algorithms and provides an easy to use graphical user interface. Source-code for MATLAB and ImageJ is freely available under a permissive open-source license. Biotechnol. Bioeng. 2014;111: 504–517. © 2013 Wiley Periodicals, Inc. PMID:24037521
International Nuclear Information System (INIS)
Patel, Vishesha; Malinovsky, Vladimir S.; Malinovskaya, Svetlana
2010-01-01
Coherent anti-Stokes Raman scattering (CARS) microscopy has been a major tool of investigation of biological structures as it contains the vibrational signature of molecules. A quantum control method based on chirped pulse adiabatic passage was recently proposed for selective excitation of a predetermined vibrational mode in CARS microscopy [Malinovskaya and Malinovsky, Opt. Lett. 32, 707 (2007)]. The method utilizes the chirp sign variation at the peak pulse amplitude and gives a robust adiabatic excitation of the desired vibrational mode. Using this method, we investigate the impact of coupling between vibrational modes in molecules on controllability of excitation of the CARS signal. We analyze two models of two coupled two-level systems (TLSs) having slightly different transitional frequencies. The first model, featuring degenerate ground states of the TLSs, gives robust adiabatic excitation and maximum coherence in the resonant TLS for positive value of the chirp. In the second model, implying nondegenerate ground states in the TLSs, a population distribution is observed in both TLSs, resulting in a lack of selectivity of excitation and low coherence. It is shown that the relative phase and coupling between the TLSs play an important role in optimizing coherence in the desired vibrational mode and suppressing unwanted transitions in CARS microscopy.
Xi, Teli; Dou, Jiazhen; Di, Jianglei; Li, Ying; Zhang, Jiwei; Ma, Chaojie; Zhao, Jianlin
2017-06-01
Short-coherence in-line phase-shifting digital holographic microscopy based on Michelson interferometer is proposed to measure internal structure in silicon. In the configuration, a short-coherence infrared laser is used as the light source in order to avoid the interference formed by the reference wave and the reflected wave from the front surface of specimen. At the same time, in-line phase-shifting configuration is introduced to overcome the problem of poor resolution and large pixel size of the infrared camera and improve the space bandwidth product of the system. A specimen with staircase structure is measured by using the proposed configuration and the 3D shape distribution are given to verify the effectiveness and accuracy of the method.
Robert, Donatien; Douillard, Thierry; Boulineau, Adrien; Brunetti, Guillaume; Nowakowski, Pawel; Venet, Denis; Bayle-Guillemaud, Pascale; Cayron, Cyril
2013-12-23
LiFePO4 and FePO4 phase distributions of entire cross-sectioned electrodes with various Li content are investigated from nanoscale to mesoscale, by transmission electron microscopy and by the new electron forward scattering diffraction technique. The distributions of the fully delithiated (FePO4) or lithiated particles (LiFePO4) are mapped on large fields of view (>100 × 100 μm(2)). Heterogeneities in thin and thick electrodes are highlighted at different scales. At the nanoscale, the statistical analysis of 64 000 particles unambiguously shows that the small particles delithiate first. At the mesoscale, the phase maps reveal a core-shell mechanism at the scale of the agglomerates with a preferential pathway along the electrode porosities. At larger scale, lithiation occurs in thick electrodes "stratum by stratum" from the surface in contact with electrolyte toward the current collector.
Yoon, Beom-Jin; Park, Jung Ok; Srinivasarao, Mohan; Smith, Michael H.; Lyon, L. Andrew
2011-03-01
The structure and dynamics of soft matter were studied by differential dynamic optical microscopy. One can retrieve q-space information through image processing and Fourier analysis, even when the feature sizes in real space image are too small to be resolved or even visible in an optical microscope. The temporal sequence of real space images were Fourier transformed, and analyzed for the temporal and spatial fluctuations of power spectrum. Here, we present the results on liquid crystal dynamics and their elastic properties, volume phase transition of hydrogels when their dimensions are sub-micron, and critical opalescence of binary mixtures (water/2,6-lutidine).
Paturzo, Melania; Finizio, Andrea; Memmolo, Pasquale; Puglisi, Roberto; Balduzzi, Donatella; Galli, Andrea; Ferraro, Pietro
2012-09-07
We show that sharp imaging and quantitative phase-contrast microcopy is possible in microfluidics in flowing turbid media by digital holography. In fact, in flowing liquids with suspended colloidal particles, clear vision is hindered and cannot be recovered by any other microscopic imaging technique. On the contrary, using digital holography, clear imaging is possible thanks to the Doppler frequency shift experienced by the photons scattered by the flowing colloidal particles, which do not contribute to the interference process, i.e. the recorded hologram. The method is illustrated and imaging results are demonstrated for pure phase objects, i.e. biological cells in microfluidic channels.
Charging of carbon thin films in scanning and phase-plate transmission electron microscopy
DEFF Research Database (Denmark)
Hettler, Simon; Kano, Emi; Dries, Manuel
2018-01-01
A systematic study on charging of carbon thin films under intense electron-beam irradiation was performed in a transmission electron microscope to identify the underlying physics for the functionality of hole-free phase plates. Thin amorphous carbon films fabricated by different deposition techni...
DEFF Research Database (Denmark)
Michael, A Y; Drejer, J O; Bagger, P V
1987-01-01
A method combining Janus green B and Thymol blue stains the anterior part of the head, the nuclear membrane, middle piece, and tail of spermatozoa light green and the nucleus deep purple. The method provides excellent stained preparations for the evaluation of sperm morphology by phase contrast...
Martinez-Torres, Cristina; Laperrousaz, Bastien; Berguiga, Lotfi; Boyer-Provera, Elise; Elezgaray, Juan; Nicolini, Franck E.; Maguer-Satta, Veronique; Arneodo, Alain; Argoul, Françoise
2015-09-01
The distribution of refractive indices (RIs) of a living cell contributes in a nonintuitive manner to its optical phase image and quite rarely can be inverted to recover its internal structure. The interpretation of the quantitative phase images of living cells remains a difficult task because (1) we still have very little knowledge on the impact of its internal macromolecular complexes on the local RI and (2) phase changes produced by light propagation through the sample are mixed with diffraction effects by the internal cell bodies. We propose to implement a two-dimensional wavelet-based contour chain detection method to distinguish internal boundaries based on their greatest optical path difference gradients. These contour chains correspond to the highest image phase contrast and follow the local RI inhomogeneities linked to the intracellular structural intricacy. Their statistics and spatial distribution are the morphological indicators suited for comparing cells of different origins and/or to follow their transformation in pathologic situations. We use this method to compare nonadherent blood cells from primary and laboratory culture origins and to assess the internal transformation of hematopoietic stem cells by the transduction of the BCR-ABL oncogene responsible for the chronic myelogenous leukemia.
International Nuclear Information System (INIS)
Liang, L.C.; Price, J.G.; Bobeck, P.
1984-01-01
Two contrasting types of roll-front uranium deposits occur in south Texas. In the barrier-bar sands of the Eocene Jackson Group, organic matter was essential to uranium reduction, whereas in the fluvial sands of the Miocene Oakville Formation, epigenetic pyrite was the reductant. In a sample of reduced Oakville ore, a uranium phase with grains ranging in diameter from < 1 to 20μm was recognized by SEM backscattered-electron imaging and wavelength-dispersive spectrometer (WDS) elemental-dot mapping. Quantitative microprobe analyses indicated that the phase is a uranium-calcium silicate-phosphate with molar Ca/P approximately equal to 1.0, U/P equal to 2.8 +/- 0.4 (n = 27), and U/Si approaching 1.0 in samples uncontaminated with quartz, feldspar, or clay minerals. Highest uranium content is 59%. Oakville ore is typically easy to leach by in-situ methods. Jackson ore contains 2 uranium phases. Sulfur-rich organic matter contains 4.1 +/- 1.6% uranium (n = 27). Although individual grains of a possible uranium mineral within the organic matter are too small to be resolved by electron imaging, a consistent molar U/Fe (0.5 +/- 0.1) suggests a uranium-iron oxide phase. Alternatively, uranium is adsorbed by or otherwise bound to the organic matter. The second phase is a uranium-calcium silicate-phosphate that differs from the Oakville ore. Molar Ca/P equals 0.8 +/- 0.2 (n = 13), and U/P equals 4.7 +/- 0.4. Small grain size (generally less than 1 μm) prevented analysis of samples uncontaminated with quartz and pyrite. The grain with highest uranium content (43%) has U/Si equal to 0.34. Jackson ore is less favorable for in-situ leaching than Oakville ore in part because the organic-associated uranium is difficult to extract
Liquid-solid phase transition of Ge-Sb-Te alloy observed by in-situ transmission electron microscopy
International Nuclear Information System (INIS)
Berlin, Katja; Trampert, Achim
2017-01-01
Melting and crystallization dynamics of the multi-component Ge-Sb-Te alloy have been investigated by in-situ transmission electron microscopy (TEM). Starting point of the phase transition study is an ordered hexagonal Ge 1 Sb 2 Te 4 thin film on Si(111) where the crystal structure and the chemical composition are verified by scanning TEM and electron energy-loss spectroscopy, respectively. The in-situ observation of the liquid phase at 600°C including the liquid-solid and liquid-vacuum interfaces and their movements was made possible due to an encapsulation of the TEM sample. The solid-liquid interface during melting displays a broad and diffuse transition zone characterized by a vacancy induced disordered state. Although the velocities of interface movements are measured to be in the nanometer per second scale, both, for crystallization and solidification, the underlying dynamic processes are considerably different. Melting reveals linear dependence on time, whereas crystallization exhibits a non-linear time-dependency featuring a superimposed start-stop motion. Our results may provide valuable insight into the atomic mechanisms at interfaces during the liquid-solid phase transition of Ge-Sb-Te alloys. - Highlights: • In-situ TEM observation of liquid Ge-Sb-Te phase transition due to encapsulation. • During melting: Observation of non-ordered interface transition due to premelting. • During solidification: Observation of non-linear time-dependent crystallization.
Liquid-solid phase transition of Ge-Sb-Te alloy observed by in-situ transmission electron microscopy
Energy Technology Data Exchange (ETDEWEB)
Berlin, Katja, E-mail: katja.berlin@pdi-berlin.de; Trampert, Achim
2017-07-15
Melting and crystallization dynamics of the multi-component Ge-Sb-Te alloy have been investigated by in-situ transmission electron microscopy (TEM). Starting point of the phase transition study is an ordered hexagonal Ge{sub 1}Sb{sub 2}Te{sub 4} thin film on Si(111) where the crystal structure and the chemical composition are verified by scanning TEM and electron energy-loss spectroscopy, respectively. The in-situ observation of the liquid phase at 600°C including the liquid-solid and liquid-vacuum interfaces and their movements was made possible due to an encapsulation of the TEM sample. The solid-liquid interface during melting displays a broad and diffuse transition zone characterized by a vacancy induced disordered state. Although the velocities of interface movements are measured to be in the nanometer per second scale, both, for crystallization and solidification, the underlying dynamic processes are considerably different. Melting reveals linear dependence on time, whereas crystallization exhibits a non-linear time-dependency featuring a superimposed start-stop motion. Our results may provide valuable insight into the atomic mechanisms at interfaces during the liquid-solid phase transition of Ge-Sb-Te alloys. - Highlights: • In-situ TEM observation of liquid Ge-Sb-Te phase transition due to encapsulation. • During melting: Observation of non-ordered interface transition due to premelting. • During solidification: Observation of non-linear time-dependent crystallization.
Application of extraction replicas and analytical electron microscopy to precipitate phase studies
International Nuclear Information System (INIS)
Kenik, E.A.; Maziasz, P.J.
1984-01-01
Extraction replicas provide a powerful extension of AEM techniques for analysis of fine precipitates. In many cases, replicas allow more accurate analyses to be performed and, in some cases, allow unique analyses which cannot be performed in-foil. However, there are limitations to the use of extraction replicas in AEM, of which the analyst must be aware. Many can be eliminated by careful preparation. Often, combined AEM studies of precipitates in-foil and on extraction replicas provide complementary and corroborative information for the fullest analysis of precipitate phases
Picosecond phase-velocity dispersion of hypersonic phonons imaged with ultrafast electron microscopy
International Nuclear Information System (INIS)
Cremons, Daniel R.; Du, Daniel X.; Flannigan, David J.
2017-01-01
We describe the direct imaging—with four-dimensional ultrafast electron microscopy—of the emergence, evolution, dispersion, and decay of photoexcited, hypersonic coherent acoustic phonons in nanoscale germanium wedges. Coherent strain waves generated via ultrafast in situ photoexcitation were imaged propagating with initial phase velocities of up to 35 km/s across discrete micrometer-scale crystal regions. We then observe that, while each wave front travels at a constant velocity, the entire wave train evolves with a time-varying phase-velocity dispersion, displaying a single-exponential decay to the longitudinal speed of sound (5 km/s) and with a mean lifetime of 280 ps. We also find that the wave trains propagate along a single in-plane direction oriented parallel to striations introduced during specimen preparation, independent of crystallographic direction. Elastic-plate modeling indicates the dynamics arise from excitation of a single, symmetric (dilatational) guided acoustic mode. Further, by precisely determining the experiment time-zero position with a plasma-lensing method, we find that wave-front emergence occurs approximately 100 ps after femtosecond photoexcitation, which matches well with Auger recombination times in germanium. We conclude by discussing the similarities between the imaged hypersonic strain-wave dynamics and electron/hole plasma-wave dynamics in strongly photoexcited semiconductors.
Linearity of amplitude and phase in tapping-mode atomic force microscopy
International Nuclear Information System (INIS)
Salapaka, M.V.; Chen, D.J.; Cleveland, J.P.
2000-01-01
In this article tapping-mode atomic force microscope dynamics is studied. The existence of a periodic orbit at the forcing frequency is shown under unrestrictive conditions. The dynamics is further analyzed using the impact model for the tip-sample interaction and a spring-mass-damper model of the cantilever. Stability of the periodic orbit is established. Closed-form expressions for various variables important in tapping-mode imaging are obtained. The linear relationship of the amplitude and the sine of the phase of the first harmonic of the periodic orbit with respect to cantilever-sample offset is shown. The study reinforces gentleness of the tapping-mode on the sample. Experimental results are in excellent qualitative agreement with the theoretical predictions. The linear relationship of the sine of the phase and the amplitude can be used to infer sample properties. The comparison between the theory and the experiments indicates essential features that are needed in a more refined model
Picosecond phase-velocity dispersion of hypersonic phonons imaged with ultrafast electron microscopy
Cremons, Daniel R.; Du, Daniel X.; Flannigan, David J.
2017-12-01
Here, we describe the direct imaging—with four-dimensional ultrafast electron microscopy—of the emergence, evolution, dispersion, and decay of photoexcited, hypersonic coherent acoustic phonons in nanoscale germanium wedges. Coherent strain waves generated via ultrafast in situ photoexcitation were imaged propagating with initial phase velocities of up to 35 km/s across discrete micrometer-scale crystal regions. We observe that, while each wave front travels at a constant velocity, the entire wave train evolves with a time-varying phase-velocity dispersion, displaying a single-exponential decay to the longitudinal speed of sound (5 km/s) and with a mean lifetime of 280 ps. We also find that the wave trains propagate along a single in-plane direction oriented parallel to striations introduced during specimen preparation, independent of crystallographic direction. Elastic-plate modeling indicates the dynamics arise from excitation of a single, symmetric (dilatational) guided acoustic mode. Further, by precisely determining the experiment time-zero position with a plasma-lensing method, we find that wave-front emergence occurs approximately 100 ps after femtosecond photoexcitation, which matches well with Auger recombination times in germanium. We conclude by discussing the similarities between the imaged hypersonic strain-wave dynamics and electron/hole plasma-wave dynamics in strongly photoexcited semiconductors.
International Nuclear Information System (INIS)
Mejía-Uriarte, E.V.; Kolokoltsev, O.; Navarrete Montesinos, M.; Camarillo, E.; Hernández A, J.; Murrieta S, H.
2015-01-01
NaCl:Mn 2+ nanostructures in the Suzuki phase have been studied by fluorescence (emission and excitation) spectroscopy and atomic force microscopy (AFM) as a function of temperature. The “as-grown” samples give rise to two broad emission bands that peak at 508 (green emission) and 610 nm (red emission). The excitation spectrum shows peaks at 227 nm and 232 nm for emission wavelengths at 508 nm and 610 nm, respectively. When the samples are heated continuously from room temperature up to 220 °C, the green emission (associated to the excitation peak at 227 nm) disappears at a temperature close to 120 °C, whilst only the red emission remains, which is characteristic of manganese ions. AFM images on the (0 0 1) surface (freshly cleaved) show several conformations of nanostructures, such as disks of 20–50 nm in diameter. Particularly, the images also reveal nanostructures with rectangular shape of ~280×160 nm 2 and ~6 nm height; these are present only in samples with green emission associated to the Suzuki phase. Then, the evidence suggests that this topographic configuration might be related to the interaction with the first neighbors and the next neighbors, according to the configuration that has been suggested for the Suzuki phase. - Highlights: • NaCl:Mn 2+ single crystals in the Suzuki phase contain rectangular nanostructures. • Double emission of manganese ions: green (508 nm) and red (610 nm) bands. • The excitation peak at 227 nm is attributed to rectangular nanostructures. • The green emission band associated to Suzuki phase is extinguished at 120 °C
Classical and quantum contents of solvable game theory on Hilbert space
International Nuclear Information System (INIS)
Cheon, Taksu; Tsutsui, Izumi
2006-01-01
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation
Liao, Jun; Wang, Zhe; Zhang, Zibang; Bian, Zichao; Guo, Kaikai; Nambiar, Aparna; Jiang, Yutong; Jiang, Shaowei; Zhong, Jingang; Choma, Michael; Zheng, Guoan
2018-02-01
We report the development of a multichannel microscopy for whole-slide multiplane, multispectral and phase imaging. We use trinocular heads to split the beam path into 6 independent channels and employ a camera array for parallel data acquisition, achieving a maximum data throughput of approximately 1 gigapixel per second. To perform single-frame rapid autofocusing, we place 2 near-infrared light-emitting diodes (LEDs) at the back focal plane of the condenser lens to illuminate the sample from 2 different incident angles. A hot mirror is used to direct the near-infrared light to an autofocusing camera. For multiplane whole-slide imaging (WSI), we acquire 6 different focal planes of a thick specimen simultaneously. For multispectral WSI, we relay the 6 independent image planes to the same focal position and simultaneously acquire information at 6 spectral bands. For whole-slide phase imaging, we acquire images at 3 focal positions simultaneously and use the transport-of-intensity equation to recover the phase information. We also provide an open-source design to further increase the number of channels from 6 to 15. The reported platform provides a simple solution for multiplexed fluorescence imaging and multimodal WSI. Acquiring an instant focal stack without z-scanning may also enable fast 3-dimensional dynamic tracking of various biological samples. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Quantitative phase microscopy for cellular dynamics based on transport of intensity equation.
Li, Ying; Di, Jianglei; Ma, Chaojie; Zhang, Jiwei; Zhong, Jinzhan; Wang, Kaiqiang; Xi, Teli; Zhao, Jianlin
2018-01-08
We demonstrate a simple method for quantitative phase imaging of tiny transparent objects such as living cells based on the transport of intensity equation. The experiments are performed using an inverted bright field microscope upgraded with a flipping imaging module, which enables to simultaneously create two laterally separated images with unequal defocus distances. This add-on module does not include any lenses or gratings and is cost-effective and easy-to-alignment. The validity of this method is confirmed by the measurement of microlens array and human osteoblastic cells in culture, indicating its potential in the applications of dynamically measuring living cells and other transparent specimens in a quantitative, non-invasive and label-free manner.
Frames and outer frames for Hilbert C^*-modules
Arambašić, Ljiljana; Bakić, Damir
2015-01-01
The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the multiplier module $M(X)$ that has the standard frame property when applied to elements of the ambient module $X$. Given a Hilbert $\\A$-module $X$, we prove that there is a bijective correspondence of the set of all adjointable surjections from the generalize...
Four-dimensional hilbert curves for R-trees
DEFF Research Database (Denmark)
Haverkort, Herman; Walderveen, Freek van
2011-01-01
Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects...... according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments...
Measurement of vibration mode shape by using Hilbert transform
International Nuclear Information System (INIS)
Kang, Min Sig
2001-01-01
This paper concerns on modal analysis of mechanical structures by using a continuous scanning laser Doppler vibrometer. In modal analysis the Hilbert transform based approach is superior to the Fourier transform based approach because of its fine accuracy and its flexible experimental settings. In this paper the Hilbert transform based approach is extended to measure area mode shape data of a structure by simply modifying the scanning pattern ranging the entire surface of the structure. The effectiveness of this proposed method is illustrated along with results of numerical simulation for a rectangular plate
Silva, D F C; Azevedo, A M; Fernandes, P; Chu, V; Conde, J P; Aires-Barros, M R
2017-03-03
Aqueous two phase systems (ATPS) offer great potential for selective separation of a wide range of biomolecules by exploring differences in molecular solubility in each of the two immiscible phases. However, ATPS use has been limited due to the difficulty in predicting the behavior of a given biomolecule in the partition environment together with the empirical and time-consuming techniques that are used for the determination of partition and extraction parameters. In this work, a fast and novel technique based on a microfluidic platform and using fluorescence microscopy was developed to determine the partition coefficients of biomolecules in different ATPS. This method consists of using a microfluidic device with a single microchannel and three inlets. In two of the inlets, solutions containing the ATPS forming components were loaded while the third inlet was fed with the FITC tagged biomolecule of interest prepared in milli-Q water. Using fluorescence microscopy, it was possible to follow the location of the FITC-tagged biomolecule and, by simply varying the pumping rates of the solutions, to quickly test a wide variety of ATPS compositions. The ATPS system is allowed 4min for stabilization and fluorescence micrographs are used to determine the partition coefficient.The partition coefficients obtained were shown to be consistent with results from macroscale ATPS partition. This process allows for faster screening of partition coefficients using only a few microliters of material for each ATPS composition and is amenable to automation. The partitioning behavior of several biomolecules with molecular weights (MW) ranging from 5.8 to 150kDa, and isoelectric points (pI) ranging from 4.7 to 6.4 was investigated, as well as the effect of the molecular weight of the polymer ATPS component. Copyright © 2016 Elsevier B.V. All rights reserved.
MR microscopy of human skin using phased-array of microcoils at 9.4 T
Energy Technology Data Exchange (ETDEWEB)
Goebel, Katharina; Leupold, Jochen; LeVan, Pierre; Hennig, Juergen; Elverfeldt, Dominik von [Dept. of Radiology, Medical Physics, University Medical Center Freiburg (Germany); Gruschke, Oliver G. [Lab. of Simulation, University of Freiburg - IMTEK (Germany); Kern, Johannes S. [Dept. of Dermatology, University Medical Center Freiburg (Germany); Korvink, Jan G. [Lab. of Simulation, University of Freiburg - IMTEK (Germany); Freiburg Institute for Advanced Studies, University of Freiburg (Germany); Baxan, Nicoleta [Dept. of Radiology, Medical Physics, University Medical Center Freiburg (Germany); Bruker BioSpin MRI GmbH, Ettlingen (Germany)
2013-07-01
MRI of the skin as non-invasive alternative to histopathology requires dedicated approaches to overcome both the low sensitivity and low contrast of standard MR investigations applied at microscale. The geometry of the skin with layers of large lateral dimensions and a few μm thickness demands exceptionally high resolution combined with large imaging matrix size. A home-made microcoil-based MR detector in planar phased-array geometry (diameter=5.5 mm) was developed to alleviate such limitations by combining the advantages of a large field-of-view and high signal-to-noise ratio. The detector was first characterized in terms of influence on B{sub 0} homogeneity and SNR. Trials on healthy and Acne inversa diseased human skin biopsies allowed the acquisition of high resolution images (30 x 30 x 100 μm{sup 3}) in reasonable scan time. Histology was subsequently performed to validate the MRI results, demonstrating the suitability of this methodological approach for the characterization and early detection of structural skin changes.
Verheyen, G; Crabbé, E; Joris, H; Van Steirteghem, A
1998-06-01
Based on the results of animal studies, round spermatid injection (ROSI) has been introduced into the clinical practice of several in-vitro fertilization (IVF) centres. The efficiency of this procedure in terms of fertilization rates and pregnancy rates, however, remains very poor. An essential aspect which does not receive enough attention is the correct identification of this type of round cell within a heterogeneous population of testicular cells. A Nikon inverted microscope equipped with phase-contrast optics (DLL) provided a clear image which allowed reliable recognition of round spermatids in cell suspensions smeared at the glass bottom of the dish. Fluorescent in-situ hybridization confirmed the haploid status of the selected cells. However, exploration of several biopsies from patients with non-obstructive azoospermia showing no spermatozoa after extensive search did not reveal any round spermatids. This observation questions whether enough effort is spent on searching for mature spermatozoa or late spermatids. Experimental investigations should precede the introduction of ROSI into the clinical practice of any IVF centre.
International Nuclear Information System (INIS)
Skoczylas, M.; Rakowski, W.; Cherubini, R.; Gerardi, S.
2011-01-01
Irradiation of individual cultured mammalian cells with a pre-selected number of ions down to one ion per single cell is a useful experimental approach to investigating the low-dose ionising radiation exposure effects and thus contributing to a more realistic human cancer risk assessment. One of the crucial tasks of all the microbeam apparatuses is the visualisation, recognition and positioning of every individual cell of the cell culture to be irradiated. Before irradiations, mammalian cells (specifically, Chinese hamster V79 cells) are seeded and grown as a monolayer on a mylar surface used as the bottom of a specially designed holder. Manual recognition of unstained cells in a bright-field microscope is a time-consuming procedure; therefore, a parallel algorithm has been conceived and developed in order to speed up this irradiation protocol step. Many technical problems have been faced to overcome the complexity of the images to be analysed: cell discrimination in an inhomogeneous background, among many disturbing bodies mainly due to the mylar surface roughness and culture medium bodies; cell shapes, depending on how they attach to the surface, which phase of the cell cycle they are in and on cell density. Preliminary results of the recognition and classification based on a method of wavelet kernels for the support vector machine classifier will be presented. (authors)
International Nuclear Information System (INIS)
Lozano, Gabriel; Barten, Tommy; Grzela, Grzegorz; Rivas, Jaime Gómez
2014-01-01
We demonstrate that an ordered array of aluminum nanopyramids, behaving as a phased array of optical antennae, strongly modifies light absorption in thin layers of dye molecules. Photoluminescence measurements as a function of the illumination angle are performed using a time-reversed Fourier microscope. This technique enables a variable-angle plane-wave illumination of nanostructures in a microscope-based setup. Our measurements reveal an enhancement of the light conversion in certain directions of illumination, which indicate the efficient diffractive coupling between the free space radiation and the surface plasmons. Numerical simulations confirm that surface modes supported by the periodic array enhance the intensity of the pump field in the space between particles, where the dye molecules are located, yielding a directional plasmonic-mediated enhancement of the optical absorption. This combined experimental and numerical characterization of the angular dependence of light absorption in nanostructures can be beneficial for the design and optimization of devices in which the harvesting of light plays a major role. (paper)
Wang, Kesheng; Cheng, Jia; Yao, Shiji; Lu, Yijia; Ji, Linhong; Xu, Dengfeng
2016-12-01
Electrostatic force measurement at the micro/nano scale is of great significance in science and engineering. In this paper, a reasonable way of applying voltage is put forward by taking an electrostatic chuck in a real integrated circuit manufacturing process as a sample, applying voltage in the probe and the sample electrode, respectively, and comparing the measurement effect of the probe oscillation phase difference by amplitude modulation atomic force microscopy. Based on the phase difference obtained from the experiment, the quantitative dependence of the absolute magnitude of the electrostatic force on the tip-sample distance and applied voltage is established by means of theoretical analysis and numerical simulation. The results show that the varying characteristics of the electrostatic force with the distance and voltage at the micro/nano scale are similar to those at the macroscopic scale. Electrostatic force gradually decays with increasing distance. Electrostatic force is basically proportional to the square of applied voltage. Meanwhile, the applicable conditions of the above laws are discussed. In addition, a comparison of the results in this paper with the results of the energy dissipation method shows the two are consistent in general. The error decreases with increasing distance, and the effect of voltage on the error is small.
International Nuclear Information System (INIS)
Waitz, T.
1999-06-01
In CoFe crystals containing 0.85, 1.5, 5.75 and 6.0at.% Fe the thermally induced martensitic phase transformations between the close packed lattices face centered cubic (fcc), double hexagonal close packed (dhcp) and hexagonal close packed (hcp) were studied. Transmission electron microscopy methods were applied including in-situ experiments; both high-resolution transmission electron microscopy (HRTEM) images and lattice fringe images were used to analyze the transformations at an atomic scale. Based on the results of both the transformations in the bulk and the in-situ transformations it is concluded that the phase transitions occur by the formation of lamellae on the close packed habit planes. The lamellae have a minimum thickness of 10 to 15 close packed planes; therefore transformation models that are based on random overlap of stacking faults can be excluded. The glissile transformation fronts of the lamellae contain transformation dislocations (partials) that are correlated on an atomic scale. In the HRTEM images partials that are only about 0.2 nm apart were resolved and analyzed in detail by circuits that are similar to Burgers circuits. Two attracting partials on adjacent close packed planes are the structural units of the transformation fronts; they are dipoles and paired partials (with a total Burgers vector of a single partial) in the case of the transformations hcp dhcp and fcc dhcp, respectively. Different arrangements of the partials at the transformation fronts lead to two different modes A and B of the phase transition. These two modes seem to be competitive processes that can be favored by different parameters of the material (as chemical composition and microstructure). Partials of mode A transformations have the same Burgers vectors; therefore the partials repel each other causing long range internal stresses and large transformation shear strains that can lead to a surface relief. Whereas, partials of mode B transformations have different
Lectures on Hilbert modular varieties and modular forms
Goren, Eyal Z
2001-01-01
This book is devoted to certain aspects of the theory of p-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of p-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelian varieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of p-adic Hilbert modular forms and the geometry of moduli spaces of abelian varieties are related. This relation is used to study q-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-exper...
Diagonalization of Bounded Linear Operators on Separable Quaternionic Hilbert Space
International Nuclear Information System (INIS)
Feng Youling; Cao, Yang; Wang Haijun
2012-01-01
By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schroedinger equation in quaternionic quantum mechanics.
Generalized noncommutative Hardy and Hardy-Hilbert type inequalities
DEFF Research Database (Denmark)
Hansen, Frank; Krulic, Kristina; Pecaric, Josip
2010-01-01
We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it ...
On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space
Directory of Open Access Journals (Sweden)
Hamdy M. Ahmed
2009-01-01
Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.
Ad Hoc Physical Hilbert Spaces in Quantum Mechanics
Czech Academy of Sciences Publication Activity Database
Fernandez, F. M.; Garcia, J.; Semorádová, Iveta; Znojil, Miloslav
2015-01-01
Roč. 54, č. 12 (2015), s. 4187-4203 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum mechanics * physical Hilbert spaces * ad hoc inner product * singular potentials regularized * low lying energies Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
Bearing fault detection utilizing group delay and the Hilbert-Huang transform
International Nuclear Information System (INIS)
Jin, Shuai; Lee, Sang-Kwon
2017-01-01
Vibration signals measured from a mechanical system are useful to detect system faults. Signal processing has been used to extract fault information in bearing systems. However, a wide vibration signal frequency band often affects the ability to obtain the effective fault features. In addition, a few oscillation components are not useful at the entire frequency band in a vibration signal. By contrast, useful fatigue information can be embedded in the noise oscillation components. Thus, a method to estimate which frequency band contains fault information utilizing group delay was proposed in this paper. Group delay as a measure of phase distortion can indicate the phase structure relationship in the frequency domain between original (with noise) and denoising signals. We used the empirical mode decomposition of a Hilbert-Huang transform to sift the useful intrinsic mode functions based on the results of group delay after determining the valuable frequency band. Finally, envelope analysis and the energy distribution after the Hilbert transform were used to complete the fault diagnosis. The practical bearing fault data, which were divided into inner and outer race faults, were used to verify the efficiency and quality of the proposed method
Discrete Hilbert transformation and its application to estimate the wind speed in Hong Kong
Energy Technology Data Exchange (ETDEWEB)
Zhu, Zuojin [Department of Thermal Science and Energy Engineering, Institute of Engineering Science, University of Science and Technology of China, Hefei, Anhui (China); Yang, Hongxing [Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong (Hong Kong)
2002-01-01
Discrete Hilbert Transform (DHT) has been applied to estimate the wind speed with the sample data sequence selected from the data record observed by the observatory in Hong Kong in June 1989, during which the data pertain to deep valleys and sharp crests due to manifold weather conditions in this region. To confirm the performance of the discrete Hilbert transformer, two harmonic input sequences were used to inspect the output signals, whether good agreement with the theoretical results is obtained. It was found that the energy spectrum and the outputs for the two different harmonic discrete waves are certainly correct. After the inspection of the DHT filter, the sample data for wind speed in Hong Kong were used for wind speed forecasting. For zero mean input sequence, the variance of the output is the same as that of the input signals, and so is the energy spectrum. The DHT of an individual input sample can really reflect the local variation performance, since it is the convolution with the reciprocal of time and the input data sequence, but there exists phase shift. For harmonic signals, the output signal holds a 90 phase delay.
Bearing fault detection utilizing group delay and the Hilbert-Huang transform
Energy Technology Data Exchange (ETDEWEB)
Jin, Shuai; Lee, Sang-Kwon [Inha University, Incheon (Korea, Republic of)
2017-03-15
Vibration signals measured from a mechanical system are useful to detect system faults. Signal processing has been used to extract fault information in bearing systems. However, a wide vibration signal frequency band often affects the ability to obtain the effective fault features. In addition, a few oscillation components are not useful at the entire frequency band in a vibration signal. By contrast, useful fatigue information can be embedded in the noise oscillation components. Thus, a method to estimate which frequency band contains fault information utilizing group delay was proposed in this paper. Group delay as a measure of phase distortion can indicate the phase structure relationship in the frequency domain between original (with noise) and denoising signals. We used the empirical mode decomposition of a Hilbert-Huang transform to sift the useful intrinsic mode functions based on the results of group delay after determining the valuable frequency band. Finally, envelope analysis and the energy distribution after the Hilbert transform were used to complete the fault diagnosis. The practical bearing fault data, which were divided into inner and outer race faults, were used to verify the efficiency and quality of the proposed method.
The method of moments and nested Hilbert spaces in quantum mechanics
International Nuclear Information System (INIS)
Adeniyi Bangudu, E.
1980-08-01
It is shown how the structures of a nested Hilbert space Hsub(I), associated with a given Hilbert space Hsub(O), may be used to simplify our understanding of the effects of parameters, whose values have to be chosen rather than determined variationally, in the method of moments. The result, as applied to non-relativistic quartic oscillator and helium atom, is to associate the parameters with sequences of Hilbert spaces, while the error of the method of moments relative to the variational method corresponds to a nesting operator of the nested Hilbert space. Difficulties hindering similar interpretations in terms of rigged Hilbert space structures are highlighted. (author)
Tychinsky, Vladimir P.; Mulyukin, Andrey L.; Lisovskii, Vitalii V.; Nikolaev, Yury A.; Kretushev, Aleksander V.; Vyshenskaya, Tatyana V.; Suzina, Nataliya E.; Duda, Vitalii I.; El-Registan, Galina I.
One of the challenging tasks in monitoring studies is to estimate heterogeneity of microbial populations by the physiological state and potential viability of individual cells, especially with regard of their ability to withstand various environmental assaults. Previously, we described some approaches based on electron microscopy methods to discriminate vegetative, dormant, and dead cells in both aged microbial cultures and environmental samples, including permafrost. We propose to extend the arsenal of microscopy methods for monitoring studies by a new non-invasive and informative method - dynamic phase microscopy (DPM). The substantial advantage of DPM is that it gives quantitative (digitized) data of undestroyed (living) microscopic objects, exemplified in our work by Bacillus licheniformis spores. Using DPM made it possible to record interference images of objects (spores) and to produce picture of their "phase thickness" (PT) that is the optical path difference in nm. Thus, it was demonstrated the remarkable difference in the PT of spores at different physiological states: dormant, germinating, and heat-killed spores had PT values of 80, 40-50, and 20 nm, respectively. The other found criterion to distinguish between spores was the PT fluctuations. In contrast to dormant and killed spores, the PT of germinating spores oscillated with amplitude of up to 7 nm, with typical frequencies of 1.3 and 3.4 Hz. A combination of the recorded PT values and PT fluctuations gave a key to detect viable and dead cells. Under the conditions that did not support germination (the lack of nutrients), we were able to follow the response of a single dormant spore and a spore population to heating from 25 °C to 70 °C. Thus, a very small temperature change (from 40 °C to 42 °C) under conditions non-favorable for germination, caused a drastic decrease in the spores' PT; the second drop in the PT values was observed during heating from 60 °C to 70 °C. These changes were
International Nuclear Information System (INIS)
Oikonomidis, Ioannis Vogiatzis; Cremona, Tiziana P; Schittny, Johannes C; Lovric, Goran; Arcadu, Filippo; Stampanoni, Marco
2017-01-01
The acinus represents the functional unit of the mammalian lung. It is defined as the small tree of gas-exchanging airways, which is fed by the most distal purely conducting airway. Different hypotheses exist on how the fine structure of the acinus changes during ventilation and development. Since in classical 2-dimensional (2D) sections of the lung the borders of the acini are not detectable, every study of acini requires 3-dimensional (3D) datasets. As a basis for further studies of pulmonary acini we imaged rodent lungs as close to life as possible using phase contrast synchrotron radiation-based X-ray tomographic microscopy (SRXTM), and developed a protocol for the segmentation of the alveolar septa. The method is based on a combined multilevel filtering approach. Seeds are automatically defined for separate regions of tissue and airspace during each 2D filtering level and then given as input to a 3D random walk segmentation. Thus, the different types of artifacts present in the images are treated separately, taking into account the sample’s structural complexity. The proposed procedure yields high-quality 3D segmentations of acinar microstructure that can be used for a reliable morphological analysis. (paper)
Wang, Xiaozhen; Lu, Tianjian; Yu, Xin; Jin, Jian-Ming; Goddard, Lynford L
2017-07-04
We studied the nanoscale thermal expansion of a suspended resistor both theoretically and experimentally and obtained consistent results. In the theoretical analysis, we used a three-dimensional coupled electrical-thermal-mechanical simulation and obtained the temperature and displacement field of the suspended resistor under a direct current (DC) input voltage. In the experiment, we recorded a sequence of images of the axial thermal expansion of the central bridge region of the suspended resistor at a rate of 1.8 frames/s by using epi-illumination diffraction phase microscopy (epi-DPM). This method accurately measured nanometer level relative height changes of the resistor in a temporally and spatially resolved manner. Upon application of a 2 V step in voltage, the resistor exhibited a steady-state increase in resistance of 1.14 Ω and in relative height of 3.5 nm, which agreed reasonably well with the predicted values of 1.08 Ω and 4.4 nm, respectively.
Energy Technology Data Exchange (ETDEWEB)
Hawley, Marilyn Emily [Los Alamos National Laboratory; Kim, Yu S [Los Alamos National Laboratory; Hjelm, Rex P [Los Alamos National Laboratory
2010-01-01
Scanning force microscopy (SFM) phase imaging provides a powerful method for directly studying and comparing phase segregation in fuel cell membrane materials due to different preparation and under different temperature and hwnidity exposures. In this work, we explored two parameters that can influence phase segregation: the properties of the solvents used in casting membrane films and how these solvents alter phase segregation after exposure to boiling water as a function of time. SFM was used under ambient conditions to image phase segregation in Nafion samples prepared using five different solvents. Samples were then subjected to water vapor maintained at 100C for periods ranging from 30 minutes to three hours and re-imaged using the same phase imaging conditions. SFM shows what appears to be an increase in phase segregation as a function of solvent polarity that changes as a function of water exposure.
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S., E-mail: judy.kim@materials.ox.ac.uk [Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 (United States); Chemical Engineering and Materials Science/Molecular and Cellular Biology, University of California-Davis, 1 Shields Avenue, Davis, CA 95616 (United States); LaGrange, T.; Reed, B.W. [Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 (United States); Knepper, R.; Weihs, T.P. [Department of Materials Science and Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218 (United States); Browning, N.D. [Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 (United States); Chemical Engineering and Materials Science/Molecular and Cellular Biology, University of California-Davis, 1 Shields Avenue, Davis, CA 95616 (United States); Campbell, G.H. [Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 (United States)
2011-05-15
Highlights: > Fast phase transformations are examined in Al/Ni reactive nanolaminates. > Results visible only by dynamic transmission electron microscopy at ns resolution. > NiAl forms under 15 ns after reaction front in all three stoichiometries studied. > DTEM imaging reveals a transient cellular morphology in nonequiatomic films. - Abstract: Phase transformations and transient morphologies are examined as exothermic formation reactions self-propagate across Al/Ni nanolaminate films. The rapid evolution of these phases and sub-micrometer morphological features requires nanoscale temporal and spatial resolution that is not available with traditional in situ electron microscopy. This work uses dynamic transmission electron microscopy to identify intermetallic products and phase morphologies, as exothermic formation reactions self-propagate in nanolaminate films grown with 3:2, 2:3 and 1:1 Al/Ni atomic ratios. Single-shot diffraction patterns with 15 ns temporal resolution reveal that the NiAl intermetallic forms within {approx}15 ns of the reaction front's arrival in all three types of films and is the only intermetallic phase to form, as the reactions self-propagate and quench very rapidly. Time-resolved imaging reveals a transient cellular morphology in the Al-rich and Ni-rich foils, but not in the equiatomic films. The cellular features in the Al-rich and Ni-rich films are attributed to a cooling trajectory through a two-phase field of liquid + NiAl.
T^{\\sigma}_{\\rho}(G) Theories and Their Hilbert Series
Cremonesi, Stefano; Mekareeya, Noppadol; Zaffaroni, Alberto
2015-01-01
We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4 superconformal gauge theories T^{\\sigma}_{\\rho}(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, \\sigma is a partition of G and \\rho a partition of the dual group G^\\vee. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G=SU(N) but some interesting results are also given for orthogonal and symplectic groups.
The Hilbert Series of the One Instanton Moduli Space
Benvenuti, Sergio; Mekareeya, Noppadol; 10.1007
2010-01-01
The moduli space of k G-instantons on R^4 for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.
The Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskii, I.M.
1984-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. We have found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. We show that the series for the amplitudes with the first two iteration subtracted converges rapidly. Our final results are in excellent agreement with exact results obtained by a direct matrix technique. (orig.)
Hilbert-Schmidt method for nucleon-deuteron scattering
International Nuclear Information System (INIS)
Moeller, K.; Narodetskij, I.M.
1983-01-01
The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. It is found that for each partial amplitude a series of s-channel resonances diverges because of the logarithmic singularities which reflect the t-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. It is shown that the series for the amplitudes with first two iterations subtracted converges rapidly. Final results are in excellent agreement with exact results obtained by a direct matrix technique
THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.
Fernández-Ruiz, María R; Wang, Lixian; Carballar, Alejandro; Burla, Maurizio; Azaña, José; LaRochelle, Sophie
2015-01-01
THz-bandwidth photonic Hilbert transformers (PHTs) are implemented for the first time, to the best of our knowledge, based on fiber Bragg grating (FBG) technology. To increase the practical bandwidth limitation of FBGs (typically <200 GHz), a superstructure based on two superimposed linearly-chirped FBGs operating in transmission has been employed. The use of a transmission FBG involves first a conversion of the non-minimum phase response of the PHT into a minimum-phase response by adding an anticipated instantaneous component to the desired system temporal impulse response. Using this methodology, a 3-THz-bandwidth integer PHT and a fractional (order 0.81) PHT are designed, fabricated, and successfully characterized.
Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system
International Nuclear Information System (INIS)
De Gandt, Francois
2006-01-01
In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?
Some means inequalities for positive operators in Hilbert spaces
Directory of Open Access Journals (Sweden)
Jin Liang
2017-01-01
Full Text Available Abstract In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities.
6th Hilbert's problem and S.Lie's infinite groups
International Nuclear Information System (INIS)
Konopleva, N.P.
1999-01-01
The progress in Hilbert's sixth problem solving is demonstrated. That became possible thanks to the gauge field theory in physics and to the geometrical treatment of the gauge fields. It is shown that the fibre bundle spaces geometry is the best basis for solution of the problem being discussed. This talk has been reported at the International Seminar '100 Years after Sophus Lie' (Leipzig, Germany)
Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
Yukawa, Masahiro
2014-01-01
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii) high- and low- frequency components etc. In this case, the use of multiple RKHSs permits a compact representation of multicomponent functions. The proposed algorithm is where t...
How were the Hilbert-Einstein equations discovered?
International Nuclear Information System (INIS)
Logunov, Anatolii A; Mestvirishvili, Mirian A; Petrov, Vladimir A
2004-01-01
The ways in which Albert Einstein and David Hilbert independently arrived at the gravitational field equations are traced. A critical analysis is presented of a number of papers in which the history of the derivation of the equations is viewed in a way that 'radically differs from the standard point of view'. The conclusions of these papers are shown to be totally unfounded. (from the history of physics)
Von Neuman representations on self-dual Hilbert W* moduli
International Nuclear Information System (INIS)
Frank, M.
1987-01-01
Von Neumann algebras M of bounded operators on self-dual Hilbert W* moduli H possessing a cyclic-separating element x-bar in H are considered. The close relation of them to certain real subspaces of H is established. Under the supposition that the underlying W*-algebra is commutative, a Tomita-Takesaki type theorem is stated. The natural cone in H arising from the pair (M, x-bar) is investigated and its properties are obtained
The Einstein-Hilbert gravitation with minimum length
Louzada, H. L. C.
2018-05-01
We study the Einstein-Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D=4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.
Marquet, Pierre
2014-09-22
Quantitative phase microscopy (QPM) has recently emerged as a new powerful quantitative imaging technique well suited to noninvasively explore a transparent specimen with a nanometric axial sensitivity. In this review, we expose the recent developments of quantitative phase-digital holographic microscopy (QP-DHM). Quantitative phase-digital holographic microscopy (QP-DHM) represents an important and efficient quantitative phase method to explore cell structure and dynamics. In a second part, the most relevant QPM applications in the field of cell biology are summarized. A particular emphasis is placed on the original biological information, which can be derived from the quantitative phase signal. In a third part, recent applications obtained, with QP-DHM in the field of cellular neuroscience, namely the possibility to optically resolve neuronal network activity and spine dynamics, are presented. Furthermore, potential applications of QPM related to psychiatry through the identification of new and original cell biomarkers that, when combined with a range of other biomarkers, could significantly contribute to the determination of high risk developmental trajectories for psychiatric disorders, are discussed.
Passeri, D; Dong, C; Angeloni, L; Pantanella, F; Natalizi, T; Berlutti, F; Marianecci, C; Ciccarello, F; Rossi, M
2014-01-01
The need for accurate measurement of the thickness of soft thin films is continuously encouraging the development of techniques suitable for this purpose. We propose a method through which the thickness of the film is deduced from the quantitative measurement of the contrast in the phase images of the sample surface acquired by magnetic force microscopy, provided that the film is deposited on a periodically patterned magnetic substrate. The technique is demonstrated by means of magnetic substrates obtained from standard floppy disks. Colonies of Staphylococcus aureus adherent to such substrates were used to obtain soft layers with limited lateral (a few microns) and vertical (hundreds of nanometers) size. The technique is described and its specific merits, limitations and potentialities in terms of accuracy and measurable thickness range are discussed. These parameters depend on the characteristics of the sensing tip/cantilever as well as of the substrates, the latter in terms of spatial period and homogeneity of the magnetic domains. In particular, with the substrates used in this work we evaluated an uncertainty of about 10%, a limit of detection of 50-100 nm and an upper detection limit (maximum measurable thickness) of 1 μm, all obtained with standard lift height values (50-100 nm). Nonetheless, these parameters can be easily optimized by selecting/realizing substrates with suitable spacing and homogeneity of the magnetic domains. For example, the upper detection limit can be increased up to 25-50 μm while the limit of detection can be reduced to a few tens of nanometers or a few nanometers. © 2013 Elsevier B.V. All rights reserved.
Patwary, Nurmohammed; Doblas, Ana; King, Sharon V.; Preza, Chrysanthe
2014-03-01
Imaging thick biological samples introduces spherical aberration (SA) due to refractive index (RI) mismatch between specimen and imaging lens immersion medium. SA increases with the increase of either depth or RI mismatch. Therefore, it is difficult to find a static compensator for SA1. Different wavefront coding methods2,3 have been studied to find an optimal way of static wavefront correction to reduce depth-induced SA. Inspired by a recent design of a radially symmetric squared cubic (SQUBIC) phase mask that was tested for scanning confocal microscopy1 we have modified the pupil using the SQUBIC mask to engineer the point spread function (PSF) of a wide field fluorescence microscope. In this study, simulated images of a thick test object were generated using a wavefront encoded engineered PSF (WFEPSF) and were restored using space-invariant (SI) and depth-variant (DV) expectation maximization (EM) algorithms implemented in the COSMOS software4. Quantitative comparisons between restorations obtained with both the conventional and WFE PSFs are presented. Simulations show that, in the presence of SA, the use of the SIEM algorithm and a single SQUBIC encoded WFE-PSF can yield adequate image restoration. In addition, in the presence of a large amount of SA, it is possible to get adequate results using the DVEM with fewer DV-PSFs than would typically be required for processing images acquired with a clear circular aperture (CCA) PSF. This result implies that modification of a widefield system with the SQUBIC mask renders the system less sensitive to depth-induced SA and suitable for imaging samples at larger optical depths.
Energy Technology Data Exchange (ETDEWEB)
Kohashi, Teruo, E-mail: teruo.kohashi.fc@hitachi.com; Motai, Kumi [Central Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395 (Japan); Nishiuchi, Takeshi; Hirosawa, Satoshi [Magnetic Materials Research Laboratory, Hitachi Metals Ltd., Osaka 618-0013 (Japan)
2014-06-09
The magnetism in the grain-boundary phase of a NdFeB sintered magnet was measured by spin-polarized scanning electron microscopy (spin SEM). A sample magnet was fractured in the ultra-high-vacuum chamber to avoid oxidation, and its magnetizations in the exposed grain-boundary phase on the fracture surface were evaluated through the spin polarization of secondary electrons. Spin-SEM images were taken as the fracture surface was milled gradually by argon ions, and the magnetization in the grain-boundary phase was quantitatively obtained separately from that of the Nd{sub 2}Fe{sub 14}B phase. The obtained magnetization shows that the grain-boundary phase of this magnet has substantial magnetization, which was confirmed to be ferromagnetic.
Moretti, Valter; Oppio, Marco
As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the
Saboo, Sugandha; Taylor, Lynne S
2017-08-30
The aim of this study was to evaluate the utility of confocal fluorescence microscopy (CFM) to study the water-induced phase separation of miconazole-poly (vinylpyrrolidone-co-vinyl acetate) (mico-PVPVA) amorphous solid dispersions (ASDs), induced during preparation, upon storage at high relative humidity (RH) and during dissolution. Different fluorescent dyes were added to drug-polymer films and the location of the dyes was evaluated using CFM. Orthogonal techniques, in particular atomic force microscopy (AFM) coupled with nanoscale infrared spectroscopy (AFM-nanoIR), were used to provide additional analysis of the drug-polymer blends. The initial miscibility of mico-PVPVA ASDs prepared under low humidity conditions was confirmed by AFM-nanoIR. CFM enabled rapid identification of drug-rich and polymer-rich phases in phase separated films prepared under high humidity conditions. The identity of drug- and polymer-rich domains was confirmed using AFM-nanoIR imaging and localized IR spectroscopy, together with Lorentz contact resonance (LCR) measurements. The CFM technique was then utilized successfully to further investigate phase separation in mico-PVPVA films exposed to high RH storage and to visualize phase separation dynamics following film immersion in buffer. CFM is thus a promising new approach to study the phase behavior of ASDs, utilizing drug and polymer specific dyes to visualize the evolution of heterogeneity in films exposed to water. Copyright © 2017 Elsevier B.V. All rights reserved.
Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.
Cheng, Rui; Chrostowski, Lukas
2018-03-01
Multichannel photonic Hilbert transformers (MPHTs) are reported. The devices are based on single compact spiral integrated Bragg gratings on silicon with coupling coefficients precisely modulated by the phase of each grating period. MPHTs with up to nine wavelength channels and a single-channel bandwidth of up to ∼625 GHz are achieved. The potential of the devices for multichannel single-sideband signal generation is suggested. The work offers a new possibility of utilizing wavelength as an extra degree of freedom in designing radio-frequency photonic signal processors. Such multichannel processors are expected to possess improved capacities and a potential to greatly benefit current widespread wavelength division multiplexed systems.
Trusiak, Maciej; Patorski, Krzysztof; Wielgus, Maciej
2012-10-08
Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.
Czech Academy of Sciences Publication Activity Database
Sun, J.L.; Huang, Y.B.; Cheng, L.; Yao, X.; Lai, Y.J.; Jirsa, Miloš
2009-01-01
Roč. 9, č. 2 (2009), 898-902 ISSN 1528-7483 R&D Projects: GA ČR GA202/08/0722 Institutional research plan: CEZ:AV0Z10100520 Keywords : high-temperature optical microscopy * growth and orientation of Sm-Ba-Cu-O phases * Sm-211 whisker substrate Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 4.162, year: 2009
Real analysis measure theory, integration, and Hilbert spaces
Stein, Elias M
2005-01-01
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
A Proof of the Hilbert-Smith Conjecture
McAuley, Louis F.
2001-01-01
The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'', Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to the orbit map of an effective action of a p-adic group on compact connected n-manifolds with the aid of some new...
On convergence of nuclear and correlation operators in Hilbert space
International Nuclear Information System (INIS)
Kubrusly, C.S.
1985-01-01
The convergence of sequences of nuclear operators on a separable Hilbert space is studied. Emphasis is given to trace-norm convergence, which is a basic property in stochastic systems theory. Obviously trace-norm convergence implies uniform convergence. The central theme of the paper focus the opposite way, by investigating when convergence in a weaker topology turns out to imply convergence in a stronger topology. The analysis carried out here is exhaustive in the following sense. All possible implications within a selected set of asymptotic properties for sequences of nuclear operators are established. The special case of correlation operators is also considered in detail. (Author) [pt
Perturbation for Frames for a Subspace of a Hilbert Space
DEFF Research Database (Denmark)
Christensen, Ole; deFlicht, C.; Lennard, C.
1997-01-01
We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...... similarresult for frames in the case where the gap between the subspaces$\\overline{span} \\{f_i \\}$ and $\\overline{span} \\{ g_i \\}$ is small enough. We give a geometric interpretation of the result....
Explicit signal to noise ratio in reproducing kernel Hilbert spaces
DEFF Research Database (Denmark)
Gomez-Chova, Luis; Nielsen, Allan Aasbjerg; Camps-Valls, Gustavo
2011-01-01
This paper introduces a nonlinear feature extraction method based on kernels for remote sensing data analysis. The proposed approach is based on the minimum noise fraction (MNF) transform, which maximizes the signal variance while also minimizing the estimated noise variance. We here propose...... an alternative kernel MNF (KMNF) in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This enables KMNF dealing with non-linear relations between the noise and the signal features jointly. Results show that the proposed KMNF provides the most noise-free features when confronted...
International Nuclear Information System (INIS)
Alikin, D. O.; Turygin, A. P.; Shur, V. Ya.; Walker, J.; Rojac, T.; Shvartsman, V. V.; Kholkin, A. L.
2015-01-01
BiFeO 3 (BFO) is a classical multiferroic material with both ferroelectric and magnetic ordering at room temperature. Doping of this material with rare-earth oxides was found to be an efficient way to enhance the otherwise low piezoelectric response of unmodified BFO ceramics. In this work, we studied two types of bulk Sm-modified BFO ceramics with compositions close to the morphotropic phase boundary (MPB) prepared by different solid-state processing methods. In both samples, coexistence of polar R3c and antipolar P bam phases was detected by conventional X-ray diffraction (XRD); the non-polar P nma or P bnm phase also has potential to be present due to the compositional proximity to the polar-to-non-polar phase boundary. Two approaches to separate the phases based on the piezoresponse force microscopy measurements have been proposed. The obtained fractions of the polar and non-polar/anti-polar phases were close to those determined by quantitative XRD analysis. The results thus reveal a useful method for quantitative determination of the phase composition in multi-phase ceramic systems, including the technologically most important MPB systems
Applications of Hilbert Spectral Analysis for Speech and Sound Signals
Huang, Norden E.
2003-01-01
A new method for analyzing nonlinear and nonstationary data has been developed, and the natural applications are to speech and sound signals. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time, which give sharp identifications of imbedded structures. This method invention can be used to process all acoustic signals. Specifically, it can process the speech signals for Speech synthesis, Speaker identification and verification, Speech recognition, and Sound signal enhancement and filtering. Additionally, as the acoustical signals from machinery are essentially the way the machines are talking to us. Therefore, the acoustical signals, from the machines, either from sound through air or vibration on the machines, can tell us the operating conditions of the machines. Thus, we can use the acoustic signal to diagnosis the problems of machines.
Multisymplectic unified formalism for Einstein-Hilbert gravity
Gaset, Jordi; Román-Roy, Narciso
2018-03-01
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.
International Roughness Index (IRI) measurement using Hilbert-Huang transform
Zhang, Wenjin; Wang, Ming L.
2018-03-01
International Roughness Index (IRI) is an important metric to measure condition of roadways. This index is usually used to justify the maintenance priority and scheduling for roadways. Various inspection methods and algorithms are used to assess this index through the use of road profiles. This study proposes to calculate IRI values using Hilbert-Huang Transform (HHT) algorithm. In particular, road profile data is provided using surface radar attached to a vehicle driving at highway speed. Hilbert-Huang transform (HHT) is used in this study because of its superior properties for nonstationary and nonlinear data. Empirical mode decomposition (EMD) processes the raw data into a set of intrinsic mode functions (IMFs), representing various dominating frequencies. These various frequencies represent noises from the body of the vehicle, sensor location, and the excitation induced by nature frequency of the vehicle, etc. IRI calculation can be achieved by eliminating noises that are not associated with the road profile including vehicle inertia effect. The resulting IRI values are compared favorably to the field IRI values, where the filtered IMFs captures the most characteristics of road profile while eliminating noises from the vehicle and the vehicle inertia effect. Therefore, HHT is an effect method for road profile analysis and for IRI measurement. Furthermore, the application of HHT method has the potential to eliminate the use of accelerometers attached to the vehicle as part of the displacement measurement used to offset the inertia effect.
Hilbert-Schmidt quantum coherence in multi-qudit systems
Maziero, Jonas
2017-11-01
Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.
Aveiro method in reproducing kernel Hilbert spaces under complete dictionary
Mai, Weixiong; Qian, Tao
2017-12-01
Aveiro Method is a sparse representation method in reproducing kernel Hilbert spaces (RKHS) that gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying RKHS. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro Method. To avoid those difficulties we propose an anew Aveiro Method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA) involving completion of a given dictionary. The new method is called Aveiro Method Under Complete Dictionary (AMUCD). The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition, bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro Method and the greedy algorithm.
Theory and experiments on Peano and Hilbert curve RFID tags
McVay, John; Hoorfar, Ahmad; Engheta, Nader
2006-05-01
Recently, there has been considerable interest in the area of Radio Frequency Identification (RFID) and Radio Frequency Tagging (RFTAG). This emerging area of interest can be applied for inventory control (commercial) as well as friend/foe identification (military) to name but a few. The current technology can be broken down into two main groups, namely passive and active RFID tags. Utilization of Space-Filling Curve (SFC) geometries, such as the Peano and Hilbert curves, has been recently investigated for use in completely passive RFID applications [1, 2]. In this work, we give an overview of our work on the space-filling curves and the potential for utilizing the electrically small, resonant characteristics of these curves for use in RFID technologies with an emphasis on the challenging issues involved when attempting to tag conductive objects. In particular, we investigate the possible use of these tags in conjunction with high impedance ground-planes made of Hilbert or Peano curve inclusions [3, 4] to develop electrically small RFID tags that may also radiate efficiently, within close proximity of large conductive objects [5].
DEFF Research Database (Denmark)
Fidorra, Matthias; Garcia, Alejandra; Ipsen, John Hjort
2009-01-01
We report a novel analytical procedure to measure the surface areas of coexisting lipid domains in giant unilamellar vesicles (GUVs) based on image processing of 3D fluorescence microscopy data. The procedure involves the segmentation of lipid domains from fluorescent image stacks...
Energy Technology Data Exchange (ETDEWEB)
Bai, Song; Ying, Puyou [Key Laboratory of Nonferrous Metal Materials Science and Engineering, Ministry of Education, Central South University, Changsha 410083 (China); School of Material Science and Engineering, Central South University, Changsha 410083 (China); Liu, Zhiyi, E-mail: liuzhiyi@csu.edu.cn [Key Laboratory of Nonferrous Metal Materials Science and Engineering, Ministry of Education, Central South University, Changsha 410083 (China); School of Material Science and Engineering, Central South University, Changsha 410083 (China); Wang, Jian; Li, Junlin [Key Laboratory of Nonferrous Metal Materials Science and Engineering, Ministry of Education, Central South University, Changsha 410083 (China); School of Material Science and Engineering, Central South University, Changsha 410083 (China)
2017-02-27
The close association between the Ω precipitation and various Ag additions is systematically investigated by quantitative transmission electron microscopy and atom probe tomography analysis. Our results suggest that the precipitation of Ω phase is strongly dependent on Ag variations. Increasing the bulk Ag content favors a denser Ω precipitation and hence leads to a greater age-hardening response of Al-Cu-Mg-Ag alloy. This phenomenon, as proposed by proximity histograms, is directly related to the greater abundance of Ag solutes within Ω precursors. This feature lowers its nucleation barrier and increases the nucleation rate of Ω phase, finally contributes to the enhanced Ω precipitation. Also, it is noted that increasing Ag remarkably restricts the precipitation of θ' phase.
Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators
DEFF Research Database (Denmark)
Kaad, Jens
2017-01-01
. The differentiable absorption theorem is then applied to construct densely defined connections (or correpondences) on Hilbert C∗C∗-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C∗C∗-module....
Directory of Open Access Journals (Sweden)
Majewski M.
2015-06-01
Full Text Available The parametric OMI (Optimization in Multiple Intervals, the Yoshida-Magalas (YM and a novel Hilbert-twin (H-twin methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.
Energy Technology Data Exchange (ETDEWEB)
McDonald, S A; Marone, F; Hintermueller, C; Stampanoni, M [Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI (Switzerland); Bensadoun, J-C; Aebischer, P, E-mail: samuel.mcdonald@psi.c [EPFL, School of Life Sciences, Station 15, 1015 Lausanne (Switzerland)
2009-09-01
The use of conventional absorption based X-ray microtomography can become limited for samples showing only very weak absorption contrast. However, a wide range of samples studied in biology and materials science can produce significant phase shifts of the X-ray beam, and thus the use of the phase signal can provide substantially increased contrast and therefore new and otherwise inaccessible information. The application of two approaches for high-throughput, high-resolution X-ray phase contrast tomography, both available on the TOMCAT beamline of the SLS, is illustrated. Differential Phase Contrast (DPC) imaging uses a grating interferometer and a phase-stepping technique. It has been integrated into the beamline environment on TOMCAT in terms of the fast acquisition and reconstruction of data and the availability to scan samples within an aqueous environment. The second phase contrast approach is a modified transfer of intensity approach that can yield the 3D distribution of the phase (refractive index) of a weakly absorbing object from a single tomographic dataset. These methods are being used for the evaluation of cell integrity in 3D, with the specific aim of following and analyzing progressive cell degeneration to increase knowledge of the mechanistic events of neurodegenerative disorders such as Parkinson's disease.
Friedrichs systems in a Hilbert space framework: Solvability and multiplicity
Antonić, N.; Erceg, M.; Michelangeli, A.
2017-12-01
The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Hamiltonian and physical Hilbert space in polymer quantum mechanics
International Nuclear Information System (INIS)
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A
2007-01-01
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg-Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed
Public channel cryptography: chaos synchronization and Hilbert's tenth problem.
Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang
2008-08-22
The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Czech Academy of Sciences Publication Activity Database
Vetushka, Aliaksi; Fejfar, Antonín; Ledinský, Martin; Rezek, Bohuslav; Stuchlík, Jiří; Kočka, Jan
2010-01-01
Roč. 7, 3-4 (2010), s. 728-731 ISSN 1862-6351 R&D Projects: GA MŠk(CZ) LC06040; GA AV ČR KAN400100701; GA MŠk LC510; GA AV ČR(CZ) IAA100100902 Institutional research plan: CEZ:AV0Z10100521 Keywords : local anodic oxidation (LAO) * conductive atomic force microscopy (C-AFM) Subject RIV: BM - Solid Matter Physics ; Magnetism http://www3.interscience.wiley.com/journal/123289759/abstract
Wu, Heng-Liang; Tong, Yujin; Peng, Qiling; Li, Na; Ye, Shen
2016-01-21
The phase transition behaviors of a supported bilayer of dipalmitoylphosphatidyl-choline (DPPC) have been systematically evaluated by in situ sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM). By using an asymmetric bilayer composed of per-deuterated and per-protonated monolayers, i.e., DPPC-d75/DPPC and a symmetric bilayer of DPPC/DPPC, we were able to probe the molecular structural changes during the phase transition process of the lipid bilayer by SFG spectroscopy. It was found that the DPPC bilayer is sequentially melted from the top (adjacent to the solution) to bottom leaflet (adjacent to the substrate) over a wide temperature range. The conformational ordering of the supported bilayer does not decrease (even slightly increases) during the phase transition process. The conformational defects in the bilayer can be removed after the complete melting process. The phase transition enthalpy for the bottom leaflet was found to be approximately three times greater than that for the top leaflet, indicating a strong interaction of the lipids with the substrate. The present SFG and AFM observations revealed similar temperature dependent profiles. Based on these results, the temperature-induced structural changes in the supported lipid bilayer during its phase transition process are discussed in comparison with previous studies.
Shahoei, Hiva; Dumais, Patrick; Yao, Jianping
2014-05-01
We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.
Al-Khafaji, M. A.; Rainforth, W. M.; Gibbs, M. R. J.; Davies, H. A.; Bishop, J. E. L.
1998-09-01
Magnetic force microscopy (MFM) has been employed to image the magnetic structure in nanocrystalline melt spun ribbon samples of NdFeB alloys of three markedly different and contrasting compositions: Low-Nd (Nd 9.5Fe 84.5B 6) containing Nd 2Fe 14B and α-Fe phases, stoichiometric (Nd 11.8Fe 82.3B 5.9), and high-Nd (Nd 18Fe 76B 6) containing Nd 2Fe 14B and Nd-rich phases. It was found that the magnetic domain length scale is significantly larger than the mean Nd 2Fe 14B grain size (˜35 nm) in each case, although small changes in force gradient occurred down to ˜20 nm. However, both the domain length scale and the tip-sample interaction `strength' were found to decrease with increasing Nd-content. An interpretation of these results in terms of the microstructure is given.
Berthier, R.; Bernier, N.; Cooper, D.; Sabbione, C.; Hippert, F.; Noé, P.
2017-09-01
The crystallization mechanisms of prototypical GeTe phase-change material thin films have been investigated by in situ scanning transmission electron microscopy annealing experiments. A novel sample preparation method has been developed to improve sample quality and stability during in situ annealing, enabling quantitative analysis and live recording of phase change events. Results show that for an uncapped 100 nm thick GeTe layer, exposure to air after fabrication leads to composition changes which promote heterogeneous nucleation at the oxidized surface. We also demonstrate that protecting the GeTe layer with a 10 nm SiN capping layer prevents nucleation at the surface and allows volume nucleation at a temperature 50 °C higher than the onset of crystallization in the oxidized sample. Our results have important implications regarding the integration of these materials in confined memory cells.
Kuppan, Saravanan; Xu, Yahong; Liu, Yijin; Chen, Guoying
2017-02-01
Understanding the reaction pathway and kinetics of solid-state phase transformation is critical in designing advanced electrode materials with better performance and stability. Despite the first-order phase transition with a large lattice mismatch between the involved phases, spinel LiMn1.5Ni0.5O4 is capable of fast rate even at large particle size, presenting an enigma yet to be understood. The present study uses advanced two-dimensional and three-dimensional nano-tomography on a series of well-formed LixMn1.5Ni0.5O4 (0growth process instead of a shrinking-core or a particle-by-particle process. Superior kinetics of (100) facets at the vertices of truncated octahedral particles promote preferential delithiation, whereas the observation of strain-induced cracking suggests mechanical degradation in the material.
Xu, Jian; Kang, Deyong; Xu, Meifang; Zhu, Xiaoqin; Zhuo, Shuangmu; Chen, Jianxin
2012-12-01
Esophageal cancer is a common malignancy with a very poor prognosis. Successful strategies for primary prevention and early detection are critically needed to control this disease. Multiphoton microscopy (MPM) is becoming a novel optical tool of choice for imaging tissue architecture and cellular morphology by two-photon excited fluorescence. In this study, we used MPM to image microstructure of human normal esophagus, carcinoma in situ (CIS), and early invasive carcinoma in order to establish the morphological features to differentiate these tissues. The diagnostic features such as the appearance of cancerous cells, the significant loss of stroma, the absence of the basement membrane were extracted to distinguish between normal and cancerous esophagus tissue. These results correlated well with the paired histological findings. With the advancement of clinically miniaturized MPM and the multi-photon probe, combining MPM with standard endoscopy will therefore allow us to make a real-time in vivo diagnosis of early esophageal cancer at the cellular level.
Sanderson, Michael J; Smith, Ian; Parker, Ian; Bootman, Martin D
2014-10-01
Fluorescence microscopy is a major tool with which to monitor cell physiology. Although the concepts of fluorescence and its optical separation using filters remain similar, microscope design varies with the aim of increasing image contrast and spatial resolution. The basics of wide-field microscopy are outlined to emphasize the selection, advantages, and correct use of laser scanning confocal microscopy, two-photon microscopy, scanning disk confocal microscopy, total internal reflection, and super-resolution microscopy. In addition, the principles of how these microscopes form images are reviewed to appreciate their capabilities, limitations, and constraints for operation. © 2014 Cold Spring Harbor Laboratory Press.
Regularization methods for ill-posed problems in multiple Hilbert scales
International Nuclear Information System (INIS)
Mazzieri, Gisela L; Spies, Ruben D
2012-01-01
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, and regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases, convergence is proved and orders and optimal orders of convergence are shown. Finally, some potential applications and open problems are discussed. (paper)
Hilbert-Schmidt expansion for the nucleon-deuteron scattering amplitude
International Nuclear Information System (INIS)
Moeller, K.; Narodetskii, I.M.
1983-01-01
The Hilbert-Schmidt method is used to sum the divergent iterative series for the partial amplitudes of nucleon-deuteron scattering in the energy region above the deuteron breakup threshold. It is observed that the Hilbert-Schmidt series for the partial amplitudes themselves diverges, which is due to the closeness of the logarithmic singularities. But if the first iterations in the series for multiple scattering are subtracted from the amplitude, the Hilbert-Schmidt series for the remainder converges rapidly. The final answer obtained in the present paper is in excellent agreement with the results obtained in exact calculations
Application of Arbitrary-Order Hilbert Spectral Analysis to Passive Scalar Turbulence
International Nuclear Information System (INIS)
Huang, Y X; Lu, Z M; Liu, Y L; Schmitt, F G; Gagne, Y
2011-01-01
In previous work [Huang et al., PRE 82, 26319, 2010], we found that the passive scalar turbulence field maybe less intermittent than what we believed before. Here we apply the same method, namely arbitrary-order Hilbert spectral analysis, to a passive scalar (temperature) time series with a Taylor's microscale Reynolds number Re λ ≅ 3000. We find that with increasing Reynolds number, the discrepancy of scaling exponents between Hilbert ξ θ (q) and Kolmogorov-Obukhov-Corrsin (KOC) theory is increasing, and consequently the discrepancy between Hilbert and structure function could disappear at infinite Reynolds number.
International Nuclear Information System (INIS)
Lettinga, M Paul; Kang, Kyongok; Imhof, Arnout; Derks, Didi; Dhont, Jan K G
2005-01-01
We investigate the kinetics of phase separation for a mixture of rod-like viruses (fd) and polymer (dextran), which effectively constitutes a system of attractive rods. This dispersion is quenched from a flow-induced fully nematic state into the region where the nematic and the isotropic phase coexist. We show experimental evidence that the kinetic pathway depends on the overall concentration. When the quench is made at high concentrations, the system is meta-stable and we observe typical nucleation-and-growth. For quenches at low concentration the system is unstable and the system undergoes a spinodal decomposition. At intermediate concentrations we see the transition between both demixing processes, where we locate the spinodal point
Phillips, Kevin G; Baker-Groberg, Sandra M; McCarty, Owen J T
2014-04-07
We describe the use of a standard optical microscope to perform quantitative measurements of mass, volume, and density on cellular specimens through a combination of bright field and differential interference contrast imagery. Two primary approaches are presented: noninterferometric quantitative phase microscopy (NIQPM), to perform measurements of total cell mass and subcellular density distribution, and Hilbert transform differential interference contrast microscopy (HTDIC) to determine volume. NIQPM is based on a simplified model of wave propagation, termed the paraxial approximation, with three underlying assumptions: low numerical aperture (NA) illumination, weak scattering, and weak absorption of light by the specimen. Fortunately, unstained cellular specimens satisfy these assumptions and low NA illumination is easily achieved on commercial microscopes. HTDIC is used to obtain volumetric information from through-focus DIC imagery under high NA illumination conditions. High NA illumination enables enhanced sectioning of the specimen along the optical axis. Hilbert transform processing on the DIC image stacks greatly enhances edge detection algorithms for localization of the specimen borders in three dimensions by separating the gray values of the specimen intensity from those of the background. The primary advantages of NIQPM and HTDIC lay in their technological accessibility using "off-the-shelf" microscopes. There are two basic limitations of these methods: slow z-stack acquisition time on commercial scopes currently abrogates the investigation of phenomena faster than 1 frame/minute, and secondly, diffraction effects restrict the utility of NIQPM and HTDIC to objects from 0.2 up to 10 (NIQPM) and 20 (HTDIC) μm in diameter, respectively. Hence, the specimen and its associated time dynamics of interest must meet certain size and temporal constraints to enable the use of these methods. Excitingly, most fixed cellular specimens are readily investigated with
Energy Technology Data Exchange (ETDEWEB)
Pawlyta, M., E-mail: miroslawa.pawlyta@polsl.pl [Silesian University of Technology, Institute of Engineering Materials and Biomaterials, Konarskiego 18A, 44-100 Gliwice (Poland); Tomiczek, B.; Dobrzański, L.A.; Kujawa, M. [Silesian University of Technology, Institute of Engineering Materials and Biomaterials, Konarskiego 18A, 44-100 Gliwice (Poland); Bierska-Piech, B. [Silesian Centre for Education and Interdisciplinary Research, 75 Pułku Piechoty 1A, 41-500 Chorzów (Poland)
2016-04-15
The porous ceramic preforms were manufactured using the powder metallurgy technique. First, the start-up material (halloysite with the addition of carbon fibres as the pore-forming agent) was slowly heated to 800 °C and then sintered at 1300 °C. Degradation of the carbon fibres enabled the open canals to form. At the end of the sintering process, the porous ceramic material consisting mainly of two phases (mullite and cristobalite) was formed, without any residual carbon content. During infiltration, the liquid metal filled the empty spaces (pores) effectively and formed the three-dimensional network of metal in the ceramic. The cristobalite was almost entirely decomposed. In the areas of its previous occurrence, there are new pores, only in the ceramic grains. The mullite, which was formed from halloysite during annealing, crystallized in the Pbam orthorhombic space group, with the (3Al{sub 2}O{sub 3}·2SiO{sub 2}) stoichiometric composition. The mullite structure does not change during the infiltration. The composite components are tightly connected. A transition zone between the ceramics and the metal, having the thickness of about 200 nm, was formed. The nanocrystalline zone, identified as γ-Al{sub 2}O{sub 3}, was formed by diffusing the product of the cristobalite decomposition into the aluminium alloy matrix. There is an additional, new phase, identified as (Mg,Si)Al{sub 2}O{sub 4} in the outer parts of the transition zone. - Highlights: • Phase changes after the infiltration of aluminium into porous mullite preforms were observed by TEM. • TEM observations confirm that during infiltration cristobalite was decomposed and the structure of mullite did not change. • Between the ceramic and the metal, a transition zone comprising a layer of γ-Al{sub 2}O{sub 3} and (Mg,Si)Al{sub 2}O{sub 4} was formed.
Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications
Gesztesy, Fritz; Malamud, Mark; Mitrea, Marius; Naboko, Serguei
2008-01-01
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
On the minimizers of calculus of variations problems in Hilbert spaces
Gomes, Diogo A.
2014-01-19
The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.
On the minimizers of calculus of variations problems in Hilbert spaces
Gomes, Diogo A.; Nurbekyan, Levon
2014-01-01
The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.
Energy Technology Data Exchange (ETDEWEB)
Jafari, M. [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan (Iran, Islamic Republic of); Ziaei-Rad, S., E-mail: szrad@cc.iut.ac.ir [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan (Iran, Islamic Republic of); Saeidi, N. [Department of Materials Engineering, Isfahan University of Technology, Isfahan (Iran, Islamic Republic of); Jamshidian, M. [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan (Iran, Islamic Republic of)
2016-07-18
The morphology and distribution of the dispersed martensite islands in the ferrite matrix plays a key role in the formation of shear bands in dual phase steels. In this study, we investigate the relationship between the martensite dispersion and the strain localization regions due to the formation of shear bands in fine-grained DP 780 steel, employing experimental observations as well as numerical simulations. SEM studies of the deformed microstructure showed that voids nucleated at ferrite-martensite interface within larger ferrite grains and regions with low local martensite fraction. The experimental results were precisely analyzed by finite element simulations based on the theory of crystal plasticity. A parametric study was then performed to obtain a deeper insight in to the effect of martensite dispersion on the strain localization of the neighboring ferrite. Crystal plasticity simulation results revealed that in a more regular structure compared to a random structure, a greater region of the ferrite phase contributes to accommodate plasticity. In addition, these regions limit the formation of main shear bands by creating barriers against stress concentration regions, results in lower growth and interaction of stress concentration regions with each others.
Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces
Ghiloni, Riccardo; Moretti, Valter; Perotti, Alessandro
2013-04-01
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.
Characterizing sequential isomorphisms on Hilbert-space effect algebras
International Nuclear Information System (INIS)
Hou Jinchuan; He Kan; Qi Xiaofei
2010-01-01
Let * be any sequential product on the Hilbert-space effect algebra E(H) with dim H≥2, and Φ:E(H)→E(H) be a bijective map. We show that if Φ satisfies Φ(A*B) = Φ(A)*Φ(B) for A,B element of E(H), then there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H). Let g:[0,1]→{λ|λ element of C, |λ|=0 or 1} be a Borel function satisfying g(0) = 0, g(1) = 1 and let us define a binary operation lozenge g on E(H) by A lozenge g B = A 1/2 g(A)Bg(A)†A 1/2 , where T† denotes the conjugate of the operator T. We also show that a bijective map Φ:E(H)→E(H) satisfies Φ(A lozenge g B) = Φ(A) lozenge g Φ(B) for A,B element of E(H) if and only if there is either a unitary or an anti-unitary operator U such that Φ(A) = UAU† for every A element of E(H).
An introduction of gauge field by the Lie-isotopic lifting of the Hilbert space
International Nuclear Information System (INIS)
Nishioka, M.
1984-01-01
It is introduced the gauge field by the Lie-isotopic lifting of the Hilbert space. Our method is different from other's in that the commutator between the isotropic element and the generators of the Lie algebra does not vanish in our case, but vanishes in other cases. Our method uses the Lie-isotopic lifting of the Hilbert space, but others do not use it
Majewski M.; Magalas L.B.
2015-01-01
The parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) and a novel Hilbert-twin (H-twin) methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in in...
Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields
International Nuclear Information System (INIS)
Albeverio, S.; Brzezniak, Z.
1994-01-01
We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)
Application of Hilbert-Huang Transform in Generating Spectrum-Compatible Earthquake Time Histories
Ni, Shun-Hao; Xie, Wei-Chau; Pandey, Mahesh
2011-01-01
Spectrum-compatible earthquake time histories have been widely used for seismic analysis and design. In this paper, a data processing method, Hilbert-Huang transform, is applied to generate earthquake time histories compatible with the target seismic design spectra based on multiple actual earthquake records. Each actual earthquake record is decomposed into several components of time-dependent amplitude and frequency by Hilbert-Huang transform. The spectrum-compatible earthquake time history ...
Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method
Brading, K. A.; Ryckman, T. A.
2008-01-01
In November and December 1915, Hilbert presented two communications to the Göttingen Academy of Sciences under the common title 'The Foundations of Physics'. Versions of each eventually appeared in the Nachrichten of the Academy. Hilbert's first communication has received significant reconsideration in recent years, following the discovery of printer's proofs of this paper, dated 6 December 1915. The focus has been primarily on the 'priority dispute' over the Einstein field equations. Our contention, in contrast, is that the discovery of the December proofs makes it possible to see the thematic linkage between the material that Hilbert cut from the published version of the first communication and the content of the second, as published in 1917. The latter has been largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two communications should be regarded as part of a wider research program within the overarching framework of 'the axiomatic method' (as Hilbert expressly stated was the case), and (b) the second communication is a fine and coherent piece of work within this framework, whose principal aim is to address an apparent tension between general invariance and causality (in the precise sense of Cauchy determination), pinpointed in Theorem I of the first communication. This is not the same problem as that found in Einstein's 'hole argument'-something that, we argue, never confused Hilbert.
Cho, Myoung-Ock; Kim, Jung Kyung; Han, Hwataik; Lee, Jeonghoon
2013-01-01
Asbestos that had been used widely as a construction material is a first-level carcinogen recognized by the World Health Organization. It can be accumulated in body by inhalation causing virulent respiratory diseases including lung cancer. In our previous study, we developed a high-throughput microscopy (HTM) system that can minimize human intervention accompanied by the conventional phase contrast microscopy (PCM) through automated counting of fibrous materials and thus significantly reduce analysis time and labor. Also, we attempted selective detection of chrysotile using DksA protein extracted from Escherichia coli through a recombinant protein production technique, and developed a dual-mode HTM (DM-HTM) by upgrading the HTM device. We demonstrated that fluorescently-labeled chrysotile asbestos fibers can be identified and enumerated automatically among other types of asbestos fibers or non-asbestos particles in a high-throughput manner through a newly modified HTM system for both reflection and fluorescence imaging. However there is a limitation to apply DM-HTM to airborne sample with current air collecting method due to the difficulty of applying the protein to dried asbestos sample. Here, we developed a technique for preparing liquid-phase asbestos sample using an impinger normally used to collect odor molecules in the air. It would be possible to improve the feasibility of the dual-mode HTM by integrating a sample preparation unit for making collected asbestos sample dispersed in a solution. The new technique developed for highly sensitive and automated asbestos detection can be a potential alternative to the conventional manual counting method, and it may be applied on site as a fast and reliable environmental monitoring tool.
Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform
Directory of Open Access Journals (Sweden)
Hui Wang
2013-01-01
Full Text Available A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT. This method can be used to test effective number of bits (ENOBs of analog-to-digital converter (ADC, avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.
Guo, Baoshan; Lei, Cheng; Kobayashi, Hirofumi; Ito, Takuro; Yalikun, Yaxiaer; Jiang, Yiyue; Tanaka, Yo; Ozeki, Yasuyuki; Goda, Keisuke
2017-05-01
The development of reliable, sustainable, and economical sources of alternative fuels to petroleum is required to tackle the global energy crisis. One such alternative is microalgal biofuel, which is expected to play a key role in reducing the detrimental effects of global warming as microalgae absorb atmospheric CO 2 via photosynthesis. Unfortunately, conventional analytical methods only provide population-averaged lipid amounts and fail to characterize a diverse population of microalgal cells with single-cell resolution in a non-invasive and interference-free manner. Here high-throughput label-free single-cell screening of lipid-producing microalgal cells with optofluidic time-stretch quantitative phase microscopy was demonstrated. In particular, Euglena gracilis, an attractive microalgal species that produces wax esters (suitable for biodiesel and aviation fuel after refinement), within lipid droplets was investigated. The optofluidic time-stretch quantitative phase microscope is based on an integration of a hydrodynamic-focusing microfluidic chip, an optical time-stretch quantitative phase microscope, and a digital image processor equipped with machine learning. As a result, it provides both the opacity and phase maps of every single cell at a high throughput of 10,000 cells/s, enabling accurate cell classification without the need for fluorescent staining. Specifically, the dataset was used to characterize heterogeneous populations of E. gracilis cells under two different culture conditions (nitrogen-sufficient and nitrogen-deficient) and achieve the cell classification with an error rate of only 2.15%. The method holds promise as an effective analytical tool for microalgae-based biofuel production. © 2017 International Society for Advancement of Cytometry. © 2017 International Society for Advancement of Cytometry.
Yamauchi, Toyohiko; Kakuno, Yumi; Goto, Kentaro; Fukami, Tadashi; Sugiyama, Norikazu; Iwai, Hidenao; Mizuguchi, Yoshinori; Yamashita, Yutaka
2014-03-01
There is an increasing need for non-invasive imaging techniques in the field of stem cell research. Label-free techniques are the best choice for assessment of stem cells because the cells remain intact after imaging and can be used for further studies such as differentiation induction. To develop a high-resolution label-free imaging system, we have been working on a low-coherence quantitative phase microscope (LC-QPM). LC-QPM is a Linnik-type interference microscope equipped with nanometer-resolution optical-path-length control and capable of obtaining three-dimensional volumetric images. The lateral and vertical resolutions of our system are respectively 0.5 and 0.93 μm and this performance allows capturing sub-cellular morphological features of live cells without labeling. Utilizing LC-QPM, we reported on three-dimensional imaging of membrane fluctuations, dynamics of filopodia, and motions of intracellular organelles. In this presentation, we report three-dimensional morphological imaging of human induced pluripotent stem cells (hiPS cells). Two groups of monolayer hiPS cell cultures were prepared so that one group was cultured in a suitable culture medium that kept the cells undifferentiated, and the other group was cultured in a medium supplemented with retinoic acid, which forces the stem cells to differentiate. The volumetric images of the 2 groups show distinctive differences, especially in surface roughness. We believe that our LC-QPM system will prove useful in assessing many other stem cell conditions.
Seizure classification in EEG signals utilizing Hilbert-Huang transform
Directory of Open Access Journals (Sweden)
Abdulhay Enas W
2011-05-01
Full Text Available Abstract Background Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG signals. Method Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. Results The t-test results in a P-value Conclusion An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.
Comments on the interacting Einstein-Hilbert drop
International Nuclear Information System (INIS)
Khanal, U.
2004-12-01
The bosonic internal co-ordinates of the Einstein-Hilbert drop is complexified to include U(1) gauge interaction. The equations of motion of the gauge fields are Maxwell equations. The EOM of the internal co-ordinates are elliptic under matter domination and hyperbolic under vacuum domination. These equations take on the familiar form of the wave equation of the interacting massless scalar field in any world spacetime that has the sum of its energy-momentum and Einstein tensors proportional to the induced metric. The reparametrization invariance of the worldtime can be used to identify it with the internal time. This results in a gauge condition that relates time to the curvature, gauge potential and energy-momentum. In gaussian normal co-ordinates of a constant curvature worldspace with real time, this condition translates into vanishing pressure, allowing a solution for the time dependence of the time-component of the vector potential. This potential has a simple pole at the origin of the complex time-plane, and another at a point on the imaginary axis. The singularity at the origin occurs only in the imaginary part of the potential. This potential in turn makes it possible to solve for the time dependence of the internal co-ordinates. Real internal co-ordinates have to be linear in worldtime. The complex internal co-ordinate also has two simple poles: one is at the same point on the imaginary axis as the potential; the other at infinity occurs only in the imaginary part. The origin turns out to be a regular point. (author)
Seizure classification in EEG signals utilizing Hilbert-Huang transform.
Oweis, Rami J; Abdulhay, Enas W
2011-05-24
Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. The t-test results in a P-value with respect to its fast response and ease to use. An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.
Soft and hard classification by reproducing kernel Hilbert space methods.
Wahba, Grace
2002-12-24
Reproducing kernel Hilbert space (RKHS) methods provide a unified context for solving a wide variety of statistical modelling and function estimation problems. We consider two such problems: We are given a training set [yi, ti, i = 1, em leader, n], where yi is the response for the ith subject, and ti is a vector of attributes for this subject. The value of y(i) is a label that indicates which category it came from. For the first problem, we wish to build a model from the training set that assigns to each t in an attribute domain of interest an estimate of the probability pj(t) that a (future) subject with attribute vector t is in category j. The second problem is in some sense less ambitious; it is to build a model that assigns to each t a label, which classifies a future subject with that t into one of the categories or possibly "none of the above." The approach to the first of these two problems discussed here is a special case of what is known as penalized likelihood estimation. The approach to the second problem is known as the support vector machine. We also note some alternate but closely related approaches to the second problem. These approaches are all obtained as solutions to optimization problems in RKHS. Many other problems, in particular the solution of ill-posed inverse problems, can be obtained as solutions to optimization problems in RKHS and are mentioned in passing. We caution the reader that although a large literature exists in all of these topics, in this inaugural article we are selectively highlighting work of the author, former students, and other collaborators.
Fukuda, Takahito; Shinomura, Masato; Xia, Peng; Awatsuji, Yasuhiro; Nishio, Kenzo; Matoba, Osamu
2017-04-01
We constructed a parallel-phase-shifting digital holographic microscopy (PPSDHM) system using an inverted magnification optical system, and succeeded in three-dimensional (3D) motion-picture imaging for 3D displacement of a microscopic object. In the PPSDHM system, the inverted and afocal magnification optical system consisted of a microscope objective (16.56 mm focal length and 0.25 numerical aperture) and a convex lens (300 mm focal length and 82 mm aperture diameter). A polarization-imaging camera was used to record multiple phase-shifted holograms with a single-shot exposure. We recorded an alum crystal, sinking down in aqueous solution of alum, by the constructed PPSDHM system at 60 frames/s for about 20 s and reconstructed high-quality 3D motion-picture image of the crystal. Then, we calculated amounts of displacement of the crystal from the amounts in the focus plane and the magnifications of the magnification optical system, and obtained the 3D trajectory of the crystal by that amounts.
Alabiso, Carlo
2015-01-01
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...
Directory of Open Access Journals (Sweden)
Magalas L.B.
2015-06-01
Full Text Available In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1 the parametric OMI (Optimization in Multiple Intervals method, two interpolated discrete Fourier transform-based (IpDFT methods: (2 the Yoshida-Magalas (YM method and (3 the classic Yoshida (Y method, (4 the novel Hilbert-twin (H-twin method based on the Hilbert transform, and (5 the conventional Hilbert transform (HT method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, aHT (t, obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low- and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.
Wavelet Based Hilbert Transform with Digital Design and Application to QCM-SS Watermarking
Directory of Open Access Journals (Sweden)
S. P. Maity
2008-04-01
Full Text Available In recent time, wavelet transforms are used extensively for efficient storage, transmission and representation of multimedia signals. Hilbert transform pairs of wavelets is the basic unit of many wavelet theories such as complex filter banks, complex wavelet and phaselet etc. Moreover, Hilbert transform finds various applications in communications and signal processing such as generation of single sideband (SSB modulation, quadrature carrier multiplexing (QCM and bandpass representation of a signal. Thus wavelet based discrete Hilbert transform design draws much attention of researchers for couple of years. This paper proposes an (i algorithm for generation of low computation cost Hilbert transform pairs of symmetric filter coefficients using biorthogonal wavelets, (ii approximation to its rational coefficients form for its efficient hardware realization and without much loss in signal representation, and finally (iii development of QCM-SS (spread spectrum image watermarking scheme for doubling the payload capacity. Simulation results show novelty of the proposed Hilbert transform design and its application to watermarking compared to existing algorithms.
Fujita, Kazuhiro; Schmidt, Andrew R.; Kim, Eun-Ah; Lawler, Michael J.; Lee, Dung Hai; Davis, J. C.; Eisaki, Hiroshi; Uchida, Shin-ichi
2012-01-01
One of the key motivations for the development of atomically resolved spectroscopic imaging scanning tunneling microscopy (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E|=Δ0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k=±(π/a0,0) to k=±(0,π/a0). Below optimal doping, this ``nodal'' arc shrinks continuously with decreasing hole density. In both the dSC and PG phases, the only broken symmetries detected in the |E|≤Δ0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E|˜ Δ1 which is associated conventionally with the ``antinodal'' states near k=±(π/a0,0) and k=±(0,π/a0). We find that these states break the expected 90°-rotational (C4) symmetry of electronic structure within CuO2 unit cells, at least down to 180°-rotational (C2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C4 symmetry breaking coexists at |E|˜Δ1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The characteristic wavevector Q of the latter is determined, empirically, by the k-space points where Bogoliubov quasiparticle interference terminates, and therefore evolves continuously with doping. The properties of these two classes of |E|˜Δ1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E|˜Δ1 and |E|≤Δ0, and to understand how this impacts the electronic
International Nuclear Information System (INIS)
Furdea, A; Wilson, J D; Eswaran, H; Lowery, C L; Govindan, R B; Preissl, H
2009-01-01
We propose a multi-stage approach using Wavelet and Hilbert transforms to identify uterine contraction bursts in magnetomyogram (MMG) signals measured using a 151 magnetic sensor array. In the first stage, we decompose the MMG signals by wavelet analysis into multilevel approximate and detail coefficients. In each level, the signals are reconstructed using the detail coefficients followed by the computation of the Hilbert transform. The Hilbert amplitude of the reconstructed signals from different frequency bands (0.1–1 Hz) is summed up over all the sensors to increase the signal-to-noise ratio. Using a novel clustering technique, affinity propagation, the contractile bursts are distinguished from the noise level. The method is applied on simulated MMG data, using a simple stochastic model to determine its robustness and to seven MMG datasets
nth roots with Hilbert-Schmidt defect operator of normal contractions
International Nuclear Information System (INIS)
Duggal, B.P.
1992-08-01
Let T be a normal contraction (on a complex separable Hilbert space H into itself) with an nth root A such that the defect operator D A =(1-A*A) 1/2 is of the Hilbert-Schmidt class C 2 . Then either A is normal or A is similar to a normal contraction. In the case in which T is hyponormal, A n =T and D A is an element of C 2 , A is a ''coupling'' of a contraction similar to a normal contraction and a contraction which is the quasi-affine transform of a unilateral shift. These results are applied to prove a (Putnam-Fuglede type) commutatively theorem for operator valued roots of commutative analytic functions and hyponormal contractions T which have an nth root with Hilbert-Schmidt defect operator. 23 refs
Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors
Directory of Open Access Journals (Sweden)
Jing-Yi Chang
2014-01-01
Full Text Available The Hilbert curve is a continuous type of fractal space-filling curve. This fractal curve visits every point in a square grid with a size of 2×2, 4×4, or any other power of two. This paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC current collectors. The current collectors are carved following first, second, and third order Hilbert fractal curves. These curves give the current collectors different free open ratios and opening perimeters. We conducted an experimental investigation into DMFC performance as a function of the free open ratio and opening perimeter on the bipolar plates. Nyquist plots of the bipolar plates are made and compared using electrochemical impedance spectroscopy (EIS experiments to understand the phenomena in depth. The results obtained in this paper could be a good reference for future current collector design.
Sima, Chaotan; Gates, J C; Holmes, C; Mennea, P L; Zervas, M N; Smith, P G R
2013-09-01
Terahertz bandwidth photonic Hilbert transformers are proposed and experimentally demonstrated. The integrated device is fabricated via a direct UV grating writing technique in a silica-on-silicon platform. The photonic Hilbert transformer operates at bandwidths of up to 2 THz (~16 nm) in the telecom band, a 10-fold greater bandwidth than any previously reported experimental approaches. Achieving this performance requires detailed knowledge of the system transfer function of the direct UV grating writing technique; this allows improved linearity and yields terahertz bandwidth Bragg gratings with improved spectral quality. By incorporating a flat-top reflector and Hilbert grating with a waveguide coupler, an ultrawideband all-optical single-sideband filter is demonstrated.
H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps
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Guillem Vallicrosa
2018-05-01
Full Text Available Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles. These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.
Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms
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Grzegorz Litak
Full Text Available We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.
On the discovery of the gravitational field equations by Einstein and Hilbert: new materials
International Nuclear Information System (INIS)
Vizgin, Vladimir P
2001-01-01
This article describes the history of discovery of the equations of gravitational field by Albert Einstein and David Hilbert in November 1915. The proof sheet of Hilbert's lecture report, made on 20 November 1915 and published in March 1916, rediscovered in 1997 in the archive of the university of Goettingen, throws new light on the history of this discovery. We also discuss the early history of the general theory of relativity that led to the expression of the general covariant equations of gravitational field. (from the history of physics)
Zhuang, L.; Khan, M.R.H.; Beeker, Willem; Beeker, W.P.; Leinse, Arne; Heideman, Rene; Roeloffzen, C.G.H.
2012-01-01
We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonatorbased optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance
International Nuclear Information System (INIS)
Llewellyn, D.J.; Llewellyn, D.J.; Belay, K.B.; Ridgway, M.C.
1998-01-01
In-situ transmission electron microscopy (TEM) has been used to characterize the solid phase epitaxial growth of amorphized GaAs at a temperature of 260 deg C. To maximize heat transfer from the heated holder to the sample and minimize electron-irradiation induced artifacts, non-conventional methodologies were utilized for the preparation of cross-sectional samples. GaAs 3x1 mm rectangular wafers were cleaved then glued face-to-face to form a wafer stack size of 3x3 mm while maintaining the TEM region at the center. This stack was subsequently polished on the cross-section to a thickness of ∼ 200 μm. A 3 mm disc was then cut perpendicular to the cross-section using a Gatan ultrasonic cutter. The disc was polished then dimpled on both sides to a thickness of ∼ 15 μm. This was ion-beam milled at liquid nitrogen temperature to an electron-transparent layer. From a comparison of in-situ and ex-situ measurements of the recrystallization rate, the actual sample temperature during in-situ characterization was estimated to deviate by ≤ 20 deg C from that of the heated holder. The influence of electron-irradiation was found to be negligible by comparing the recrystallization rate and microstructure of irradiated and unirradiated regions of comparable thickness. Similarly, the influence of the 'thin-foil effect' was found to be negligible by comparing the recrystallization rate and microstructure of thick and thin regions, the former determined after the removal of the sample from the microscope and further ion-beam milling of tens of microns of material. In conclusion, the potential influence of artifacts during in-situ TEM can be minimized by the appropriate choice of sample preparation procedures. (authors)
Leakage radiation interference microscopy.
Descrovi, Emiliano; Barakat, Elsie; Angelini, Angelo; Munzert, Peter; De Leo, Natascia; Boarino, Luca; Giorgis, Fabrizio; Herzig, Hans Peter
2013-09-01
We present a proof of principle for a new imaging technique combining leakage radiation microscopy with high-resolution interference microscopy. By using oil immersion optics it is demonstrated that amplitude and phase can be retrieved from optical fields, which are evanescent in air. This technique is illustratively applied for mapping a surface mode propagating onto a planar dielectric multilayer on a thin glass substrate. The surface mode propagation constant estimated after Fourier transformation of the measured complex field is well matched with an independent measurement based on back focal plane imaging.
A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces
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Singthong Urailuk
2010-01-01
Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.
Hilbert scheme of points on cyclic quotient singularities of type (p,1)
Gyenge, Ádám
2016-01-01
In this note we investigate the generating series of the Euler characteristics of Hilbert scheme of points on cyclic quotient singularities of type (p,1). We link the appearing combinatorics to p-fountains, a generalization of the notion of fountain of coins. We obtain a representation of the generating series as coefficient of a two variable generating series.
Experimental validation of a structural damage detection method based on marginal Hilbert spectrum
Banerji, Srishti; Roy, Timir B.; Sabamehr, Ardalan; Bagchi, Ashutosh
2017-04-01
Structural Health Monitoring (SHM) using dynamic characteristics of structures is crucial for early damage detection. Damage detection can be performed by capturing and assessing structural responses. Instrumented structures are monitored by analyzing the responses recorded by deployed sensors in the form of signals. Signal processing is an important tool for the processing of the collected data to diagnose anomalies in structural behavior. The vibration signature of the structure varies with damage. In order to attain effective damage detection, preservation of non-linear and non-stationary features of real structural responses is important. Decomposition of the signals into Intrinsic Mode Functions (IMF) by Empirical Mode Decomposition (EMD) and application of Hilbert-Huang Transform (HHT) addresses the time-varying instantaneous properties of the structural response. The energy distribution among different vibration modes of the intact and damaged structure depicted by Marginal Hilbert Spectrum (MHS) detects location and severity of the damage. The present work investigates damage detection analytically and experimentally by employing MHS. The testing of this methodology for different damage scenarios of a frame structure resulted in its accurate damage identification. The sensitivity of Hilbert Spectral Analysis (HSA) is assessed with varying frequencies and damage locations by means of calculating Damage Indices (DI) from the Hilbert spectrum curves of the undamaged and damaged structures.
Analysis of the Cofrentes instability with the Hilbert-Huang transform
International Nuclear Information System (INIS)
Blazquez, J.; Galindo, A.
2010-01-01
The most obvious application of the Hilbert-Huang transform is the denoising (signal isolation). In this article, the dynamic system is the power of a BWR reactor that undergoes instability. The signal and the dynamic systems are described, which in this case corresponds to a current incident in a commercial BWR reactor (Cofrentes). Finally, empirical modes are calculated and the results are analyzed.
Pairs of dual Gabor frames generated by functions of Hilbert-Schmidt type
DEFF Research Database (Denmark)
Christiansen, Lasse Hjuler
2015-01-01
where each member may be written as a linear combination of integer translates of any B-spline. We introduce functions of Hilbert-Schmidt type along with a new method which allows us to associate to certain such functions finite families of recursively defined dual windows of arbitrary smoothness...
Heterotic reduction of Courant algebroid connections and Einstein–Hilbert actions
Energy Technology Data Exchange (ETDEWEB)
Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Prague 186 75 (Czech Republic); Vysoký, Jan, E-mail: vysoky@math.cas.cz [Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, Prague 115 67 (Czech Republic); Mathematical Sciences Institute, Australian National University, Acton ACT 2601 (Australia)
2016-08-15
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein–Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.
Heterotic reduction of Courant algebroid connections and Einstein–Hilbert actions
International Nuclear Information System (INIS)
Jurčo, Branislav; Vysoký, Jan
2016-01-01
We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein–Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.
Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.
Corry, Leo
2018-04-28
The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces
Directory of Open Access Journals (Sweden)
Hu Changsong
2010-01-01
Full Text Available We consider two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces. We proved that the proposed algorithms strongly converge to a common fixed point of a countable family of nonexpansive mappings which solves the corresponding variational inequality. Our results improve and extend the corresponding ones announced by many others.
Hilbert space representation of the SOq(N)-covariant Heisenberg algebra
International Nuclear Information System (INIS)
Hebecker, A.; Weich, W.
1993-01-01
The differential calculus on SO q (N)-covariant quantum planes is rewritten in polar co-ordinates. Thus a Hilbert space formulation of q-deformed quantum mechanics can be developed particularly suitable for spherically symmetric potentials. The simplest case of a free particle is solved showing a discrete energy spectrum. (orig.)
Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics
Corry, Leo
2018-04-01
The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.
The classes of the quasihomogeneous Hilbert schemes of points on the plane
Buryak, A.
2012-01-01
Abstract: In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of -quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the -Catalan numbers. Finally, we
Weighted Traffic Equilibrium Problem in Non Pivot Hilbert Spaces with Long Term Memory
International Nuclear Information System (INIS)
Giuffre, Sofia; Pia, Stephane
2010-01-01
In the paper we consider a weighted traffic equilibrium problem in a non-pivot Hilbert space and prove the equivalence between a weighted Wardrop condition and a variational inequality with long term memory. As an application we show, using recent results of the Senseable Laboratory at MIT, how wireless devices can be used to optimize the traffic equilibrium problem.
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.
Wang, Aizhen; Yang, Bicheng
2017-01-01
By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.
A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function
Directory of Open Access Journals (Sweden)
Aizhen Wang
2017-06-01
Full Text Available Abstract By means of the weight functions, the technique of real analysis and Hermite-Hadamard’s inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.
International Nuclear Information System (INIS)
Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.
1984-09-01
The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)
Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1990-07-01
The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs
Energy Technology Data Exchange (ETDEWEB)
Birch, C J; Lehmann, N I; Hawker, A J; Marshall, J A; Gust, I D [Fairfield Hospital for Communicable Diseases, Victoria (Australia). Virology Dept.
1979-07-01
Four techniques were compared for their practicability, speed, and sensitivity for the detection of human rotavirus. Radioimmunoassay (RIA) and enzyme-linked immunosorbent assay (ELISA) were found to be the most sensitive means of identifying rotavirus and, once processed, up to 40 specimens could be examined daily. Electron microscopy, although less sensitive than these techniques, had the advantage of being able to detect other viral agents present in faecal extracts. Indirect immunofluorescence failed to detect rotavirus as often as the other three methods. In laboratories where routine examination of faecal specimens from patients with gastroenteritis is required, ELISA and RIA are useful alternatives to electron microscopy.
International Nuclear Information System (INIS)
Birch, C.J.; Lehmann, N.I.; Hawker, A.J.; Marshall, J.A.; Gust, I.D.
1979-01-01
Four techniques were compared for their practicability, speed, and sensitivity for the detection of human rotavirus. Radioimmunoassay (RIA) and enzyme-linked immunosorbent assay (ELISA) were found to be the most sensitive means of identifying rotavirus and, once processed, up to 40 specimens could be examined daily. Electron microscopy, although less sensitive than these techniques, had the advantage of being able to detect other viral agents present in faecal extracts. Indirect immunofluorescence failed to detect rotavirus as often as the other three methods. In laboratories where routine examination of faecal specimens from patients with gastroenteritis is required, ELISA and RIA are useful alternatives to electron microscopy. (author)
Alternative structures and bi-Hamiltonian systems on a Hilbert space
International Nuclear Information System (INIS)
Marmo, G; Scolarici, G; Simoni, A; Ventriglia, F
2005-01-01
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide a few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and the non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems
Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
On the one hand, a rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space and as we move to the second quantization, a Fock space. On the other hand, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we utilize some novel reinterpretations of basic E (∞) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. Proceeding in this way, we gain a better understanding of the physico-mathematical structure of quantum spacetime which is at the heart of the paradoxical and non-intuitive outcome of the famous quantum two-slit gedanken experiment
Martins, Luis Gustavo Nogueira; Stefanello, Michel Baptistella; Degrazia, Gervásio Annes; Acevedo, Otávio Costa; Puhales, Franciano Scremin; Demarco, Giuliano; Mortarini, Luca; Anfossi, Domenico; Roberti, Débora Regina; Costa, Felipe Denardin; Maldaner, Silvana
2016-11-01
In this study we analyze natural complex signals employing the Hilbert-Huang spectral analysis. Specifically, low wind meandering meteorological data are decomposed into turbulent and non turbulent components. These non turbulent movements, responsible for the absence of a preferential direction of the horizontal wind, provoke negative lobes in the meandering autocorrelation functions. The meandering characteristic time scales (meandering periods) are determined from the spectral peak provided by the Hilbert-Huang marginal spectrum. The magnitudes of the temperature and horizontal wind meandering period obtained agree with the results found from the best fit of the heuristic meandering autocorrelation functions. Therefore, the new method represents a new procedure to evaluate meandering periods that does not employ mathematical expressions to represent observed meandering autocorrelation functions.
Hilbert Series and Mixed Branches of T[SU(N)] theories
Energy Technology Data Exchange (ETDEWEB)
Carta, Federico [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Hayashi, Hirotaka [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Tokai University,4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292 (Japan)
2017-02-07
We consider mixed branches of 3dN=4T[SU(N)] theory. We compute the Hilbert series of the Coulomb branch part of the mixed branch from a restriction rule acting on the Hilbert series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch sublocus where the mixed branch stems. This restriction can be understood directly from the type IIB brane picture by a relation between the magnetic charges of the monopoles and brane position moduli. We also apply the restriction rule to the Higgs branch part of a given mixed branch by exploiting 3d mirror symmetry. Both cases show complete agreement with the results calculated by different methods.
International Nuclear Information System (INIS)
Mei Jianwei
2012-01-01
We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein-like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the m-ignorable coordinates then becomes a global SL(m, R) gauge symmetry of the reduced action. Related to each non-vanishing angular velocity, there is a particular SL(2, R) subgroup, which can be extended to the Witt algebra on the black hole horizons. The classical Einstein-Hilbert action thus has k-copies of infinite-dimensional conformal symmetries on a given black hole horizon, with k being the number of non-vanishing angular velocities of the black hole. (paper)
Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms
International Nuclear Information System (INIS)
Chauhan, Kapil; Ng, Henry C H; Marusic, Ivan
2010-01-01
Oil-film interferometry is rapidly becoming the preferred method for direct measurement of wall shear stress in studies of wall-bounded turbulent flows. Although being widely accepted as the most accurate technique, it does have inherent measurement uncertainties, one of which is associated with determining the fringe spacing. This is the focus of this paper. Conventional analysis methods involve a certain level of user input and thus some subjectivity. In this paper, we consider empirical mode decomposition (EMD) and the Hilbert transform as an alternative tool for analyzing oil-film interferograms. In contrast to the commonly used Fourier-based techniques, this new method is less subjective and, as it is based on the Hilbert transform, is superior for treating amplitude and frequency modulated data. This makes it particularly robust to wide differences in the quality of interferograms
A two-step Hilbert transform method for 2D image reconstruction
International Nuclear Information System (INIS)
Noo, Frederic; Clackdoyle, Rolf; Pack, Jed D
2004-01-01
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fan-beam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained
Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform
Zheng, Yang; Chen, Xihao; Zhu, Rui
2017-07-01
Frequency hopping (FH) signal is widely adopted by military communications as a kind of low probability interception signal. Therefore, it is very important to research the FH signal detection algorithm. The existing detection algorithm of FH signals based on the time-frequency analysis cannot satisfy the time and frequency resolution requirement at the same time due to the influence of window function. In order to solve this problem, an algorithm based on wavelet decomposition and Hilbert-Huang transform (HHT) was proposed. The proposed algorithm removes the noise of the received signals by wavelet decomposition and detects the FH signals by Hilbert-Huang transform. Simulation results show the proposed algorithm takes into account both the time resolution and the frequency resolution. Correspondingly, the accuracy of FH signals detection can be improved.
Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space
Cao, ChunJun; Carroll, Sean M.
2018-04-01
We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.
Directory of Open Access Journals (Sweden)
Isti Qomah
2017-01-01
Full Text Available Kerusakan batang rotor merupakan salah satu jenis kerusakan pada motor induksi yang dapat menyebabkan masalah serius. Kerusakan tersebut dapat mencapai 5% - 10% dari seluruh kasus gangguan motor induksi. Oleh karena itu, perlu adanya diagnosis awal yang mendeteksi adanya gangguan pada rotor motor induksi, agar dapat dilakukan perbaikan lebih cepat dan tanggap sebelum terjadi gangguan yang lebih besar. Tugas Akhir ini membahas terkait teknik deteksi kerusakan batang rotor pada motor induksi dengan menggunakan analisis arus mula. Sistem yang digunakan berbasis decomposition wavelet transform terlebih dahulu kemudian dilanjutkan dengan analisis berbasis hilbert transform sebagai perangkat pengolahan sinyal sehingga mampu mendeteksi motor dalam keadaan sehat atau mengalami kerusakan. Pengujian sistem dilakukan dalam beberapa kondisi, yaitu kondisi tanpa beban dan berbeban. Selain itu, kondisi yang diberikan adalah kecacatan mulai dai 1BRB hingga 3BRB. Hasil pengujian membuktikan bahwa decomposition wavelet transform dan Hilbert transform mampu mendeteksi perbedaan kondisi pada motor induksi normal ataupun rusak pada batang rotor.
Explicit solution of Riemann-Hilbert problems for the Ernst equation
Klein, C.; Richter, O.
1998-01-01
Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.
International Nuclear Information System (INIS)
Liu, Yangqing; Tan, Yi; Xie, Huiqiao; Wang, Wenhao; Gao, Zhe
2014-01-01
An improved Hilbert-Huang transform method is developed to the time-frequency analysis of non-stationary signals in tokamak plasmas. Maximal overlap discrete wavelet packet transform rather than wavelet packet transform is proposed as a preprocessor to decompose a signal into various narrow-band components. Then, a correlation coefficient based selection method is utilized to eliminate the irrelevant intrinsic mode functions obtained from empirical mode decomposition of those narrow-band components. Subsequently, a time varying vector autoregressive moving average model instead of Hilbert spectral analysis is performed to compute the Hilbert spectrum, i.e., a three-dimensional time-frequency distribution of the signal. The feasibility and effectiveness of the improved Hilbert-Huang transform method is demonstrated by analyzing a non-stationary simulated signal and actual experimental signals in fusion plasmas
Controlled G-Frames and Their G-Multipliers in Hilbert spaces
Rahimi, Asghar; Fereydooni, Abolhassan
2012-01-01
Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and synthesis. Weighted and controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator Also g-frames are the most popular generalization of frames that include almost all of the frame extens...
A simple proof to an extension of a theorem of A. Pazy in Hilbert space
International Nuclear Information System (INIS)
Djafari Rouhani, B.
1990-08-01
We prove that if (x n ) n≥0 is a non expansive sequence in a Hilbert space H, the sequence ( n x n ) n≥1 converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (x n+1 -x n ) n≥0 . This result was previously proved; the proof we give here is even much simpler and can be extended to a Banach space. 29 refs
Response to the Comment by G. Emch on projective group representations in quaternionic Hilbert space
International Nuclear Information System (INIS)
Adler, S.L.
1996-01-01
We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations. copyright 1996 American Institute of Physics
Apisa, Paul
2017-01-01
We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varying families of points over orbifold covers of genus two Hilbert modular surfaces, solve the finite blocking problem on genus two translation surfaces, and show that there is at ...
Bazargani, Hamed Pishvai; Burla, Maurizio; Chrostowski, Lukas; Azaña, José
2016-11-01
We experimentally demonstrate high-performance integer and fractional-order photonic Hilbert transformers based on laterally apodized Bragg gratings in a silicon-on-insulator technology platform. The sub-millimeter-long gratings have been fabricated using single-etch electron beam lithography, and the resulting HT devices offer operation bandwidths approaching the THz range, with time-bandwidth products between 10 and 20.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, using...... the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space
Petkova, Violeta
2006-01-01
A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Energy Technology Data Exchange (ETDEWEB)
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
International Nuclear Information System (INIS)
Agaltsov, A. D.; Novikov, R. G.
2014-01-01
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given
Nonrelativistic multichannel quantum scattering theory in a two Hilbert space formulation
International Nuclear Information System (INIS)
Chandler, C.
1977-08-01
A two-Hilbert-space form of an abstract scattering theory specifically applicable to multichannel quantum scattering problems is outlined. General physical foundations of the theory are reviewed. Further topics discussed include the invariance principle, asymptotic completeness of the wave operators, representations of the scattering operator in terms of transition operators and fundamental equations that these transition operators satisfy. Outstanding problems, including the difficulties of including Coulomb interactions in the theory, are pointed out. (D.P.)
Vertex operators, non-abelian orbifolds and the Riemann-Hilbert problem
International Nuclear Information System (INIS)
Gato, B.; Massachusetts Inst. of Tech., Cambridge
1990-01-01
We show how to construct the oscillator part of vertex operators for the bosonic string moving on non-abelian orbifolds, using the conserved charges method. When the three-string vertices are twisted by non-commuting group elements, the construction of the conserved charges becomes the Riemann-Hilbert problem with monodromy matrices given by the twists. This is solvable for any given configuration and any non-abelian orbifold. (orig.)
Approximately dual frames in Hilbert spaces and applications to Gabor frames
Christensen, Ole; Laugesen, Richard S.
2011-01-01
Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames, by using the Walnut representation of the frame operator to estimate the deviation from equality in...
Estimates of solutions of certain classes of second-order differential equations in a Hilbert space
International Nuclear Information System (INIS)
Artamonov, N V
2003-01-01
Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained
Limit distribution function of inhomogeneities in regions with random boundary in the Hilbert space
International Nuclear Information System (INIS)
Rasulova, M.Yu.; Tashpulatov, S.M.
2004-10-01
The interaction of charged particle systems with a membrane consisting of nonhomogeneities which are randomly distributed by the same law in the vicinity of appropriate sites of a planax crystal lattice is studied. A system of equations for the self-consistent potential U 1 (x,ξ 0 ,..., ξ N ,...) and the density of induced charges σ(x,ξ 0 ,...,ξ N ,...) is solved on Hilbert space. (author)
Hilbert spaces contractively included in the Hardy space of the bidisk
Alpay, D.; Bolotnikov, V.; Dijksma, A.; Sadosky, C.
We study the reproducing kernel Hilbert spaces h(D-2,S) with kernels of the form I-S(z(1),z(2)>)S(w(1),w(2))*/(1-z(1)w(1)*) (1-z(2)w(2)*) where S(z(1),z(2)) is a Schur function of two variables z(1),z(2)is an element of D. They are analogs of the spaces h(D,S) with reproducing kernel
INFORMATIVE ENERGY METRIC FOR SIMILARITY MEASURE IN REPRODUCING KERNEL HILBERT SPACES
Directory of Open Access Journals (Sweden)
Songhua Liu
2012-02-01
Full Text Available In this paper, information energy metric (IEM is obtained by similarity computing for high-dimensional samples in a reproducing kernel Hilbert space (RKHS. Firstly, similar/dissimilar subsets and their corresponding informative energy functions are defined. Secondly, IEM is proposed for similarity measure of those subsets, which converts the non-metric distances into metric ones. Finally, applications of this metric is introduced, such as classification problems. Experimental results validate the effectiveness of the proposed method.
Quantum limits to information about states for finite dimensional Hilbert space
International Nuclear Information System (INIS)
Jones, K.R.W.
1990-01-01
A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs
Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories
Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto
2014-01-01
This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.
Directory of Open Access Journals (Sweden)
George Isac
2004-01-01
Full Text Available In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.
Alpay, Daniel
2015-01-01
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
Cai, Jianhua
2017-05-01
The time-frequency analysis method represents signal as a function of time and frequency, and it is considered a powerful tool for handling arbitrary non-stationary time series by using instantaneous frequency and instantaneous amplitude. It also provides a possible alternative to the analysis of the non-stationary magnetotelluric (MT) signal. Based on the Hilbert-Huang transform (HHT), a time-frequency analysis method is proposed to obtain stable estimates of the magnetotelluric response function. In contrast to conventional methods, the response function estimation is performed in the time-frequency domain using instantaneous spectra rather than in the frequency domain, which allows for imaging the response parameter content as a function of time and frequency. The theory of the method is presented and the mathematical model and calculation procedure, which are used to estimate response function based on HHT time-frequency spectrum, are discussed. To evaluate the results, response function estimates are compared with estimates from a standard MT data processing method based on the Fourier transform. All results show that apparent resistivities and phases, which are calculated from the HHT time-frequency method, are generally more stable and reliable than those determined from the simple Fourier analysis. The proposed method overcomes the drawbacks of the traditional Fourier methods, and the resulting parameter minimises the estimation bias caused by the non-stationary characteristics of the MT data.
International Nuclear Information System (INIS)
Iwamoto, Hiroyuki; Tanaka, Nobuo; Hill, Simon G
2010-01-01
This paper concerns the active vibration control of a rectangular panel using smart sensors from the viewpoint of an active wave control theory. The objective of this paper is to present a new type of filter which enables the measurement of the wave amplitude of a rectangular panel in real time for the application of an adaptive feedforward control system which inactivates vibration modes. Firstly, a novel wave filtering method using smart PVDF sensors is proposed. It is found that the shaping function of smart sensors is a complex function. To realize the smart sensor in a practical situation, a Hilbert transformer is utilized to implement a phase shifter of 90° for broadband frequencies. Then, from the viewpoint of a numerical analysis, the characteristics of the proposed wave filter and the performance of the adaptive feedforward control system using the wave filter are discussed. Finally, experiments implementing the active wave control theory which uses the proposed wave filter are conducted, demonstrating the validity of the proposed method in suppressing the vibration of a rectangular panel
International Nuclear Information System (INIS)
Li, Yan Jun; Lee, Seung Hwan; Kinoshita, Yukinori; Wen, Huanfei; Naitoh, Yoshitaka; Sugawara, Yasuhiro; Ma, Zong Min; Nomura, Hikaru
2016-01-01
We present an experimental study of coexisting p(2 × 1) and c(6 × 2) phases on an oxygen-terminated Cu(110) surface by noncontact atomic force microscopy (NC-AFM) at 78 K. Ball models of the growth processes of coexisting p(2 × 1)/c(6 × 2) phases on a terrace and near a step are proposed. We found that the p(2 × 1) and c(6 × 2) phases are grown from the super Cu atoms on both sides of O–Cu–O rows of an atomic spacing. In this paper, we summarize our investigations of an oxygen-terminated Cu(110) surface by NC-AFM employing O- and Cu-terminated tips. Also, we state several problems and issues for future investigation. (paper)
Electron microscopy in metallurgy
International Nuclear Information System (INIS)
Loretto, M.H.
1980-01-01
The aim of this paper is to review briefly the contribution which (TEM) transmission electron microscopy (including high voltage electron microscopy (HVEM)) has made to metallurgy. Since it is straightforward with modern electron microscopes to extract the crystallographic information which provides the basis for any interpretation, the major problem in most metallurgical work lies in assessing how the structure (which TEM has characterised) has arisen and which properties of the specimen can be understood in terms of this structure. Radiation damage, quenching, phase transformations, grain boundaries and plastic deformation have been the main fields in which TEM has contributed significantly. After briefly summarising the role of TEM in each field, examples of recent work will be used to indicate current TEM activity in physical metallurgy. (author)
Effective realistic interactions for low momentum Hilbert spaces
International Nuclear Information System (INIS)
Weber, Dennis
2012-01-01
Realistic nucleon-nucleon potentials are an essential ingredient of modern microscopic many-body calculations. These potentials can be represented in two different ways: operator representation or matrix element representation. In operator representation the potential is represented by a set of quantum mechanical operators while in matrix element representation it is defined by the matrix elements in a given basis. Many modern potentials are constructed directly in matrix element representation. While the matrix element representation can be calculated from the operator representation, the determination of the operator representation from the matrix elements is more difficult. Some methods to solve the nuclear many-body problem, such as Fermionic Molecular Dynamics (FMD) or the Green's Function Monte Carlo (GFMC) method, however require explicitly the operator representation of the potential, as they do not work in a fixed many-body basis. It is therefore desirable to derive an operator representation also for the interactions given by matrix elements. In this work a method is presented which allows the derivation of an approximate operator representation starting from the momentum space partial wave matrix elements of the interaction. For that purpose an ansatz for the operator representation is chosen. The parameters in the ansatz are determined by a fit to the partial wave matrix elements. Since a perfect reproduction of the matrix elements in general cannot be achieved with a finite number of operators and the quality of the results depends on the choice of the ansatz, the obtained operator representation is tested in nuclear many-body calculations and the results are compared with those from the initial interaction matrix elements. For the calculation of the nucleon-nucleon scattering phase shifts and the deuteron properties a computer code written within this work is used. For larger nuclei the No Core Shell Model (NCSM) and FMD are applied. The described
Directory of Open Access Journals (Sweden)
Juan Ospina
2006-12-01
Full Text Available Hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. An adaptation of Tien D. Kieu¿s quantum hypercomputational algorithm is carried out for the dynamical algebra su(1, 1 of the Poschl-Teller potentials. The classically incomputable problem that is resolved with this hypercomputational algorithm is Hilbert¿s tenth problem. We indicated that an essential mathematical condition of these algorithms is the existence of infinitedimensional unitary irreducible representations of low dimensional dynamical algebras that allow the construction of coherent states of the Barut-Girardello type. In addition, we presented as a particular case of our hypercomputational algorithm on Poschl-Teller potentials, the hypercomputational algorithm on an infinite square well presented previously by the authors.Los hipercomputadores computan funciones o números, o en general solucionan problemas que no pueden ser computados o solucionados por una máquina de Turing. Se presenta una adaptación del algoritmo cuántico hipercomputacional propuesto por Tien D. Kieu, al álgebra dinámica su(1, 1 realizada en los potenciales Pöschl-Teller. El problema clásicamente incomputable que se resuelve con este algoritmo hipercomputacional es el d´ecimo problema de Hilbert. Se señala que una condición matemática fundamental para estos algoritmos es la existencia de una representación unitaria infinito dimensional irreducible de álgebras de baja dimensión que admitan la construcción de estados coherentes del tipo Barut-Girardello. Adicionalmente se presenta como caso límite del algoritmo propuesto sobre los potenciales Pöschl-Teller, el algoritmo hipercomputacional sobre la caja de potencial infinita construido previamente por los autores.
Directory of Open Access Journals (Sweden)
H. C. de Souza-Araújo
1955-12-01
Full Text Available Hansen's Bacillus: By electron microscopy this bacillus shows membrane and halo, this being more visible when sorrounding the globi or bundles of bacilli; shows, also, free granules of various sizes which were before considered as dust of the dyes; shows external granules bound with the membrane and some times branching. By phases contrast microscopy examining leproma suspensions and subcataneous lymph at 400 x we saw many free granules with intense rotatory movement; granulated bacilli with screw, skip or stroke motion, producing slow progressive motion. All such elementes are surrounded by a halo, corresponding to the classical gloea. By a patient and delayed examination we were able to see that the internal granules are motile and help the progression of the bacilli, giving the impression that the cytoplasm is liquid. By a lasting observation we could see the larger granules form prolapse, like a pseudopode and abandon the bacilli and going in very rapid rotatory movement. There are branched bacilli; there are pedunculated fred granules like comets. The addition of a drop of formol at the preparation stops all movements. Stefansky's Bacillus: Repeated examination by RCA electron microscope, type EMU-25 of fresh suspensions of rat lepromas, led us to confirm the close relationship between human and murine leprosy agents. We examined also material from carabo (Lepra bubalorum from Java, but due to fixation, the material was unsuitable for comparative studies. The Stefansky's bacilli showed also emmbranes and halos, internal or external granules (smaller than those of Hansen's bacillus. The bacilli shaded by chromium look thicker and shorter than those of Hansen. Due to electron bombardment both, Hansen's and Stefansky's baccilli suffer considerable alterations in their structure, showing black barrs of chromatin condensation at their extremities as also in their centers. By phase microscopy the Stefansky's bacilli showed elements with 1, 2
Peckys, Diana B; Stoerger, Christof; Latta, Lorenz; Wissenbach, Ulrich; Flockerzi, Veit; de Jonge, Niels
2017-08-01
TMEM16A is a membrane protein forming a calcium-activated chloride channel. A homodimeric stoichiometry of the TMEM16 family of proteins has been reported but an important question is whether the protein resides always in a dimeric configuration in the plasma membrane or whether monomers of the protein are also present in its native state within in the intact plasma membrane. We have determined the stoichiometry of the human (h)TMEM16A within whole COS-7 cells in liquid. For the purpose of detecting TMEM16A subunits, single proteins were tagged by the streptavidin-binding peptide within extracellular loops accessible by streptavidin coated quantum dot (QD) nanoparticles. The labeled proteins were then imaged using correlative light microscopy and environmental scanning electron microscopy (ESEM) using scanning transmission electron microscopy (STEM) detection. The locations of 19,583 individual proteins were determined of which a statistical analysis using the pair correlation function revealed the presence of a dimeric conformation of the protein. The amounts of detected label pairs and single labels were compared between experiments in which the TMEM16A SBP-tag position was varied, and experiments in which tagged and non-tagged TMEM16A proteins were present. It followed that hTMEM16A resides in the plasma membrane as dimer only and is not present as monomer. This strategy may help to elucidate the stoichiometry of other membrane protein species within the context of the intact plasma membrane in future. Copyright © 2017 Elsevier Inc. All rights reserved.
Quantum computation via local control theory: Direct sum vs. direct product Hilbert spaces
International Nuclear Information System (INIS)
Sklarz, Shlomo E.; Tannor, David J.
2006-01-01
The central objective in any quantum computation is the creation of a desired unitary transformation; the mapping that this unitary transformation produces between the input and output states is identified with the computation. In [S.E. Sklarz, D.J. Tannor, arXiv:quant-ph/0404081 (submitted to PRA) (2004)] it was shown that local control theory can be used to calculate fields that will produce such a desired unitary transformation. In contrast with previous strategies for quantum computing based on optimal control theory, the local control scheme maintains the system within the computational subspace at intermediate times, thereby avoiding unwanted decay processes. In [S.E. Sklarz et al.], the structure of the Hilbert space had a direct sum structure with respect to the computational register and the mediating states. In this paper, we extend the formalism to the important case of a direct product Hilbert space. The final equations for the control algorithm for the two cases are remarkably similar in structure, despite the fact that the derivations are completely different and that in one case the dynamics is in a Hilbert space and in the other case the dynamics is in a Liouville space. As shown in [S.E. Sklarz et al.], the direct sum implementation leads to a computational mechanism based on virtual transitions, and can be viewed as an extension of the principles of Stimulated Raman Adiabatic Passage from state manipulation to evolution operator manipulation. The direct product implementation developed here leads to the intriguing concept of virtual entanglement - computation that exploits second-order transitions that pass through entangled states but that leaves the subsystems nearly separable at all intermediate times. Finally, we speculate on a connection between the algorithm developed here and the concept of decoherence free subspaces
Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.
Stępień, Grzegorz
2018-03-17
The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.
Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space
Directory of Open Access Journals (Sweden)
Grzegorz Stępień
2018-03-01
Full Text Available The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems—interior and exterior orientation of sensors—to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data. The accuracy of the results in the laboratory test is on the level of 10−6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author’s 2017 Total Free Station (TFS transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation—MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.
Foundations of phase-space quantum mechanics
International Nuclear Information System (INIS)
Guz, W.
1984-01-01
In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper. (author)
Construction of rigged Hilbert spaces to describe resonances and virtual states
International Nuclear Information System (INIS)
Gadella, M.
1983-01-01
In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t > 0 and the other for t < 0, hence showing the irreversibility of the decaying process
DEFF Research Database (Denmark)
Vincent, Claire Louise; Giebel, Gregor; Pinson, Pierre
2010-01-01
a 4-yr time series of 10-min wind speed observations. An adaptive spectral analysis method called the Hilbert–Huang transform is chosen for the analysis, because the nonstationarity of time series of wind speed observations means that they are not well described by a global spectral analysis method...... such as the Fourier transform. The Hilbert–Huang transform is a local method based on a nonparametric and empirical decomposition of the data followed by calculation of instantaneous amplitudes and frequencies using the Hilbert transform. The Hilbert–Huang transformed 4-yr time series is averaged and summarized...
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
Directory of Open Access Journals (Sweden)
Juguo Su
2012-01-01
Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.
Tang, Shaojie; Yang, Yi; Tang, Xiangyang
2012-01-01
Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner. The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small
An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field
International Nuclear Information System (INIS)
Vostokov, S V; Lorenz, F
2003-01-01
Based on the pairing on Cartier curves explicitly constructed in the previous paper of the authors, an explicit formula for the Hilbert symbol is constructed in a multidimensional local field of characteristic zero with residue field of positive characteristic on the formal module of a one-dimensional Honda formal group. In the proof a Shafarevich basis on the formal module is constructed, and so-called integer μ-modules in two-dimensional local rings of a special form ( μ-rings) are studied
Directory of Open Access Journals (Sweden)
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Construction of rigged Hilbert spaces to describe resonances and virtual states
International Nuclear Information System (INIS)
Gadella, M.
1984-01-01
In the present communication we present a mathematical formalism for the description of resonances and virtual states. We start by constructing rigged Hilbert spaces of Hardy class functions restricted to the positive half of the real line. Then resonances and virtual states can be written as generalized eigenvectors of the total Hamiltonian. We also define time evolution on functionals. We see that the time evolution group U(t) splits into two semigroups, one for t>0 and the other for t<0, hence showing the irreversibility of the decaying process. (orig.)
Vogt, Dominik Walter; Leonhardt, Rainer
2017-07-10
We report on data processing for continuous wave (CW) terahertz (THz) spectroscopy measurements based on a Hilbert spectral analysis to achieve MHz resolution. As an example we investigate the spectral properties of a whispering gallery mode (WGM) THz bubble resonator at critical coupling. The experimental verification clearly demonstrates the significant advantages in relative frequency resolution and required acquisition time of the proposed method over the traditional data analysis. An effective frequency resolution, only limited by the precision and stability of the laser beat signal, can be achieved without complex extensions to a standard commercially available CW THz spectrometer.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
2011-01-01
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers...... in a totally real field of degree n over with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
On knottings in the physical Hilbert space of LQG as given by the EPRL model
International Nuclear Information System (INIS)
Bahr, Benjamin
2011-01-01
We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that the physical Hilbert space, as defined by the sum over all spin foams, contains no information about knotting classes of graphs anymore.
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Michael; Gribonval, Remi
2017-01-01
We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to Rm that satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP with high probability. We also describe a generic technique ...
Recipes for stable linear embeddings from Hilbert spaces to R^m
Puy, Gilles; Davies, Mike; Gribonval, Rémi
2015-01-01
We consider the problem of constructing a linear map from a Hilbert space $\\mathcal{H}$ (possibly infinite dimensional) to $\\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\\mathcal{S} \\subset \\mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\\mathcal{S}$ with h...
Diagonalization of a self-adjoint operator acting on a Hilbert module
Directory of Open Access Journals (Sweden)
Parfeny P. Saworotnow
1985-01-01
Full Text Available For each bounded self-adjoint operator T on a Hilbert module H over an H*-algebra A there exists a locally compact space m and a certain A-valued measure μ such that H is isomorphic to L2(μ⊗A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.
The kinematical Hilbert space of loop quantum gravity from BF theories
International Nuclear Information System (INIS)
Cianfrani, Francesco
2011-01-01
In this work, it is demonstrated how the kinematical Hilbert space of loop quantum gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations are discussed.
An Hilbert space approach for a class of arbitrage free implied volatilities models
Brace, A.; Fabbri, G.; Goldys, B.
2007-01-01
We present an Hilbert space formulation for a set of implied volatility models introduced in \\cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface ${\\hat\\sigma}_t(T,K)$. We will focus on the family obtained fixing a strike $K$ and varying $T$. In order to...
A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line
Its, A.; Sukhanov, V.
2016-05-01
The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.
Four-nucleon problem in terms of scattering of Hilbert-Schmidt resonances
International Nuclear Information System (INIS)
Narodetsky, I.M.
1974-01-01
The four-body integral equations are written in terms of the scattering amplitudes for the Hilbert-Schmidt resonances corresponding to the 3*1 and 2*2 subsystems. As a result, the four-body problem is reduced to the many channel two-body problem. A simple diagram technique is introduced which is the generalization of the usual time-ordered nonrelativistic one. The connection between the amplitudes of the two-body reactions and the scattering amplitudes for the resonances is obtained
Riemann-Hilbert approach to the time-dependent generalized sine kernel
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann-Hilbert based analysis. (orig.)
Frandsen, Athela F.
2016-01-01
Polarized light microscopy (PLM) is a technique which employs the use of polarizing filters to obtain substantial optical property information about the material which is being observed. This information can be combined with other microscopy techniques to confirm or elucidate the identity of an unknown material, determine whether a particular contaminant is present (as with asbestos analysis), or to provide important information that can be used to refine a manufacturing or chemical process. PLM was the major microscopy technique in use for identification of materials for nearly a century since its introduction in 1834 by William Fox Talbot, as other techniques such as SEM (Scanning Electron Microscopy), FTIR (Fourier Transform Infrared spectroscopy), XPD (X-ray Powder Diffraction), and TEM (Transmission Electron Microscopy) had not yet been developed. Today, it is still the only technique approved by the Environmental Protection Agency (EPA) for asbestos analysis, and is often the technique first applied for identification of unknown materials. PLM uses different configurations in order to determine different material properties. With each configuration additional clues can be gathered, leading to a conclusion of material identity. With no polarizing filter, the microscope can be used just as a stereo optical microscope, and view qualities such as morphology, size, and number of phases. With a single polarizing filter (single polars), additional properties can be established, such as pleochroism, individual refractive indices, and dispersion staining. With two polarizing filters (crossed polars), even more can be deduced: isotropy vs. anisotropy, extinction angle, birefringence/degree of birefringence, sign of elongation, and anomalous polarization colors, among others. With the use of PLM many of these properties can be determined in a matter of seconds, even for those who are not highly trained. McCrone, a leader in the field of polarized light microscopy, often
Xu, Wenjun; Tang, Chen; Su, Yonggang; Li, Biyuan; Lei, Zhenkun
2018-02-01
In this paper, we propose an image decomposition model Shearlet-Hilbert-L 2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L 2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet-Hilbert-L 2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet-Hilbert-L 2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL-Hilbert-L 2 .
Energy Technology Data Exchange (ETDEWEB)
Martínez, Javier A. [Instituto de Ciencia y Tecnología de Materiales (IMRE), Universidad de La Habana, Zapata y G, El Vedado, Plaza de la Revolución, La Habana 10400 (Cuba); Valenzuela B, José [Centro de Nanociencias y Nanotecnología (CNyN), Universidad Nacional Autónoma de México (UNAM) , km 107 Carretera Tijuana-Ensenada, Ensenada, BC 22860 (Mexico); Cao Milán, R. [Facultad de Química, Universidad de La Habana, Zapata y G, El Vedado, Plaza de la Revolución, La Habana 10400 (Cuba); Herrera, José [Instituto de Ciencia y Tecnología de Materiales (IMRE), Universidad de La Habana, Zapata y G, El Vedado, Plaza de la Revolución, La Habana 10400 (Cuba); Farías, Mario H. [Centro de Nanociencias y Nanotecnología (CNyN), Universidad Nacional Autónoma de México (UNAM) , km 107 Carretera Tijuana-Ensenada, Ensenada, BC 22860 (Mexico); Hernández, Mayra P., E-mail: mayrap@fisica.uh.cu [Instituto de Ciencia y Tecnología de Materiales (IMRE), Universidad de La Habana, Zapata y G, El Vedado, Plaza de la Revolución, La Habana 10400 (Cuba)
2014-11-30
Highlights: • New phases of sulfur on gold: hexamer and (√(2)×√(2)) were observed by STM. • Hexamers and (√(2)×√(2)) structures coexist with well-known octomers. • Formation of sulfur multilayer by K{sub 2}DTC{sub 2}pz hydrolysis under alkaline condition. • Top octomer layer have dynamic behavior while (√(2)×√(2)) and hexamer were static. • A model is presented to explain sulfur multilayer formation on Au(100). - Abstract: Piperazine-dithiocarbamate of potassium (K{sub 2}DTC{sub 2}pz) was used as a new precursor for the spontaneous deposition of sulfur on the Au(100) surface in alkaline solution. Two new sulfur phases were studied by scanning tunneling microscopy (STM). These phases were formed by six sulfur atoms (S{sub 6} phase, hexamer) and by four sulfur atoms (S{sub 4} phase, tetramer with (√(2)×√(2)) structure), and they were observed in coexistence with the well-known quasi-square patterns formed by eight sulfur atoms (S{sub 8} phase, octomer). A model was proposed where sulfur multilayers were formed by a (√(2)×√(2)) phase adsorbed directly on the gold surface while one of the other structures: hexamers or octomers were deposited on top. Sulfur layers were formed on gold terraces, vacancies and islands produced by lifting reconstructed surface. Sequential high-resolution STM images allowed the direct observation of the dynamic of the octomers, while the (√(2)×√(2)) structure remained static. Images also showed the reversible association/dissociation of the octomer.
International Nuclear Information System (INIS)
Martínez, Javier A.; Valenzuela B, José; Cao Milán, R.; Herrera, José; Farías, Mario H.; Hernández, Mayra P.
2014-01-01
Highlights: • New phases of sulfur on gold: hexamer and (√(2)×√(2)) were observed by STM. • Hexamers and (√(2)×√(2)) structures coexist with well-known octomers. • Formation of sulfur multilayer by K 2 DTC 2 pz hydrolysis under alkaline condition. • Top octomer layer have dynamic behavior while (√(2)×√(2)) and hexamer were static. • A model is presented to explain sulfur multilayer formation on Au(100). - Abstract: Piperazine-dithiocarbamate of potassium (K 2 DTC 2 pz) was used as a new precursor for the spontaneous deposition of sulfur on the Au(100) surface in alkaline solution. Two new sulfur phases were studied by scanning tunneling microscopy (STM). These phases were formed by six sulfur atoms (S 6 phase, hexamer) and by four sulfur atoms (S 4 phase, tetramer with (√(2)×√(2)) structure), and they were observed in coexistence with the well-known quasi-square patterns formed by eight sulfur atoms (S 8 phase, octomer). A model was proposed where sulfur multilayers were formed by a (√(2)×√(2)) phase adsorbed directly on the gold surface while one of the other structures: hexamers or octomers were deposited on top. Sulfur layers were formed on gold terraces, vacancies and islands produced by lifting reconstructed surface. Sequential high-resolution STM images allowed the direct observation of the dynamic of the octomers, while the (√(2)×√(2)) structure remained static. Images also showed the reversible association/dissociation of the octomer
International Nuclear Information System (INIS)
Kraft, G.; Yang, T.C.H.; Richards, T.; Tobias, C.A.
1980-01-01
This chapter briefly describes the techniques of optical microscopy, scanning and transmission electron microscopy, soft x-ray microscopy and compares these latter techniques with heavy-ion microscopy. The resolution obtained with these various types of microscopy are compared and the influence of the etching procedure on total resolution is discussed. Several micrographs of mammalian cells are included
Energy Technology Data Exchange (ETDEWEB)
Krumeich, F., E-mail: krumeich@inorg.chem.ethz.ch [Laboratory of Inorganic Chemistry, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich (Switzerland); Mueller, E.; Wepf, R.A. [Electron Microscopy ETH Zurich (EMEZ), Wolfgang-Pauli-Strasse 16, 8093 Zurich (Switzerland); Conrad, M.; Reich, C.; Harbrecht, B. [Department of Chemistry and Centre of Materials Science, Philipps-Universitaet, Hans-Meerwein-Strasse, 35032 Marburg (Germany); Nesper, R. [Laboratory of Inorganic Chemistry, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich (Switzerland)
2012-10-15
While HRTEM is the well-established method to characterize the structure of dodecagonal tantalum (vanadium) telluride quasicrystals and their periodic approximants, phase-contrast imaging performed on an aberration-corrected scanning transmission electron microscope (STEM) represents a favorable alternative. The (Ta,V){sub 151}Te{sub 74} clusters, the basic structural unit in all these phases, can be visualized with high resolution. A dependence of the image contrast on defocus and specimen thickness has been observed. In thin areas, the projected crystal potential is basically imaged with either dark or bright contrast at two defocus values close to Scherzer defocus as confirmed by image simulations utilizing the principle of reciprocity. Models for square-triangle tilings describing the arrangement of the basic clusters can be derived from such images. - Graphical abstract: PC-STEM image of a (Ta,V){sub 151}Te{sub 74} cluster. Highlights: Black-Right-Pointing-Pointer C{sub s}-corrected STEM is applied for the characterization of dodecagonal quasicrystals. Black-Right-Pointing-Pointer The projected potential of the structure is mirrored in the images. Black-Right-Pointing-Pointer Phase-contrast STEM imaging depends on defocus and thickness. Black-Right-Pointing-Pointer For simulations of phase-contrast STEM images, the reciprocity theorem is applicable.
International Nuclear Information System (INIS)
Famy, C.; Brough, A.R.; Taylor, H.F.W.
2003-01-01
Scanning electron microscopy (SEM) microanalyses of the calcium-silicate-hydrate (C-S-H) gel in Portland cement pastes rarely represent single phases. Essential experimental requirements are summarised and new procedures for interpreting the data are described. These include, notably, plots of Si/Ca against other atom ratios, 3D plots to allow three such ratios to be correlated and solution of linear simultaneous equations to test and quantify hypotheses regarding the phases contributing to individual microanalyses. Application of these methods to the C-S-H gel of a 1-day-old mortar identified a phase with Al/Ca=0.67 and S/Ca=0.33, which we consider to be a highly substituted ettringite of probable composition C 6 A 2 S-bar 2 H 34 or {Ca 6 [Al(OH) 6 ] 2 ·24H 2 O}(SO 4 ) 2 [Al(OH) 4 ] 2 . If this is true for Portland cements in general, it might explain observed discrepancies between observed and calculated aluminate concentrations in the pore solution. The C-S-H gel of a similar mortar aged 600 days contained unsubstituted ettringite and an AFm phase with S/Ca=0.125
The solution of the sixth Hilbert problem: the ultimate Galilean revolution
D'Ariano, Giacomo Mauro
2018-04-01
I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.
Energy Technology Data Exchange (ETDEWEB)
Huang, Xianjun, E-mail: xianjun.huang@manchester.ac.uk [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom); College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China); Hu, Zhirun [School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL (United Kingdom); Liu, Peiguo [College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China)
2014-11-15
This paper proposes a new type of graphene based tunable radar absorbing screen. The absorbing screen consists of Hilbert curve metal strip array and chemical vapour deposition (CVD) graphene sheet. The graphene based screen is not only tunable when the chemical potential of the graphene changes, but also has broadband effective absorption. The absorption bandwidth is from 8.9GHz to 18.1GHz, ie., relative bandwidth of more than 68%, at chemical potential of 0eV, which is significantly wider than that if the graphene sheet had not been employed. As the chemical potential varies from 0 to 0.4eV, the central frequency of the screen can be tuned from 13.5GHz to 19.0GHz. In the proposed structure, Hilbert curve metal strip array was designed to provide multiple narrow band resonances, whereas the graphene sheet directly underneath the metal strip array provides tunability and averagely required surface resistance so to significantly extend the screen operation bandwidth by providing broadband impedance matching and absorption. In addition, the thickness of the screen has been optimized to achieve nearly the minimum thickness limitation for a nonmagnetic absorber. The working principle of this absorbing screen is studied in details, and performance under various incident angles is presented. This work extends applications of graphene into tunable microwave radar cross section (RCS) reduction applications.
Directory of Open Access Journals (Sweden)
Yaqeen S Mezaal
Full Text Available This paper presents new Wide Bandpass Filter (WBPF and Narrow Bandstop Filter (NBSF incorporating two microstrip resonators, each resonator is based on 2nd iteration of Hilbert fractal geometry. The type of filter as pass or reject band has been adjusted by coupling gap parameter (d between Hilbert resonators using a substrate with a dielectric constant of 10.8 and a thickness of 1.27 mm. Numerical simulation results as well as a parametric study of d parameter on filter type and frequency responses are presented and studied. WBPF has designed at resonant frequencies of 2 and 2.2 GHz with a bandwidth of 0.52 GHz, -28 dB return loss and -0.125 dB insertion loss while NBSF has designed for electrical specifications of 2.37 GHz center frequency, 20 MHz rejection bandwidth, -0.1873 dB return loss and 13.746 dB insertion loss. The proposed technique offers a new alternative to construct low-cost high-performance filter devices, suitable for a wide range of wireless communication systems.
Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius
Rabounski, Dmitri; Borissova, Larissa
2010-04-01
Consider space inside a sphere of incompressible liquid, and space surrounding a mass-point. Metrics of the spaces were deduced in 1916 by Karl Schwarzschild. 1) Our calculation shows that a liquid sphere can be in the state of gravitational collapse (g00 = 0) only if its mass and radius are close to those of the Universe (M = 8.7x10^55 g, a = 1.3x10^28 cm). However if the same mass is presented as a mass-point, the radius of collapse rg (Hilbert radius) is many orders lesser: g00 = 0 realizes in a mass-point's space by other conditions. 2) We considered a liquid sphere whose radius meets, formally, the Hilbert radius of a mass-point bearing the same mass: a = rg, however the liquid sphere is not a collapser (see above). We show that in this case the metric of the liquid sphere's internal space can be represented as de Sitter's space metric, wherein λ = 3/a^2 > 0: physical vacuum (due to the λ-term) is the same as the field of an ideal liquid where ρ0 0 (the mirror world liquid). The gravitational redshift inside the sphere is produced by the non-Newtonian force of repulsion (which is due to the λ-term, λ = 3/a^2 > 0); it is also calculated.
International Nuclear Information System (INIS)
Huang, Xianjun; Hu, Zhirun; Liu, Peiguo
2014-01-01
This paper proposes a new type of graphene based tunable radar absorbing screen. The absorbing screen consists of Hilbert curve metal strip array and chemical vapour deposition (CVD) graphene sheet. The graphene based screen is not only tunable when the chemical potential of the graphene changes, but also has broadband effective absorption. The absorption bandwidth is from 8.9GHz to 18.1GHz, ie., relative bandwidth of more than 68%, at chemical potential of 0eV, which is significantly wider than that if the graphene sheet had not been employed. As the chemical potential varies from 0 to 0.4eV, the central frequency of the screen can be tuned from 13.5GHz to 19.0GHz. In the proposed structure, Hilbert curve metal strip array was designed to provide multiple narrow band resonances, whereas the graphene sheet directly underneath the metal strip array provides tunability and averagely required surface resistance so to significantly extend the screen operation bandwidth by providing broadband impedance matching and absorption. In addition, the thickness of the screen has been optimized to achieve nearly the minimum thickness limitation for a nonmagnetic absorber. The working principle of this absorbing screen is studied in details, and performance under various incident angles is presented. This work extends applications of graphene into tunable microwave radar cross section (RCS) reduction applications
The solution of the sixth Hilbert problem: the ultimate Galilean revolution.
D'Ariano, Giacomo Mauro
2018-04-28
I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
International Nuclear Information System (INIS)
Wang, Zuo-Cai; Ren, Wei-Xin; Chen, Gen-Da
2012-01-01
This paper presents a recursive Hilbert transform method for the time-varying property identification of large-scale shear-type buildings with limited sensor deployments. An observer technique is introduced to estimate the building responses from limited available measurements. For an n-story shear-type building with l measurements (l ≤ n), the responses of other stories without measurements can be estimated based on the first r mode shapes (r ≤ l) as-built conditions and l measurements. Both the measured responses and evaluated responses and their Hilbert transforms are then used to track any variation of structural parameters of a multi-story building over time. Given floor masses, both the stiffness and damping coefficients of the building are identified one-by-one from the top to the bottom story. When variations of parameters are detected, a new developed branch-and-bound technique can be used to update the first r mode shapes with the identified parameters. A 60-story shear building with abruptly varying stiffness at different floors is simulated as an example. The numerical results indicate that the proposed method can detect variations of the parameters of large-scale shear-type buildings with limited sensor deployments at appropriate locations. (paper)
Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian
International Nuclear Information System (INIS)
Edelstein, Jose D.; Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge
2006-01-01
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like general relativity plus corrections due to matter sources, it is shown that the non-minimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions
From Kant to Hilbert a source book in the foundations of mathematics
Ewald, William Bragg
1996-01-01
This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume. - ;Immanuel Kant''s Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number. theory, analysis, logic and set theory--with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are repro...
Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations
Carbone, Francesco; Sorriso-Valvo, Luca; Alberti, Tommaso; Lepreti, Fabio; Chen, Christopher H. K.; Němeček, Zdenek; Šafránková, Jana
2018-05-01
The properties of inertial- and kinetic-range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size and to the presence of strong nonstationary behavior and large-scale structures, the classical analysis in terms of structure functions may prove to be unsuccessful in detecting the power-law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral-break scale. These results provide important constraints on models of kinetic-range turbulence in the solar wind.
Prediction of unknown deep foundation lengths using the Hilbert Huang Transform (HHT
Directory of Open Access Journals (Sweden)
Ahmed T.M. Farid
2012-08-01
Full Text Available Prediction of unknown deep foundation embedment depth is a great deal nowadays, especially in case of upgrading or rehabilitation of old structures. Many old bridges and marine or pier structures in the United States are established using deep foundations system of timber piles and their foundation records do not exist. Non-Destructive Testing (NDT or Non-Destructive Evaluation (NDE method for a great variety of materials and structures has become an integral part of many tests. However, the process of testing long piles, deeply embedded in the ground, is more complex than (NDT of the other structural materials. This paper summarizes some of the most common non-destructive test methods for deep foundations and presents a new method called the Hilbert Huang Transform (HHT. This Hilbert Huang Transform (HHT method is used now by a wide range in a different health monitoring of many systems. In this paper, some field tests on the timber Piles of one bridge at North Carolina was performed to verify the using the (HHT method for predicting the embedded depth of the unknown piles. Percentage of the accuracy achieved using HHT method for pile length compared to the actual pile length data was performed. Finally, a recommendation is presented for the limitation of using this new method as a new non-destructive method for deep foundations.
Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.
Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico
2013-04-01
The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].
Singh, S P; Kang, Sungsam; Kang, Jeon Woong; So, Peter T C; Dasari, Ramanchandra Rao; Yaqoob, Zahid; Barman, Ishan
2017-09-07
Minimizing morbidities and mortalities associated with skin cancers requires sustained research with the goal of obtaining fresh insights into disease onset and progression under specific stimuli, particularly the influence of ultraviolet rays. In the present study, label-free profiling of skin fibroblasts exposed to time-bound ultra-violet radiation has been performed using quantitative phase imaging and Raman spectroscopy. Statistically significant differences in quantifiable biophysical parameters, such as matter density and cell dry mass, were observed with phase imaging. Accurate estimation of changes in the biochemical constituents, notably nucleic acids and proteins, was demonstrated through a combination of Raman spectroscopy and multivariate analysis of spectral patterns. Overall, the findings of this study demonstrate the promise of these non-perturbative optical modalities in accurately identifying cellular phenotypes and responses to external stimuli by combining molecular and biophysical information.
International Nuclear Information System (INIS)
Beleggia, M.; Pozzi, G.
2001-01-01
An approach is presented for the calculation of the electron optical phase shift experienced by high-energy electrons in a transmission electron microscope, when they interact with the magnetic field associated with superconducting fluxons in a thin specimen tilted with respect to the beam. It is shown that by decomposing the vector potential in its Fourier components and by calculating the phase shift of each component separately, it is possible to obtain the Fourier transform of the electron optical phase shift, which can be inverted either analytically or numerically. It will be shown how this method can be used to recover the result, previously obtained by the real-space approach, relative to the case of a straight flux tube perpendicular to the specimen surfaces. Then the method is applied to the case of a London fluxon in a thin film, where the bending and the broadening of the magnetic-field lines due to the finite specimen thickness are now correctly taken into account and not treated approximately by means of a parabolic fit. Finally, it will be shown how simple models for the pancake structure of the fluxon can be analyzed within this framework and the main features of electron transmission images predicted
International Nuclear Information System (INIS)
Sengupta, S.K.; Nathan, N.P.; Ganesan, V.; Shome, S.
2005-01-01
The alkaline complexes of the Southern Granulite Terrain (SGT) are generally restricted within NNW-SSE-trending Dharmapuri Shear Zone (DSZ), extending from Gudiyatham in the north and Bhavani in the south in Tamil Nadu. REE-rich phases have been studied under EDX (Energy Dispersive X-rays) from the different alkaline suites of Tamil Nadu. In Elagiri, the Th-rich epidote/allanite is concentrically zoned and occurs in the outermost coarse sub-solvus syenite, indicating that the REE concentration is restricted within the late-stage magmatic activity. In Koratti, the apatites are LREE rich. In Samalpatti Complex, the carbonatites host a number of REE-rich minerals commonly classified as betafite, along with nioborutite and nioboilmenite. The niobo-rutile and niobo-ilmenite show exsolved texture. The betafite is zoned with mendelyeerite. Some of the molybdenite in Samalpatti is dendritic indicating incomplete crystallisation. In Sivamalai, the REE phases are generally associated with ferrosyenite and nepheline syenite as adsorbed grains around apatite or carbonate. The REE minerals are Zr-REE titanate, REE-titano silicate and REE-yttrium silicate. In the Pikkili Complex, the REE minerals generally occur as rim around apatite and calcite. A discrete metamict allanite grain with radial cracks occurs within syenite. In Pakkanadu Complex zoned allanite occurs with distinct chemical zonation in syenite. Monazite and celesto-barite are associated with barite suggesting that the REE phases are developed in the late intrusive stage. (author)
Directory of Open Access Journals (Sweden)
Ali Hadi Abdulwahid
2016-12-01
Full Text Available Nowadays, the use of distributed generation (DG has increased because of benefits such as increased reliability, reduced losses, improvement in the line capacity, and less environmental pollution. The protection of microgrids, which consist of generation sources, is one of the most crucial concerns of basic distribution operators. One of the key issues in this field is the protection of microgrids against permanent and temporary failures by improving the safety and reliability of the network. The traditional method has a number of disadvantages. The reliability and stability of a power system in a microgrid depend to a great extent on the efficiency of the protection scheme. The application of Artificial Intelligence approaches was introduced recently in the protection of distribution networks. The fault detection method depends on differential relay based on Hilbert Space-Based Power (HSBP theory to achieve fastest primary protection. It is backed up by a total harmonic distortion (THD detection method that takes over in case of a failure in the primary method. The backup protection would be completely independent of the main protection. This is rarely attained in practice. This paper proposes a new algorithm to improve protection performance by adaptive network-based fuzzy inference system (ANFIS. The protection can be obtained in a novel way based on this theory. An advantage of this algorithm is that the protection system operates in fewer than two cycles after the occurrence of the fault. Another advantage is that the error detection is not dependent on the selection of threshold values, and all types of internal fault can identify and show that the algorithm operates correctly for all types of faults while preventing unwanted tripping, even if the data were distorted by current transformer (CT saturation or by data mismatches. The simulation results show that the proposed circuit can identify the faulty phase in the microgrid quickly and
Toyooka, Kiminori; Sato, Mayuko; Kutsuna, Natsumaro; Higaki, Takumi; Sawaki, Fumie; Wakazaki, Mayumi; Goto, Yumi; Hasezawa, Seiichiro; Nagata, Noriko; Matsuoka, Ken
2014-09-01
Rapid growth of plant cells by cell division and expansion requires an endomembrane trafficking system. The endomembrane compartments, such as the Golgi stacks, endosome and vesicles, are important in the synthesis and trafficking of cell wall materials during cell elongation. However, changes in the morphology, distribution and number of these compartments during the different stages of cell proliferation and differentiation have not yet been clarified. In this study, we examined these changes at the ultrastructural level in tobacco Bright yellow 2 (BY-2) cells during the log and stationary phases of growth. We analyzed images of the BY-2 cells prepared by the high-pressure freezing/freeze substitution technique with the aid of an auto-acquisition transmission electron microscope system. We quantified the distribution of secretory and endosomal compartments in longitudinal sections of whole cells by using wide-range gigapixel-class images obtained by merging thousands of transmission electron micrographs. During the log phase, all Golgi stacks were composed of several thick cisternae. Approximately 20 vesicle clusters (VCs), including the trans-Golgi network and secretory vesicle cluster, were observed throughout the cell. In the stationary-phase cells, Golgi stacks were thin with small cisternae, and only a few VCs were observed. Nearly the same number of multivesicular body and small high-density vesicles were observed in both the stationary and log phases. Results from electron microscopy and live fluorescence imaging indicate that the morphology and distribution of secretory-related compartments dramatically change when cells transition from log to stationary phases of growth. © The Author 2014. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com.
Directory of Open Access Journals (Sweden)
Mohit Padamchand Gandhi
Full Text Available BACKGROUND: The Revised National Tuberculosis Control Program (RNTCP of India recommends follow-up sputum smear examination at two months into the continuation phase of treatment. The main intent of this (mid-CP follow-up is to detect patients not responding to treatment around two-three months earlier than at the end of the treatment. However, the utility of mid-CP follow-up under programmatic conditions has been questioned. We undertook a multi-district study to determine if mid-CP follow-up is able to detect cases of treatment failures early among all types of patients with sputum smear-positive TB. METHODOLOGY: We reviewed existing records of patients with sputum smear-positive TB registered under the RNTCP in 43 districts across three states of India during a three month period in 2009. We estimated proportions of patients that could be detected as a case of treatment failure early, and assessed the impact of various policy options on laboratory workload and number needed to test to detect one case of treatment failure early. RESULTS: Of 10055 cases, mid-CP follow-up was done in 6944 (69% cases. Mid-CP follow-up could benefit 117/8015 (1.5% new and 206/2040 (10% previously-treated sputum smear-positive cases by detecting their treatment failure early. Under the current policy, 31 patients had to be tested to detect one case of treatment failure early. All cases of treatment failure would still be detected early if mid-CP follow-up were discontinued for new sputum smear-positive cases who become sputum smear-negative after the intensive-phase of treatment. This would reduce the related laboratory workload by 69% and only 10 patients would need to be tested to detect one case of treatment failure early. CONCLUSION: Discontinuation of mid-CP follow-up among new sputum smear-positive cases who become sputum smear-negative after completing the intensive-phase of treatment will reduce the laboratory workload without impacting overall early
International Nuclear Information System (INIS)
Khrennikov, A.
2005-01-01
We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
International Nuclear Information System (INIS)
Ding You; Rovelli, Carlo
2010-01-01
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit). We also generalize the definition of the volume operator in the spin-foam model to the Lorentzian signature and show that it matches the one of loop quantum gravity, as in the Euclidean case.
Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction
Sauloy, Jacques
2017-01-01
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equat...
3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries
DEFF Research Database (Denmark)
Ujang, Uznir; Antón Castro, Francesc/François; Azri, Suhaibah
2014-01-01
The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using...... method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban...... objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA...
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
Regularization in Hilbert space under unbounded operators and general source conditions
International Nuclear Information System (INIS)
Hofmann, Bernd; Mathé, Peter; Von Weizsäcker, Heinrich
2009-01-01
The authors study ill-posed equations with unbounded operators in Hilbert space. This setup has important applications, but only a few theoretical studies are available. First, the question is addressed and answered whether every element satisfies some general source condition with respect to a given self-adjoint unbounded operator. This generalizes a previous result from Mathé and Hofmann (2008 Inverse Problems 24 015009). The analysis then proceeds to error bounds for regularization, emphasizing some specific points for regularization under unbounded operators. The study finally reviews two examples within the light of the present study, as these are fractional differentiation and some Cauchy problems for the Helmholtz equation, both studied previously and in more detail by U Tautenhahn and co-authors
Directory of Open Access Journals (Sweden)
Lajmert Paweł
2018-01-01
Full Text Available In the paper a cutting stability in the milling process of nickel based alloy Inconel 625 is analysed. This problem is often considered theoretically, but the theoretical finding do not always agree with experimental results. For this reason, the paper presents different methods for instability identification during real machining process. A stability lobe diagram is created based on data obtained in impact test of an end mill. Next, the cutting tests were conducted in which the axial cutting depth of cut was gradually increased in order to find a stability limit. Finally, based on the cutting force measurements the stability estimation problem is investigated using the recurrence plot technique and Hilbert vibration decomposition method.
A Riemann-Hilbert formulation for the finite temperature Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Cornagliotto, Martina [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); DESY Hamburg, Theory Group,Notkestrasse 85, D-22607 Hamburg (Germany); Mattelliano, Massimo; Tateo, Roberto [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy)
2015-06-03
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.
Li, Xuelong; Li, Zhonghui; Wang, Enyuan; Feng, Junjun; Chen, Liang; Li, Nan; Kong, Xiangguo
2016-09-01
This study provides a new research idea concerning rock burst prediction. The characteristics of microseismic (MS) waveforms prior to and during the rock burst were studied through the Hilbert-Huang transform (HHT). In order to demonstrate the advantage of the MS features extraction based on HHT, the conventional analysis method (Fourier transform) was also used to make a comparison. The results show that HHT is simple and reliable, and could extract in-depth information about the characteristics of MS waveforms. About 10 days prior to the rock burst, the main frequency of MS waveforms transforms from the high-frequency to low-frequency. What's more, the waveforms energy also presents accumulation characteristic. Based on our study results, it can be concluded that the MS signals analysis through HHT could provide valuable information about the coal or rock deformation and fracture.
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
Directory of Open Access Journals (Sweden)
Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
The Schrödinger–Robinson inequality from stochastic analysis on a complex Hilbert space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2013-01-01
We explored the stochastic analysis on a complex Hilbert space to show that one of the cornerstones of quantum mechanics (QM), namely Heisenberg's uncertainty relation, can be derived in the classical probabilistic framework. We created a new mathematical representation of quantum averages: as averages with respect to classical random fields. The existence of a classical stochastic model matching with Heisenberg's uncertainty relation makes the connection between classical and quantum probabilistic models essentially closer. In real physical situations, random fields are valued in the L 2 -space. Hence, although we model QM and not QFT, the classical systems under consideration have an infinite number of degrees of freedom. And in our modeling, infinite-dimensional stochastic analysis is the basic mathematical tool. (comment)
Fano, Guido
2017-01-01
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result...
Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira
2014-06-01
Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Scattering analysis of asymmetric metamaterial resonators by the Riemann-Hilbert approach
DEFF Research Database (Denmark)
Kaminski, Piotr Marek; Ziolkowski, Richard W.; Arslanagic, Samel
2016-01-01
This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell with an ap......This work presents an analytical treatment of an asymmetric metamaterial-based resonator excited by an electric line source, and explores its beam shaping capabilities. The resonator consists of two concentric cylindrical material layers covered with an infinitely thin conducting shell...... with an aperture. Exact analytical solution of the problem is derived; it is based on the n-series approach which is casted into the equivalent Riemann-Hilbert problem. The examined configuration leads to large enhancements of the radiated field and to steerable Huygens-like directivity patterns. Particularly...
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering
Pelinovsky, Dmitry E.; Sulem, Catherine
A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.
On using the Hilbert transform for blind identification of complex modes: A practical approach
Antunes, Jose; Debut, Vincent; Piteau, Pilippe; Delaune, Xavier; Borsoi, Laurent
2018-01-01
The modal identification of dynamical systems under operational conditions, when subjected to wide-band unmeasured excitations, is today a viable alternative to more traditional modal identification approaches based on processing sets of measured FRFs or impulse responses. Among current techniques for performing operational modal identification, the so-called blind identification methods are the subject of considerable investigation. In particular, the SOBI (Second-Order Blind Identification) method was found to be quite efficient. SOBI was originally developed for systems with normal modes. To address systems with complex modes, various extension approaches have been proposed, in particular: (a) Using a first-order state-space formulation for the system dynamics; (b) Building complex analytic signals from the measured responses using the Hilbert transform. In this paper we further explore the latter option, which is conceptually interesting while preserving the model order and size. Focus is on applicability of the SOBI technique for extracting the modal responses from analytic signals built from a set of vibratory responses. The novelty of this work is to propose a straightforward computational procedure for obtaining the complex cross-correlation response matrix to be used for the modal identification procedure. After clarifying subtle aspects of the general theoretical framework, we demonstrate that the correlation matrix of the analytic responses can be computed through a Hilbert transform of the real correlation matrix, so that the actual time-domain responses are no longer required for modal identification purposes. The numerical validation of the proposed technique is presented based on time-domain simulations of a conceptual physical multi-modal system, designed to display modes ranging from normal to highly complex, while keeping modal damping low and nearly independent of the modal complexity, and which can prove very interesting in test bench
Correlated Light Microscopy and Electron Microscopy
Sjollema, Klaas A.; Schnell, Ulrike; Kuipers, Jeroen; Kalicharan, Ruby; Giepmans, Ben N. G.; MullerReichert, T; Verkade, P
2012-01-01
Understanding where, when, and how biomolecules (inter)act is crucial to uncover fundamental mechanisms in cell biology. Recent developments in fluorescence light microscopy (FLM) allow protein imaging in living cells and at the near molecular level. However, fluorescence microscopy only reveals
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Microsphere imaging with confocal microscopy and two photon microscopy
International Nuclear Information System (INIS)
Chun, Hyung Su; An, Kyung Won; Lee, Jai Hyung
2002-01-01
We have acquired images of polystyrene and fused-silica microsphere by using conventional optical microscopy, confocal microscopy and two-photon microscopy, and performed comparative analysis of these images. Different from conventional optical microscopy, confocal and two-photon microscopy had good optical sectioning capability. In addition, confocal microscopy and two-photon microscopy had better lateral resolution than conventional optical microscopy. These results are attributed to confocality and nonlinearity of confocal microscopy and two photon microscopy, respectively.
Electron microscopy for Engineers
International Nuclear Information System (INIS)
Jones, I P
2009-01-01
This paper reviews the application of (mainly) Transmission Electron Microscopy (TEM) in an engineering context. The first two sections are TEM and chemical in nature; the final three sections are more general and include aspects of Scanning Electron Microscopy (SEM).
Electron microscopy of surfaces
International Nuclear Information System (INIS)
Venables, J.A.
1981-01-01
Electron beam techniques used to study clean surfaces and surface processes on a microscopic scale are reviewed. Recent experimental examples and possible future developments are discussed. Special emphasis is given to (i) transmission diffraction and microscopy techniques, including atomic imaging; (ii) Auger microscopy on bulk and thin film samples; (iii) secondary electron microscopy, especially low energy secondaries for work-function imaging and photoelectron imaging; and (iv) reflection electron microscopy and diffraction. (orig.)
Heath, Julian
2005-10-01
The past decade has seen huge advances in the application of microscopy in all areas of science. This welcome development in microscopy has been paralleled by an expansion of the vocabulary of technical terms used in microscopy: terms have been coined for new instruments and techniques and, as microscopes reach even higher resolution, the use of terms that relate to the optical and physical principles underpinning microscopy is now commonplace. The Dictionary of Microscopy was compiled to meet this challenge and provides concise definitions of over 2,500 terms used in the fields of light microscopy, electron microscopy, scanning probe microscopy, x-ray microscopy and related techniques. Written by Dr Julian P. Heath, Editor of Microscopy and Analysis, the dictionary is intended to provide easy navigation through the microscopy terminology and to be a first point of reference for definitions of new and established terms. The Dictionary of Microscopy is an essential, accessible resource for: students who are new to the field and are learning about microscopes equipment purchasers who want an explanation of the terms used in manufacturers' literature scientists who are considering using a new microscopical technique experienced microscopists as an aide mémoire or quick source of reference librarians, the press and marketing personnel who require definitions for technical reports.
Frame transforms, star products and quantum mechanics on phase space
International Nuclear Information System (INIS)
Aniello, P; Marmo, G; Man'ko, V I
2008-01-01
Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G x G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed
Independence and totalness of subspaces in phase space methods
Vourdas, A.
2018-04-01
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.
Transmission acoustic microscopy investigation
Maev, Roman; Kolosov, Oleg; Levin, Vadim; Lobkis, Oleg
The nature of acoustic contrast, i.e. the connection of the amplitude and phase of the output signal of the acoustic microscope with the local values of the acoustic parameters of the sample (density, elasticity, viscosity) is a central problem of acoustic microscopy. A considerable number of studies have been devoted to the formation of the output signal of the reflection scanning acoustic microscope. For the transmission acoustic microscope (TAM) this problem has remained almost unstudied. Experimental investigation of the confocal system of the TAM was carried out on an independently manufactured laboratory mockup of the TAM with the working frequency of the 420 MHz. Acoustic lenses with the radius of curvature of about 500 microns and aperture angle of 45 deg were polished out in the end faces of two cylindrical sound conductors made from Al2O3 single crystals with an axis parallel to the axis C of the crystal (the length of the sound conductor is 20 mm; diameter, 6 mm). At the end faces of the sound conductor, opposite to the lenses, CdS transducers with a diameter of 2 mm were disposed. The electric channel of the TAM provided a possibility for registering the amplitude of the microscope output signal in the case of the dynamic range of the 50 dB.
International Nuclear Information System (INIS)
Bach, A.
1981-01-01
A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)
Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua
2016-01-01
The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through c...
SUR UNE CERTAINE CLASSE D’OPERATEURS A SPECTRE CONCENTRE EN UN POINT DANS UN ESPACE DE HILBERT
Directory of Open Access Journals (Sweden)
B BENDOUKHA
2000-12-01
Full Text Available Le présent travail est consacré à l'étude de certaines classes d’opérateurs qui sont parfaitement définis par leur spectre. Pour ces opérateurs (définis dans des espaces de Hilbert abstraits, on donnera une représentation explicite et uniquement à l’aide du spectre dans l’espace des fonctions à carrés intégrables.
International Nuclear Information System (INIS)
Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio
2012-01-01
This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)
Directory of Open Access Journals (Sweden)
Roque A. Osornio-Rios
2013-04-01
Full Text Available Power quality disturbance (PQD monitoring has become an important issue due to the growing number of disturbing loads connected to the power line and to the susceptibility of certain loads to their presence. In any real power system, there are multiple sources of several disturbances which can have different magnitudes and appear at different times. In order to avoid equipment damage and estimate the damage severity, they have to be detected, classified, and quantified. In this work, a smart sensor for detection, classification, and quantification of PQD is proposed. First, the Hilbert transform (HT is used as detection technique; then, the classification of the envelope of a PQD obtained through HT is carried out by a feed forward neural network (FFNN. Finally, the root mean square voltage (Vrms, peak voltage (Vpeak, crest factor (CF, and total harmonic distortion (THD indices calculated through HT and Parseval’s theorem as well as an instantaneous exponential time constant quantify the PQD according to the disturbance presented. The aforementioned methodology is processed online using digital hardware signal processing based on field programmable gate array (FPGA. Besides, the proposed smart sensor performance is validated and tested through synthetic signals and under real operating conditions, respectively.
Searching the beginning of BWR power instability events with the Hilbert Huang transform
International Nuclear Information System (INIS)
Blázquez, Juan; Montalvo, Cristina; García-Berrocal, Agustín; Balbás, Miguel
2013-01-01
Highlights: ► The report of the instability is enriched by including its beginning and its end. ► The Hilbert Huang transform (HHT) is used for indentifying both. ► The first Intrinsic Mode Function (IMF) detects both. ► The methodology is applied to neutron detector signals from two plants. ► The Decay Ratio of IMF 1 is calculated. - Abstract: When a BWR instability takes place, the Regulator usually demands a report which must include many aspects such as the initial time of the instability and also the measurements adopted by the operator at that time. This initial time normally is difficult to know from the available data. In this work, a methodology is proposed to determine accurately when the instability began based on the Hilbert–Huang transform. The Empirical Mode Decomposition is applied to neutron detector signals coming from two plants which have recorded them during real instability events. The first intrinsic mode function shows sharply the beginning and the end of the incident. Besides, through the instantaneous amplitude and frequency of the first mode a kind of Decay Ratio can be assigned allowing us to obtain a sharper description of the instability
Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces
International Nuclear Information System (INIS)
Höhn, Philipp A.
2014-01-01
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in the quantum theory, an according formalism for constrained variational discrete systems is constructed. While this paper focuses on global evolution moves and, for simplicity, restricts to flat configuration spaces R N , a Paper II [P. A. Höhn, “Quantization of systems with temporally varying discretization. II. Local evolution moves,” J. Math. Phys., e-print http://arxiv.org/abs/arXiv:1401.7731 [gr-qc].] discusses local evolution moves. In order to link the covariant and canonical picture, the dynamics of the quantum states is generated by propagators which satisfy the canonical constraints and are constructed using the action and group averaging projectors. This projector formalism offers a systematic method for tracing and regularizing divergences in the resulting state sums. Non-trivial coarse graining evolution moves lead to non-unitary, and thus irreversible, projections of physical Hilbert spaces and Dirac observables such that these concepts become evolution move dependent on temporally varying discretizations. The formalism is illustrated in a toy model mimicking a “creation from nothing.” Subtleties arising when applying such a formalism to quantum gravity models are discussed
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
International Nuclear Information System (INIS)
Kaplitskii, V M
2014-01-01
The function Ψ(x,y,s)=e iy Φ(−e iy ,s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L 2 (Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles
Hilbert-Huang transform analysis of long-term solar magnetic activity
Deng, Linhua
2018-04-01
Astronomical time series analysis is one of the hottest and most important problems, and becomes the suitable way to deal with the underlying dynamical behavior of the considered nonlinear systems. The quasi-periodic analysis of solar magnetic activity has been carried out by various authors during the past fifty years. In this work, the novel Hilbert-Huang transform approach is applied to investigate the yearly numbers of polar faculae in the time interval from 1705 to 1999. The detected periodicities can be allocated to three components: the first one is the short-term variations with periods smaller than 11 years, the second one is the mid- term variations with classical periods from 11 years to 50 years, and the last one is the long-term variations with periods larger than 50 years. The analysis results improve our knowledge on the quasi-periodic variations of solar magnetic activity and could be provided valuable constraints for solar dynamo theory. Furthermore, our analysis results could be useful for understanding the long-term variations of solar magnetic activity, providing crucial information to describe and forecast solar magnetic activity indicators.
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
Energy Technology Data Exchange (ETDEWEB)
Lehman, Landon; Martin, Adam [Department of Physics, University of Notre Dame,Nieuwland Science Hall, Notre Dame, IN 46556 (United States)
2016-02-12
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N{sub f}=1 operators.
NINJA data analysis with a detection pipeline based on the Hilbert-Huang transform
International Nuclear Information System (INIS)
Stroeer, Alexander; Camp, Jordan
2009-01-01
The NINJA data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert-Huang transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above signal-to-noise ratio, SNR 5 in coincidence, with 43 missed events characterized by SNR < 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a final characterization of the event.
Parallel magnetic resonance imaging as approximation in a reproducing kernel Hilbert space
International Nuclear Information System (INIS)
Athalye, Vivek; Lustig, Michael; Martin Uecker
2015-01-01
In magnetic resonance imaging data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. To understand and design k-space sampling patterns, a theoretical framework is needed to analyze how well arbitrary sampling patterns reconstruct unsampled k-space using receive coil information. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a reproducing kernel Hilbert space with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional image-domain g-factor noise analysis to both noise amplification and approximation errors in k-space. This is demonstrated with numerical examples. (paper)
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
International Nuclear Information System (INIS)
Lehman, Landon; Martin, Adam
2016-01-01
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N_f=1 operators.
International Nuclear Information System (INIS)
Antonino-Daviu, J.; Rodriguez, P. Jover; Riera-Guasp, M.; Arkkio, A.; Roger-Folch, J.; Perez, R.B.
2009-01-01
The identification and extraction of characteristic patterns are proposed in this work for the diagnosis and evaluation of mixed eccentricities in induction electrical machines with parallel stator branches. Whereas the classical diagnosis approaches, deeply spread in the industrial environment, are based on the Fourier analysis of the steady-state current, the basis of the proposed methodology consist of analysing the current demanded by the machine during the connection process (startup transient); the objective is to extract the characteristic evolution during the transient of some harmonic components created by the fault; this evolution is caused by the dependence of these components on the slip (s), a quantity varying during the startup transient from 1 to almost 0. For this feature extraction, the Hilbert-Huang Transform (HHT) is proposed. An analysis of the behaviour of this transform in comparison with another time-frequency approach used in other works, the Discrete Wavelet Transform (DWT), is also presented in the paper. The results show the usefulness of the methodology for the reliable diagnosis of the mixed eccentricity fault and for the correct discrimination against other types of failures.
Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection
Janssens, Eline; De Beenhouwer, Jan; Van Dael, Mattias; De Schryver, Thomas; Van Hoorebeke, Luc; Verboven, Pieter; Nicolai, Bart; Sijbers, Jan
2018-03-01
X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400 × 400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria.
Directory of Open Access Journals (Sweden)
P Bhattacharya
2016-09-01
Full Text Available The wind resource varies with of the day and the season of the year and even some extent from year to year. Wind energy has inherent variances and hence it has been expressed by distribution functions. In this paper, we present some methods for estimating Weibull parameters in case of a low wind speed characterization, namely, shape parameter (k, scale parameter (c and characterize the discrete wind data sample by the discrete Hilbert transform. We know that the Weibull distribution is an important distribution especially for reliability and maintainability analysis. The suitable values for both shape parameter and scale parameters of Weibull distribution are important for selecting locations of installing wind turbine generators. The scale parameter of Weibull distribution also important to determine whether a wind farm is good or not. Thereafter the use of discrete Hilbert transform (DHT for wind speed characterization provides a new era of using DHT besides its application in digital signal processing. Basically in this paper, discrete Hilbert transform has been applied to characterize the wind sample data measured on College of Engineering and Management, Kolaghat, East Midnapore, India in January 2011.
A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis
CERN. Geneva
2000-01-01
A new method for analysing non-linear and non-stationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero crossing and extreme, and also having symmetric envelopes defined by the local maximal and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical non-l...
Sculpturing the electron wave function using nanoscale phase masks
Energy Technology Data Exchange (ETDEWEB)
Shiloh, Roy, E-mail: royshilo@post.tau.ac.il; Lereah, Yossi; Lilach, Yigal; Arie, Ady
2014-09-15
Electron beams are extensively used in lithography, microscopy, material studies and electronic chip inspection. Today, beams are mainly shaped using magnetic or electric forces, enabling only simple shaping tasks such as focusing or scanning. Recently, binary amplitude gratings achieved complex shapes. These, however, generate multiple diffraction orders, hence the desired shape, appearing only in one order, retains little of the beam energy. Here we demonstrate a method in electron-optics for arbitrarily shaping electron beams into a single desired shape, by precise patterning of a thin-membrane. It is conceptually similar to shaping light beams using refractive or diffractive glass elements such as lenses or holograms – rather than applying electromagnetic forces, the beam is controlled by spatially modulating its wavefront. Our method allows for nearly-maximal energy transference to the designed shape, and may avoid physical damage and charging effects that are the scorn of commonly-used (e.g. Zernike and Hilbert) phase-plates. The experimental demonstrations presented here – on-axis Hermite–Gauss and Laguerre–Gauss (vortex) beams, and computer-generated holograms – are a first example of nearly-arbitrary manipulation of electron beams. Our results herald exciting prospects for microscopic material studies, enables electron lithography with fixed sample and beam and high resolution electronic chip inspection by structured electron illumination. - Highlights: • Nanoscale-patterned membranes are used to shape electron beams. • Designing on-axis phase plates outside the back focal plane is possible. • Computer-generated holograms enable nearly-arbitrary beam shaping. • Applications in microscopy, lithography, chip inspection and material sciences.
New microscopy for nanoimaging
Kinjo, Y; Watanabe, M
2002-01-01
Two types of new microscopy, namely, X-ray contact microscopy (XRCM) in combination with atomic force microscopy (AFM) and X-ray projection microscopy (XRPM) using synchrotron radiation and zone plate optics were used to image the fine structures of human chromosomes. In the XRCM plus AFM system, location of X-ray images on a photoresist has become far easier than that with our previous method using transmission electron microscopy coupled with the replica method. In addition, the images obtained suggested that the conformation of chromatin fiber differs from the current textbook model regarding the architecture of a eukaryotic chromosome. X-ray images with high contrast of the specimens could be obtained with XRPM. The resolution of each microscopy was about 30 and 200-300 nm for XRCM plus AFM and XRPM, respectively. (author)