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 ...

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

Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis.

Science.gov (United States)

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.

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.

Hilbert's programs and beyond

CERN Document Server

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.

Two-shot fringe pattern phase-amplitude demodulation using Gram-Schmidt orthonormalization with Hilbert-Huang pre-filtering.

Science.gov (United States)

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.

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.

Science.gov (United States)

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.

Optofluidic time-stretch quantitative phase microscopy.

Science.gov (United States)

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.

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.

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

Detecting phase singularities and rotor center trajectories based on the Hilbert transform of intraatrial electrograms in an atrial voxel model

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.

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

Science.gov (United States)

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.

Exponential Hilbert series of equivariant embeddings

OpenAIRE

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...

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)

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

Power Spectral Density and Hilbert Transform

Science.gov (United States)

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

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.

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 ...

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

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....

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...

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.

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

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)

Quantum Hilbert Hotel.

Science.gov (United States)

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.

Hilbert schemes of points and infinite dimensional Lie algebras

CERN Document Server

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...

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.

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

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.

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

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)

Lectures on Hilbert schemes of points on surfaces

CERN Document Server

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...

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

Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute Envelope Of Free Decaying Oscillations Embedded In Noise, And The Logarithmic Decrement In High-Resolution Mechanical Spectroscopy HRMS

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.

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.

Hilbert schemes of points on some classes surface singularities

OpenAIRE

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...

Lectures on Hilbert modular varieties and modular forms

CERN Document Server

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...

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.

Automated flaw detection scheme for cast austenitic stainless steel weld specimens using Hilbert-Huang transform of ultrasonic phased array data

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

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

Effects of phase change on reflection in phase-measuring interference microscopy

OpenAIRE

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...

Theory of linear operators in Hilbert space

CERN Document Server

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.

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.

Spectral Theory of Operators on Hilbert Spaces

CERN Document Server

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

On Hilbert space of paths

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

Detection of secondary phases in duplex stainless steel by magnetic force microscopy and scanning Kelvin probe force microscopy

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.

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

Science.gov (United States)

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.

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.

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...

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)

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

Science.gov (United States)

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

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.

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

Science.gov (United States)

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.

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.

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.

Frames and outer frames for Hilbert C^*-modules

OpenAIRE

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...

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

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

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps

Directory of Open Access Journals (Sweden)

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.

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)

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...

Holography microscopy as an artifact-free alternative to phase-contrast.

Science.gov (United States)

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.

Compact diffraction phase microscopy for quantitative visualization of cells in biomedical applications

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)

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...

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

THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.

Science.gov (United States)

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.

Quantum mechanics in an evolving Hilbert space

Science.gov (United States)

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.

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.

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.

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

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

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....

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.)

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.

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

Hilbert space methods in partial differential equations

CERN Document Server

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.

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...

Invariant Hilbert spaces of holomorphic functions

NARCIS (Netherlands)

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

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

Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication.

Science.gov (United States)

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.

Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.

Science.gov (United States)

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.

Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

Science.gov (United States)

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.

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.

Imaging of phase change materials below a capping layer using correlative infrared near-field microscopy and electron microscopy

Science.gov (United States)

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 ).

Semiclassical propagation: Hilbert space vs. Wigner representation

Science.gov (United States)

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.

Magnetomyographic recording and identification of uterine contractions using Hilbert-wavelet transforms

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

Characterization and quantitative determination of calcium aluminate clinker phases through reflected light microscopy

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

Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

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.

Reproducing kernel Hilbert spaces of Gaussian priors

NARCIS (Netherlands)

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

Elements of Hilbert spaces and operator theory

CERN Document Server

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...

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

A primer on Hilbert space theory linear spaces, topological spaces, metric spaces, normed spaces, and topological groups

CERN Document Server

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...

Vertical integration from the large Hilbert space

Science.gov (United States)

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.

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)

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.)

Single particle analysis based on Zernike phase contrast transmission electron microscopy.

Science.gov (United States)

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.

Quantitative optical microscopy: measurement of cellular biophysical features with a standard optical microscope.

Science.gov (United States)

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

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.

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

Weaving Hilbert space fusion frames

OpenAIRE

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...

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

Science.gov (United States)

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'.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

Science.gov (United States)

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).

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.

Time-frequency analysis of non-stationary fusion plasma signals using an improved Hilbert-Huang transform

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

Application of Hilbert-Huang Transform in Generating Spectrum-Compatible Earthquake Time Histories

OpenAIRE

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 ...

Improved cancer risk stratification and diagnosis via quantitative phase microscopy (Conference Presentation)

Science.gov (United States)

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.

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

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.

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

Novel microwave photonic fractional hilbert transformer using a ring resonator-based optical all-pass filter

NARCIS (Netherlands)

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

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

Image decomposition model Shearlet-Hilbert-L2 with better performance for denoising in ESPI fringe patterns.

Science.gov (United States)

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 .

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

Time-resolved imaging refractometry of microbicidal films using quantitative phase microscopy.

Science.gov (United States)

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.

Spinors in Hilbert Space

Science.gov (United States)

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.

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

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. �

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 ...

Hilbert's Grand Hotel with a series twist

Science.gov (United States)

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.

Structure of Hilbert space operators

CERN Document Server

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

Explicit solution of Riemann-Hilbert problems for the Ernst equation

Science.gov (United States)

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.

Quantitative tracking of tumor cells in phase-contrast microscopy exploiting halo artifact pattern

Science.gov (United States)

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.

Experimental validation of a structural damage detection method based on marginal Hilbert spectrum

Science.gov (United States)

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.

Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

Science.gov (United States)

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.

Flipping interferometry and its application for quantitative phase microscopy in a micro-channel.

Science.gov (United States)

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.

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

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.

Means of Hilbert space operators

CERN Document Server

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.

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

T^{\\sigma}_{\\rho}(G) Theories and Their Hilbert Series

CERN Document Server

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.

Introduction to Hilbert space and the theory of spectral multiplicity

CERN Document Server

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.

Diffraction phase microscopy realized with an automatic digital pinhole

Science.gov (United States)

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.

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.

Notes on qubit phase space and discrete symplectic structures

International Nuclear Information System (INIS)

Livine, Etera R

2010-01-01

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.

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)

The Einstein-Hilbert gravitation with minimum length

Science.gov (United States)

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.

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.

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)

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.

Clustering in Hilbert simplex geometry

KAUST Repository

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.

The Hilbert Series of the One Instanton Moduli Space

CERN Document Server

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.

Phase microscopy using light-field reconstruction method for cell observation.

Science.gov (United States)

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.

Concerning the Hilbert 16th problem

CERN Document Server

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

Quantitative phase-digital holographic microscopy: a new imaging modality to identify original cellular biomarkers of diseases

KAUST Repository

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.

On the minimizers of calculus of variations problems in Hilbert spaces

KAUST Repository

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

KAUST Repository

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.

Live cell refractometry using microfluidic devices.

Science.gov (United States)

Lue, Niyom; Popescu, Gabriel; Ikeda, Takahiro; Dasari, Ramachandra R; Badizadegan, Kamran; Feld, Michael S

2006-09-15

Using Hilbert phase microscopy for extracting quantitative phase images, we measured the average refractive index associated with live cells in culture. To decouple the contributions to the phase signal from the cell refractive index and thickness, we confined the cells in microchannels. The results are confirmed by comparison with measurements of spherical cells in suspension.

Hilbert-Schmidt quantum coherence in multi-qudit systems

Science.gov (United States)

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.

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.)

Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories

Science.gov (United States)

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.

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.

Direct observation of dopant distribution in GaAs compound semiconductors using phase-shifting electron holography and Lorentz microscopy.

Science.gov (United States)

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.

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

International Nuclear Information System (INIS)

Muthukumar, Balasundaram

2007-01-01

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry

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

Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms

Directory of Open Access Journals (Sweden)

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)

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

Advantages of intermediate X-ray energies in Zernike phase contrast X-ray microscopy.

Science.gov (United States)

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.

A Proof of the Hilbert-Smith Conjecture

OpenAIRE

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...

Correction of phase-shifting error in wavelength scanning digital holographic microscopy

Science.gov (United States)

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.

Ultrastructural organization of premature condensed chromosomes at S-phase as observed by atomic force microscopy

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

Science.gov (United States)

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.

Sparsity-based multi-height phase recovery in holographic microscopy

KAUST Repository

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.

Sparsity-based multi-height phase recovery in holographic microscopy

Science.gov (United States)

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.

Integrated reconfigurable photonic filters based on interferometric fractional Hilbert transforms.

Science.gov (United States)

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.

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

Multisymplectic unified formalism for Einstein-Hilbert gravity

Science.gov (United States)

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.

Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

OpenAIRE

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...

Combined multi-plane phase retrieval and super-resolution optical fluctuation imaging for 4D cell microscopy

Science.gov (United States)

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.

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.)

Gas-phase synthesis of magnesium nanoparticles : A high-resolution transmission electron microscopy study

NARCIS (Netherlands)

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

On the representation of contextual probabilistic dynamics in the complex Hilbert space: Linear and nonlinear evolutions, Schrodinger dynamics

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)

Deleterious phases precipitation on superduplex stainless steel UNS S32750: characterization by light optical and scanning electron microscopy

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.

Photon-counting-based diffraction phase microscopy combined with single-pixel imaging

Science.gov (United States)

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.

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

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.

Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform

Science.gov (United States)

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.

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)

Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

OpenAIRE

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.

An advanced complex analysis problem book topological vector spaces, functional analysis, and Hilbert spaces of analytic functions

CERN Document Server

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.

Theory and experiments on Peano and Hilbert curve RFID tags

Science.gov (United States)

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].

Digital holographic microscopy of phase separation in multicomponent lipid membranes

Science.gov (United States)

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.

Independence and totalness of subspaces in phase space methods

Science.gov (United States)

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.

Concomitant use of polarization and positive phase contrast microscopy for the study of microbial cells

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

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.

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

Quantum de Finetti theorem in phase-space representation

International Nuclear Information System (INIS)

Leverrier, Anthony; Cerf, Nicolas J.

2009-01-01

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

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.

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.

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

Sequential processing of quantitative phase images for the study of cell behaviour in real-time digital holographic microscopy.

Science.gov (United States)

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.

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

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

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

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...

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

Aveiro method in reproducing kernel Hilbert spaces under complete dictionary

Science.gov (United States)

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.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

Science.gov (United States)

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)].

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

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)

Phase gradient algorithm based on co-axis two-step phase-shifting interferometry and its application

Science.gov (United States)

Wang, Yawei; Zhu, Qiong; Xu, Yuanyuan; Xin, Zhiduo; Liu, Jingye

2017-12-01

A phase gradient method based on co-axis two-step phase-shifting interferometry, is used to reveal the detailed information of a specimen. In this method, the phase gradient distribution can only be obtained by calculating both the first-order derivative and the radial Hilbert transformation of the intensity difference between two phase-shifted interferograms. The feasibility and accuracy of this method were fully verified by the simulation results for a polystyrene sphere and a red blood cell. The empirical results demonstrated that phase gradient is sensitive to changes in the refractive index and morphology. Because phase retrieval and tedious phase unwrapping are not required, the calculation speed is faster. In addition, co-axis interferometry has high spatial resolution.

A New Method for Non-linear and Non-stationary Time Series Analysis:
The Hilbert Spectral Analysis

CERN Multimedia

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...

Laser Light-field Fusion for Wide-field Lensfree On-chip Phase Contrast Microscopy of Nanoparticles

Science.gov (United States)

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.

Characterisation of phases in nanostructured, multilayered titanium alloys by analytical and high-resolution electron microscopy.

Science.gov (United States)

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.

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.

Self-interference fluorescence microscopy with three-phase detection for depth-resolved confocal epi-fluorescence imaging.

Science.gov (United States)

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.

The classes of the quasihomogeneous Hilbert schemes of points on the plane

NARCIS (Netherlands)

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

From Kant to Hilbert a source book in the foundations of mathematics

CERN Document Server

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...

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)

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.

Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform.

Science.gov (United States)

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.

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...

Direct characterization of phase transformations and morphologies in moving reaction zones in Al/Ni nanolaminates using dynamic transmission electron microscopy

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.

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?

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.)

Cyclotomy and Ramanujan sums in quantum phase locking

International Nuclear Information System (INIS)

Planat, Michel; Rosu, Haret C.

2003-01-01

Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement

Real analysis measure theory, integration, and Hilbert spaces

CERN Document Server

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

Poschl-Teller potentials based solution to Hilbert's tenth problem Pöschl-Teller potentials based solution to Hilbert's tenth problem

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.

Deciphering complex, functional structures with synchrotron-based absorption and phase contrast tomographic microscopy

Science.gov (United States)

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].

Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces

OpenAIRE

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...

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

OpenAIRE

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...

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.

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

The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems

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.

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

International Roughness Index (IRI) measurement using Hilbert-Huang transform

Science.gov (United States)

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.

Conformal symmetries of the Einstein-Hilbert action on horizons of stationary and axisymmetric black holes

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)

Employing the Hilbert-Huang Transform to analyze observed natural complex signals: Calm wind meandering cases

Science.gov (United States)

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.

Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations

Science.gov (United States)

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.

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)

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

Science.gov (United States)

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.

Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy.

Science.gov (United States)

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.

Hilbert scheme of points on cyclic quotient singularities of type (p,1)

OpenAIRE

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.

Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders

KAUST Repository

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.

Full-angle tomographic phase microscopy of flowing quasi-spherical cells.

Science.gov (United States)

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.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

Science.gov (United States)

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.

Dual-polarization interference microscopy for advanced quantification of phase associated with the image field.

Science.gov (United States)

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.

Hilbert spaces contractively included in the Hardy space of the bidisk

NARCIS (Netherlands)

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

Berry phase in entangled systems

International Nuclear Information System (INIS)

Bertlmann, R.A.; Hasegawa, Y.; Hiesmayr, B.C.; Durstberger, C.

2005-01-01

Full text: The influence of the geometric phase, in particular the Berry phase, on an entangled spin-1/2 system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the 'spin-echo' method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a CHSH-Bell inequality. Furthermore, we suggest an experimental realization of our setup within neutron interferometry. It is possible to create entanglement between different degrees of freedom (spin and spatial degree of freedom) for a single neutron. The influence of the geometrical phase on the entangled neutron state is tested experimentally which is work in progress. (author)

Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

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)

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

Science.gov (United States)

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'.

Comparison of the layer structure of vapor phase and leached SRL glass by use of AEM [analytical electron microscopy

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

Geometry of quantum dynamics in infinite-dimensional Hilbert space

Science.gov (United States)

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.

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.)

Approximately dual frames in Hilbert spaces and applications to Gabor frames

OpenAIRE

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...

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....

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.)

Electrical characterization of Ge–Sb–Te phase change nano-pillars using conductive atomic force microscopy

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

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

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.

Science.gov (United States)

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.

Distinction of heterogeneity on Au nanostructured surface based on phase contrast imaging of atomic force microscopy

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.

Deteksi Kerusakan Batang Rotor Pada Motor Induksi Menggunakan Analisis Arus Mula Berbasis Hilbert Transform

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.

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.

Applications of Hilbert Spectral Analysis for Speech and Sound Signals

Science.gov (United States)

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.

A study of phase separation in peptide-loaded HPMC films using T(zero)-modulated temperature DSC, atomic force microscopy, and scanning electron microscopy.

Science.gov (United States)

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

Fresnel zone-plate based X-ray microscopy in Zernike phase contrast with sub-50 nm resolution at NSRL

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.

Fresnel zone-plate based X-ray microscopy in Zernike phase contrast with sub-50 nm resolution at NSRL

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.

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.

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

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

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.

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...

Transmission electron microscopy investigation of interfaces in a two-phase TiAl alloy

Science.gov (United States)

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.

Water-induced phase separation of miconazole-poly (vinylpyrrolidone-co-vinyl acetate) amorphous solid dispersions: Insights with confocal fluorescence microscopy.

Science.gov (United States)

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.

Towards non-invasive 3D hepatotoxicity assays with optical coherence phase microscopy

Science.gov (United States)

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.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

Science.gov (United States)

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).

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.

Recipes for stable linear embeddings from Hilbert spaces to R^m

OpenAIRE

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

OpenAIRE

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...

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.

New approaches for the analysis of confluent cell layers with quantitative phase digital holographic microscopy

Science.gov (United States)

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.

Phase-selective staining of metal salt for scanning electron microscopy imaging of block copolymer film

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.

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of −1-Order and Applications

Directory of Open Access Journals (Sweden)

Bicheng Yang

2007-10-01

Full Text Available Some character of the symmetric homogenous kernel of −1-order in Hilbert-type operator T:lr→lr (r>1 is obtained. Two equivalent inequalities with the symmetric homogenous kernel of −λ-order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.

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

Gas-phase synthesis of magnesium nanoparticles: A high-resolution transmission electron microscopy study

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

Automatic phase aberration compensation for digital holographic microscopy based on deep learning background detection.

Science.gov (United States)

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.

High resolution electron microscopy of the triply incommensurate phase of 2H-TaSe2

Science.gov (United States)

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.

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.

Imaging bacterial spores by soft-x-ray microscopy

International Nuclear Information System (INIS)

Stead, A.D.; Ford, T.W.; Judge, J.

1997-01-01

Bacterial spores are able to survive dehydration, but neither the physiological nor structural basis of this have been fully elucidated. Furthermore, once hydrated, spores often require activation before they will germinate. Several treatments can be used to activate spores, but in the case of Bacillus subtlis the most effective is heat treatment. The physiological mechanism associated with activation is also not understood, but some workers suggest that the loss of calcium from the spores may be critical. However, just prior to germination, the spores change from being phase bright to phase dark when viewed by light microscopy. Imaging spores by soft x-ray microscopy is possible without fixation. Thus, in contrast to electron microscopy, it is possible to compare the structure of dehydrated and hydrated spores in a manner not possible previously. A further advantage is that it is possible to monitor individual spores by phase contrast light microscopy immediately prior to imaging with soft x-rays; whereas, with both electron microscopy and biochemical studies, it is a population of spores being studied without knowledge of the phase characteristics of individual spores. This study has therefore tried to compare dehydrated and hydrated spores and to determine if there is a mass loss from individual spores as they pass the transition from being phase bright to phase dark

Imaging bacterial spores by soft-x-ray microscopy

Energy Technology Data Exchange (ETDEWEB)

Stead, A.D.; Ford, T.W. [Univ. of London, Surrey (United Kingdom); Judge, J. [Unilever plc, Sharnbrook (United Kingdom)] [and others

1997-04-01

Bacterial spores are able to survive dehydration, but neither the physiological nor structural basis of this have been fully elucidated. Furthermore, once hydrated, spores often require activation before they will germinate. Several treatments can be used to activate spores, but in the case of Bacillus subtlis the most effective is heat treatment. The physiological mechanism associated with activation is also not understood, but some workers suggest that the loss of calcium from the spores may be critical. However, just prior to germination, the spores change from being phase bright to phase dark when viewed by light microscopy. Imaging spores by soft x-ray microscopy is possible without fixation. Thus, in contrast to electron microscopy, it is possible to compare the structure of dehydrated and hydrated spores in a manner not possible previously. A further advantage is that it is possible to monitor individual spores by phase contrast light microscopy immediately prior to imaging with soft x-rays; whereas, with both electron microscopy and biochemical studies, it is a population of spores being studied without knowledge of the phase characteristics of individual spores. This study has therefore tried to compare dehydrated and hydrated spores and to determine if there is a mass loss from individual spores as they pass the transition from being phase bright to phase dark.

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.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area.

Science.gov (United States)

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

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

Label-free imaging of developing vasculature in zebrafish with phase variance optical coherence microscopy

Science.gov (United States)

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.

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

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.)

Magnetism in grain-boundary phase of a NdFeB sintered magnet studied by spin-polarized scanning electron microscopy

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.

Weibull Distribution for Estimating the Parameters and Application of Hilbert Transform in case of a Low Wind Speed at Kolaghat

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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.

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.

Single-Atom Gating of Quantum State Superpositions

Energy Technology Data Exchange (ETDEWEB)

Moon, Christopher

2010-04-28

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space - or Hilbert space - is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral1 can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real-space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.

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

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.

Science.gov (United States)

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.

The Pegg–Barnett phase operator and the discrete Fourier transform

International Nuclear Information System (INIS)

Perez-Leija, Armando; Szameit, Alexander; Andrade-Morales, Luis A; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2016-01-01

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg–Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London–Susskind–Glogower phase operator, whose natural logarithm gives rise to the Pegg–Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties. (invited comment)

Multifocus microscopy with precise color multi-phase diffractive optics applied in functional neuronal imaging.

Science.gov (United States)

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.

Mesoscopic structural phase progression in photo-excited VO2 revealed by time-resolved x-ray diffraction microscopy

Science.gov (United States)

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.

Study on a phase space representation of quantum theory

International Nuclear Information System (INIS)

Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.

2013-01-01

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

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)

Nanoscale nuclear architecture for cancer diagnosis by spatial-domain low-coherence quantitative phase microscopy

Science.gov (United States)

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.

Dispersion theory and sum rules for the non-minimum phase problem in optical spectroscopy

International Nuclear Information System (INIS)

Peiponen, Kai-Erik

2009-01-01

Dispersion relations and sum rules for integer powers of an optical response function are given in the case of the non-minimum phase problem. These relations were obtained using the concept of the Hilbert transform and Blaschke product. The theory presented in this paper is useful both in basic and applied studies of non-minimum phase functions in optics, and also other fields of physics such as high energy physics.

Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer.

Science.gov (United States)

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.

Simple and fast spectral domain algorithm for quantitative phase imaging of living cells with digital holographic microscopy

Science.gov (United States)

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.

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

X-ray differential phase-contrast tomographic reconstruction with a phase line integral retrieval filter

International Nuclear Information System (INIS)

Fu, Jian; Hu, Xinhua; Li, Chen

2015-01-01

We report an alternative reconstruction technique for x-ray differential phase-contrast computed tomography (DPC-CT). This approach is based on a new phase line integral projection retrieval filter, which is rooted in the derivative property of the Fourier transform and counteracts the differential nature of the DPC-CT projections. It first retrieves the phase line integral from the DPC-CT projections. Then the standard filtered back-projection (FBP) algorithms popular in x-ray absorption-contrast CT are directly applied to the retrieved phase line integrals to reconstruct the DPC-CT images. Compared with the conventional DPC-CT reconstruction algorithms, the proposed method removes the Hilbert imaginary filter and allows for the direct use of absorption-contrast FBP algorithms. Consequently, FBP-oriented image processing techniques and reconstruction acceleration softwares that have already been successfully used in absorption-contrast CT can be directly adopted to improve the DPC-CT image quality and speed up the reconstruction

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.

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.

Dysprosium disilicide nanostructures on silicon(001) studied by scanning tunneling microscopy and transmission electron microscopy

International Nuclear Information System (INIS)

Ye Gangfeng; Nogami, Jun; Crimp, Martin A.

2006-01-01

The microstructure of self-assembled dysprosium silicide nanostructures on silicon(001) has been studied by scanning tunneling microscopy and transmission electron microscopy. The studies focused on nanostructures that involve multiple atomic layers of the silicide. Cross-sectional high resolution transmission electron microscopy images and fast Fourier transform analysis showed that both hexagonal and orthorhombic/tetragonal silicide phases were present. Both the magnitude and the anisotropy of lattice mismatch between the silicide and the substrate play roles in the morphology and epitaxial growth of the nanostructures formed

A four-phase strategy for the implementation of reflectance confocal microscopy in dermatology.

Science.gov (United States)

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.

Space Inside a Liquid Sphere Transforms into De Sitter Space by Hilbert Radius

Science.gov (United States)

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.

A Hilbert transform method for parameter identification of time-varying structures with observer techniques

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)

The Hilbert-Huang Transform-Based Denoising Method for the TEM Response of a PRBS Source Signal

Science.gov (United States)

Hai, Li; Guo-qiang, Xue; Pan, Zhao; Hua-sen, Zhong; Khan, Muhammad Younis

2016-08-01

The denoising process is critical in processing transient electromagnetic (TEM) sounding data. For the full waveform pseudo-random binary sequences (PRBS) response, an inadequate noise estimation may result in an erroneous interpretation. We consider the Hilbert-Huang transform (HHT) and its application to suppress the noise in the PRBS response. The focus is on the thresholding scheme to suppress the noise and the analysis of the signal based on its Hilbert time-frequency representation. The method first decomposes the signal into the intrinsic mode function, and then, inspired by the thresholding scheme in wavelet analysis; an adaptive and interval thresholding is conducted to set to zero all the components in intrinsic mode function which are lower than a threshold related to the noise level. The algorithm is based on the characteristic of the PRBS response. The HHT-based denoising scheme is tested on the synthetic and field data with the different noise levels. The result shows that the proposed method has a good capability in denoising and detail preservation.

Wide Bandpass and Narrow Bandstop Microstrip Filters based on Hilbert fractal geometry: design and simulation results.

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.

Context based mixture model for cell phase identification in automated fluorescence microscopy

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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

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

Experimental evaluation of the ‘transport-of-intensity’ equation for magnetic phase reconstruction in Lorentz transmission electron microscopy

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

Verification of Equivalence of the Axial Gauge to the Coulomb Gauge in QED by Embedding in the Indefinite Metric Hilbert Space : Particles and Fields

OpenAIRE

Yuji, NAKAWAKI; Azuma, TANAKA; Kazuhiko, OZAKI; Division of Physics and Mathematics, Faculty of Engineering Setsunan University; Junior College of Osaka Institute of Technology; Faculty of General Education, Osaka Institute of Technology

1994-01-01

Gauge Equivalence of the A_3=0 (axial) gauge to the Coulomb gauge is directly verified in QED. For that purpose a pair of conjugate zero-norm fields are introduced. This enables us to construct a canonical formulation in the axial gauge embedded in the indefinite metric Hilbert space in such a way that the Feynman rules are not altered. In the indefinite metric Hilbert space we can implement a gauge transformation, which otherwise has to be carried out only by hand, as main parts of a canonic...

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

Investigation of shape memory of red blood cells using optical tweezers and quantitative phase microscopy

Science.gov (United States)

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.

Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

OpenAIRE

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.

Friedrichs systems in a Hilbert space framework: Solvability and multiplicity

Science.gov (United States)

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.

Spatially resolved quantitative mapping of thermomechanical properties and phase transition temperatures using scanning probe microscopy

Science.gov (United States)

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.

An Hilbert space approach for a class of arbitrage free implied volatilities models

OpenAIRE

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...

Assessment of occupational exposure to asbestos fibers: Contribution of analytical transmission electron microscopy analysis and comparison with phase-contrast microscopy.

Science.gov (United States)

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.

Short-coherence in-line phase-shifting infrared digital holographic microscopy for measurement of internal structure in silicon

Science.gov (United States)

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.

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

Quantitative phase separation in multiferroic Bi0.88Sm0.12FeO3 ceramics via piezoresponse force microscopy

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

Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders

KAUST Repository

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

Scanning force microscopy study of phase segregation in fuel cell membrane materials as a function of solvent polarity and relative humidity

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.

High resolution transmission electron microscopy studies of {sigma} phase in Ni-based single crystal superalloys

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

Leakage radiation interference microscopy.

Science.gov (United States)

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.

Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces

Science.gov (United States)

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.

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

Experimental investigations of two-phase flow measurement using ultrasonic sensors

OpenAIRE

Abbagoni, Baba Musa

2016-01-01

This thesis presents the investigations conducted in the use of ultrasonic technology to measure two-phase flow in both horizontal and vertical pipe flows which is important for the petroleum industry. However, there are still key challenges to measure parameters of the multiphase flow accurately. Four methods of ultrasonic technologies were explored. The Hilbert-Huang transform (HHT) was first applied to the ultrasound signals of air-water flow on horizontal flow for measur...

Quantum Geometric Phase in Majorana's Stellar Representation: Mapping onto a Many-Body Aharonov-Bohm Phase

Science.gov (United States)

Bruno, Patrick

2012-06-01

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Convex analysis and monotone operator theory in Hilbert spaces

CERN Document Server

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...

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

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.

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.

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

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.

Periodic Points in Genus Two: Holomorphic Sections over Hilbert Modular Varieties, Teichmuller Dynamics, and Billiards

OpenAIRE

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 ...

On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

OpenAIRE

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...

Quantitative phase microscopy using deep neural networks

Science.gov (United States)

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.

On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

International Nuclear Information System (INIS)

Manakov, S V; Santini, P M

2008-01-01

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking

On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

Energy Technology Data Exchange (ETDEWEB)

Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)

2008-02-08

We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

Smart wave filtering method of a rectangular panel using Hilbert transformers and its application to an adaptive control system

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

Canonically conjugate pairs and phase operators

International Nuclear Information System (INIS)

Schoenhammer, K.

2002-01-01

For quantum mechanics on a lattice the position ('particle number') operator and the quasimomentum ('phase') operator obey canonical commutation relations (CCRs) only on a dense set of the Hilbert space. We compare exact numerical results for a particle in a linear and a quadratic potential on the lattice with the expectations, when the CCRs are assumed to be strictly obeyed. Only for sufficiently smooth eigenfunctions does this lead to reasonable results. In the long time limit the use of the CCRs can lead to a qualitatively wrong dynamics even if the initial state is in the dense set

Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution

International Nuclear Information System (INIS)

Bohm, A.; Boya, L.J.; Mostafazadeh, A.; Rudolph, G.

1993-03-01

The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors

Off-diagonal generalization of the mixed-state geometric phase

International Nuclear Information System (INIS)

Filipp, Stefan; Sjoeqvist, Erik

2003-01-01

The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed-state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed-state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into two parts: one part where each basis vector undergoes cyclic evolution and one part where all basis vectors are permuted among each other. We also demonstrate a purification based experimental procedure for the two lowest-order mixed-state phases and consider a physical scenario for a full characterization of the qubit mixed-state geometric phases in terms of polarization-entangled photon pairs. An alternative second order off-diagonal mixed-state geometric phase, which can be tested in single-particle experiments, is proposed

Unexplored regions in QFT: an alternative resolution of the gauge-theoretic clash between localization and the Hilbert space of quantum theory

International Nuclear Information System (INIS)

Schroer, Bert; FU-Berlin

2012-02-01

Massive quantum matter of prescribed spin permits infinitely many possibilities of covariantization in terms of spinorial (undotted/dotted) pointlike fields, whereas massless nite helicity representations lead to large gap in this spinorial spectrum which for s=1 excludes vector potentials. Since the nonexistence of such pointlike generators is the result of a deep structural clash between modular localization and the Hilbert space setting of QT, there are two ways out: gauge theory which sacrifices the Hilbert space and keeps the pointlike formalism and the use of string like potentials which allows to preserve the Hilbert space. The latter setting contains also string-localized charge-carrying operators whereas the gauge theoretic formulation is limited to point-like generated observables. This description also gives a much better insight into the Higgs mechanism which leads to a revival of the more physical 'Schwinger-Higgs' screening idea. The new formalism is not limited to m=0, s=1, it leads to renormalizable inter- actions in the sense of power-counting for all s in massless representations. The existence of string like vector potentials is preempted by the Aharonov-Bohm effect in QFT; it is well-known that the use of pointlike vector potentials in Stokes theorem would with lead to wrong results. Their use in Maxwell's equations is known to lead to zero Maxwell charge. The role of string-localization in the problem behind the observed invisibility and confinement of gluons and quarks leads to new questions and problems. (author)

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.

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.

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...

Automatic neuron segmentation and neural network analysis method for phase contrast microscopy images.

Science.gov (United States)

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.

Fresnel diffraction correction by phase-considered iteration procedure in soft X-ray projection microscopy

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.

Differential dynamic optical microscopy for the characterization of soft matter: liquid crystal dynamics, volume phase transition of hydrogels, and phase transition of binary mixtures

Science.gov (United States)

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).

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

Rosette of rosettes of Hilbert spaces in the indefinite metric state space of the quantized Maxwell field

International Nuclear Information System (INIS)

Gessner, W.; Ernst, V.

1980-01-01

The indefinite metric space O/sub M/ of the covariant form of the quantized Maxwell field M is analyzed in some detail. S/sub M/ contains not only the pre-Hilbert space X 0 of states of transverse photons which occurs in the Gupta--Bleuler formalism of the free M, but a whole rosette of continuously many, isomorphic, complete, pre-Hilbert spaces L/sup q/ disjunct up to the zero element o of S/sub M/. The L/sup q/ are the maximal subspaces of S/sub M/ which allow the usual statistical interpretation. Each L/sup q/ corresponds uniquely to one square integrable, spatial distribution j/sup o/(x) of the total charge Q=0. If M is in any state from L/sup q/, the bare charge j 0 (x) appears to be inseparably dressed by the quantum equivalent of its proper, classical Coulomb field E(x). The vacuum occurs only in the state space L 0 of the free Maxwell field. Each L/sup q/ contains a secondary rosette of continuously many, up to o disjunct, isomorphic Hilbert spaces H/sub g//sup q/ related to different electromagnetic gauges. The space H/sub o//sup q/, which corresponds to the Coulomb gauge within the Lorentz gauge, plays a physically distinguished role in that only it leads to the usual concept of energy. If M is in any state from H/sub g//sup q/, the bare 4-current j 0 (x), j(x), where j(x) is any square integrable, transverse current density in space, is endowed with its proper 4-potential which depends on the chosen gauge, and with its proper, gauge independent, Coulomb--Oersted field E(x), B(x). However, these fields exist only in the sense of quantum mechanical expectation values equipped with the corresponding field fluctuations. So they are basically different from classical electromagnetic fields

The nanoscale phase distinguishing of PCL-PB-PCL blended in epoxy resin by tapping mode atomic force microscopy

Science.gov (United States)

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.

Dual light-emitting diode-based multichannel microscopy for whole-slide multiplane, multispectral and phase imaging.

Science.gov (United States)

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.

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).

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...

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 $\\mathbb{S}^2$.

Atomic resolution three-dimensional electron diffraction microscopy

International Nuclear Information System (INIS)

Miao Jianwei; Ohsuna, Tetsu; Terasaki, Osamu; Hodgson, Keith O.; O'Keefe, Michael A.

2002-01-01

We report the development of a novel form of diffraction-based 3D microscopy to overcome resolution barriers inherent in high-resolution electron microscopy and tomography. By combining coherent electron diffraction with the oversampling phasing method, we show that the 3D structure of a nanocrystal can be determined ab initio at a resolution of 1 Angstrom from 29 simulated noisy diffraction patterns. This new form of microscopy can be used to image the 3D structures of nanocrystals and noncrystalline samples, with resolution limited only by the quality of sample diffraction

Quantitative transmission electron microscopy and atom probe tomography study of Ag-dependent precipitation of Ω phase in Al-Cu-Mg alloys

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.

In Situ Transmission Electron Microscopy Observation of Nanostructural Changes in Phase-Change Memory

KAUST Repository

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.

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.

Quantitative DIC microscopy using an off-axis self-interference approach.

Science.gov (United States)

Fu, Dan; Oh, Seungeun; Choi, Wonshik; Yamauchi, Toyohiko; Dorn, August; Yaqoob, Zahid; Dasari, Ramachandra R; Feld, Michael S

2010-07-15

Traditional Normarski differential interference contrast (DIC) microscopy is a very powerful method for imaging nonstained biological samples. However, one of its major limitations is the nonquantitative nature of the imaging. To overcome this problem, we developed a quantitative DIC microscopy method based on off-axis sample self-interference. The digital holography algorithm is applied to obtain quantitative phase gradients in orthogonal directions, which leads to a quantitative phase image through a spiral integration of the phase gradients. This method is practically simple to implement on any standard microscope without stringent requirements on polarization optics. Optical sectioning can be obtained through enlarged illumination NA.

High resolution terahertz spectroscopy of a whispering gallery mode bubble resonator using Hilbert analysis.

Science.gov (United States)

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.

Resolving Nonstationary Spectral Information in Wind Speed Time Series Using the Hilbert-Huang Transform

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...

Characterization of duplex stainless steels by TEM [transmission electron microscopy], SANS [small-angle neutron scattering], and APFIM [atom-probe field ion microscopy] techniques

International Nuclear Information System (INIS)

Chung, H.M.; Chopra, O.K.

1987-06-01

Results are presented of complementary characterization of aged duplex stainless steels by advanced metallographic techniques, including transmission and high-voltage electron microscopies; small-angle neutron scattering; and atom-probe field ion microscopy. On the basis of the characterization, the mechanisms of aging embrittlement have been shown to be associated with the precipitation of Ni- and Si-rich G phase and Cr-rich α' in the ferrite, and M 23 C 6 carbides on the austenite-ferrite phase boundaries. 19 refs., 19 figs., 1 tab

On-line quantile regression in the RKHS (Reproducing Kernel Hilbert Space) for operational probabilistic forecasting of wind power

International Nuclear Information System (INIS)

Gallego-Castillo, Cristobal; Bessa, Ricardo; Cavalcante, Laura; Lopez-Garcia, Oscar

2016-01-01

Wind power probabilistic forecast is being used as input in several decision-making problems, such as stochastic unit commitment, operating reserve setting and electricity market bidding. This work introduces a new on-line quantile regression model based on the Reproducing Kernel Hilbert Space (RKHS) framework. Its application to the field of wind power forecasting involves a discussion on the choice of the bias term of the quantile models, and the consideration of the operational framework in order to mimic real conditions. Benchmark against linear and splines quantile regression models was performed for a real case study during a 18 months period. Model parameter selection was based on k-fold crossvalidation. Results showed a noticeable improvement in terms of calibration, a key criterion for the wind power industry. Modest improvements in terms of Continuous Ranked Probability Score (CRPS) were also observed for prediction horizons between 6 and 20 h ahead. - Highlights: • New online quantile regression model based on the Reproducing Kernel Hilbert Space. • First application to operational probabilistic wind power forecasting. • Modest improvements of CRPS for prediction horizons between 6 and 20 h ahead. • Noticeable improvements in terms of Calibration due to online learning.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

Science.gov (United States)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

Graphene based tunable fractal Hilbert curve array broadband radar absorbing screen for radar cross section reduction

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.

Graphene based tunable fractal Hilbert curve array broadband radar absorbing screen for radar cross section reduction

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

Differential Galois theory through Riemann-Hilbert correspondence an elementary introduction

CERN Document Server

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...

Field-based dynamic light scattering microscopy: theory and numerical analysis.

Science.gov (United States)

Joo, Chulmin; de Boer, Johannes F

2013-11-01

We present a theoretical framework for field-based dynamic light scattering microscopy based on a spectral-domain optical coherence phase microscopy (SD-OCPM) platform. SD-OCPM is an interferometric microscope capable of quantitative measurement of amplitude and phase of scattered light with high phase stability. Field-based dynamic light scattering (F-DLS) analysis allows for direct evaluation of complex-valued field autocorrelation function and measurement of localized diffusive and directional dynamic properties of biological and material samples with high spatial resolution. In order to gain insight into the information provided by F-DLS microscopy, theoretical and numerical analyses are performed to evaluate the effect of numerical aperture of the imaging optics. We demonstrate that sharp focusing of fields affects the measured diffusive and transport velocity, which leads to smaller values for the dynamic properties in the sample. An approach for accurately determining the dynamic properties of the samples is discussed.

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.

Effects of phase and coupling between the vibrational modes on selective excitation in coherent anti-Stokes Raman scattering microscopy

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.

Quantum Unique Ergodicity for Eisenstein Series on the Hilbert Modular Group over a Totally Real Field

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....

Phase correlation of foreign exchange time series

Science.gov (United States)

Wu, Ming-Chya

2007-03-01

Correlation of foreign exchange rates in currency markets is investigated based on the empirical data of USD/DEM and USD/JPY exchange rates for a period from February 1 1986 to December 31 1996. The return of exchange time series is first decomposed into a number of intrinsic mode functions (IMFs) by the empirical mode decomposition method. The instantaneous phases of the resultant IMFs calculated by the Hilbert transform are then used to characterize the behaviors of pricing transmissions, and the correlation is probed by measuring the phase differences between two IMFs in the same order. From the distribution of phase differences, our results show explicitly that the correlations are stronger in daily time scale than in longer time scales. The demonstration for the correlations in periods of 1986-1989 and 1990-1993 indicates two exchange rates in the former period were more correlated than in the latter period. The result is consistent with the observations from the cross-correlation calculation.

Exploring neural cell dynamics with digital holographic microscopy

KAUST Repository

Marquet, Pierre; Depeursinge, Christian D.; Magistretti, Pierre J.

2013-01-01

In this review, we summarize how the new concept of digital optics applied to the field of holographic microscopy has allowed the development of a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM) technique at the nanoscale particularly suitable for cell imaging. Particular emphasis is placed on the original biological ormation provided by the quantitative phase signal. We present the most relevant DH-QPM applications in the field of cell biology, including automated cell counts, recognition, classification, three-dimensional tracking, discrimination between physiological and pathophysiological states, and the study of cell membrane fluctuations at the nanoscale. In the last part, original results show how DH-QPM can address two important issues in the field of neurobiology, namely, multiple-site optical recording of neuronal activity and noninvasive visualization of dendritic spine dynamics resulting from a full digital holographic microscopy tomographic approach. Copyright © 2013 by Annual Reviews.

Exploring neural cell dynamics with digital holographic microscopy

KAUST Repository

Marquet, Pierre

2013-07-11

In this review, we summarize how the new concept of digital optics applied to the field of holographic microscopy has allowed the development of a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM) technique at the nanoscale particularly suitable for cell imaging. Particular emphasis is placed on the original biological ormation provided by the quantitative phase signal. We present the most relevant DH-QPM applications in the field of cell biology, including automated cell counts, recognition, classification, three-dimensional tracking, discrimination between physiological and pathophysiological states, and the study of cell membrane fluctuations at the nanoscale. In the last part, original results show how DH-QPM can address two important issues in the field of neurobiology, namely, multiple-site optical recording of neuronal activity and noninvasive visualization of dendritic spine dynamics resulting from a full digital holographic microscopy tomographic approach. Copyright © 2013 by Annual Reviews.

Design and Development of a compact and ruggest phase and flouresence microscope for space utilization, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — In this SBIR Phase 1 we propose to develop a novel microscope by integrating Fourier phase contrast microscopy (FPCM) and epi-fluorescence microscopy. In FPCM, the...

Improved phase sensitivity in spectral domain phase microscopy using line-field illumination and self phase-referencing

Science.gov (United States)

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

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system.

Science.gov (United States)

Zhao, Hui; Li, Yingcai

2010-08-01

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle.

Transmission electron microscopy characterization of the interfacial structure of a galvanized dual-phase steel

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.

Non-commutative geometry on quantum phase-space

International Nuclear Information System (INIS)

Reuter, M.

1995-06-01

A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

Microstructural and micromechanical characterisation of TiAl alloys using atomic force microscopy and nanoindentation

International Nuclear Information System (INIS)

Gebhard, S.; Pyczak, F.; Goeken, M.

2009-01-01

Different microstructures were generated in the Ti-45Al-4.6Nb-0.2B-0.2C and Ti-45Al-1Cr alloys (at.%) by heat treatment. The microstructures were investigated using nanoindentation and atomic force microscopy which was compared with transmission electron microscopy. Topographic contrast is usually used for phase identification in the atomic force microscope. However, it was found that the topographic order of the phases changes with different microstructures and specimen preparations. Nanoindentation measurements provided local hardness values not obtainable by other methods and enabled clear distinction of the phases. The hardness values can give information on surrounding microstructure and solid solution hardening. The mean lamellar spacing of the colonies was measured using both atomic force microscopy and transmission electron microscopy. Atomic force microscopy was found to be suitable to determine the spacing between α 2 /γ-interfaces offering the advantages of easier sample preparation and fewer specimens compared to evaluation by TEM analysis.

Wearable Sensor-Based Human Activity Recognition Method with Multi-Features Extracted from Hilbert-Huang Transform.

Science.gov (United States)

Xu, Huile; Liu, Jinyi; Hu, Haibo; Zhang, Yi

2016-12-02

Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT) or wavelet transform (WT). However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT) for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA) and instantaneous frequency (IF) by means of empirical mode decomposition (EMD), as well as instantaneous energy density (IE) and marginal spectrum (MS) derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.

Automated Method for the Rapid and Precise Estimation of Adherent Cell Culture Characteristics from Phase Contrast Microscopy Images

Science.gov (United States)

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

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)

Evaluation of virtual microscopy in medical histology teaching.

Science.gov (United States)

Mione, Sylvia; Valcke, Martin; Cornelissen, Maria

2013-01-01

Histology stands as a major discipline in the life science curricula, and the practice of teaching it is based on theoretical didactic strategies along with practical training. Traditionally, students achieve practical competence in this subject by learning optical microscopy. Today, students can use newer information and communication technologies in the study of digital microscopic images. A virtual microscopy program was recently introduced at Ghent University. Since little empirical evidence is available concerning the impact of virtual microscopy (VM) versus optical microscopy (OM) on the acquisition of histology knowledge, this study was set up in the Faculty of Medicine and Health Sciences. A pretest-post test and cross-over design was adopted. In the first phase, the experiment yielded two groups in a total population of 199 students, Group 1 performing the practical sessions with OM versus Group 2 performing the same sessions with VM. In the second phase, the research subjects switched conditions. The prior knowledge level of all research subjects was assessed with a pretest. Knowledge acquisition was measured with a post test after each phase (T1 and T2). Analysis of covariance was carried out to study the differential gain in knowledge at T1 and T2, considering the possible differences in prior knowledge at the start of the study. The results pointed to non-significant differences at T1 and at T2. This supports the assumption that the acquisition of the histology knowledge is independent of the microscopy representation mode (VM versus OM) of the learning material. The conclusion that VM is equivalent to OM offers new directions in view of ongoing innovations in medical education technology. Copyright © 2013 American Association of Anatomists.

Visualization of phase evolution in model organic photovoltaic structures via energy-filtered transmission electron microscopy.

Science.gov (United States)

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.

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

Science.gov (United States)

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.

Helium ion microscopy based wall thickness and surface roughness analysis of polymer foams obtained from high internal phase emulsion

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

Helium ion microscopy based wall thickness and surface roughness analysis of polymer foams obtained from high internal phase emulsion

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.

Determination of partition coefficients of biomolecules in a microfluidic aqueous two phase system platform using fluorescence microscopy.

Science.gov (United States)

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.

Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field

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....

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

Science.gov (United States)

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.

Investigation of the martensitic phase transformations in CoFe single crystals using high-resolution transmission electron microscopy

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

Regularized iterative integration combined with non-linear diffusion filtering for phase-contrast x-ray computed tomography.

Science.gov (United States)

Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter

2014-12-29

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

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)

Quantitative phase imaging and differential interference contrast imaging for biological TEM

International Nuclear Information System (INIS)

Allman, B.E.; McMahon, P.J.; Barone-Nugent, E.D.; Nugent, E.D.

2002-01-01

Full text: Phase microscopy is a central technique in science. An experienced microscopist uses this effect to visualise (edge) structure within transparent samples by slightly defocusing the microscope. Although widespread in optical microscopy, phase contrast transmission electron microscopy (TEM) has not been widely adopted. TEM for biological specimens has largely relied on staining techniques to yield sufficient contrast. We show here a simple method for quantitative TEM phase microscopy that quantifies this phase contrast effect. Starting with conventional, digital, bright field images of the sample, our algorithm provides quantitative phase information independent of the sample's bright field intensity image. We present TEM phase images of a range of stained and unstained, biological and material science specimens. This independent phase and intensity information is then used to emulate a range of phase visualisation images familiar to optical microscopy, e.g. differential interference contrast. The phase images contain features not visible with the other imaging modalities. Further, if the TEM samples have been prepared on a microtome to a uniform thickness, the phase information can be converted into refractive index structure of the specimen. Copyright (2002) Australian Society for Electron Microscopy Inc

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)

Experimental transmission electron microscopy studies and phenomenological model of bismuth-based superconducting compounds; Etudes experimentales par microscopie electronique en transmission et modele phenomenologique des composes supraconducteurs a base de bismuth

Energy Technology Data Exchange (ETDEWEB)

Elboussiri, Khalid

1991-09-26

The main part of this thesis is devoted to an experimental study by transmission electron microscopy of the different phases of the superconducting bismuth cuprates Bi{sub 2}Sr{sub 2}Ca{sub n-1}Cu{sub n}O{sub 2n+4}. In high resolution electron microscopy, the two types of incommensurate modulation realized in these compounds have been observed. A model of structure has been proposed from which the simulated images obtained are consistent with observations. The medium resolution images correlated with the electron diffraction data have revealed existence of a multi-soliton regime with latent lock in phases of commensurate periods between 4b and 10b. At last, a description of different phases of these compounds as a result of superstructures from a disordered perovskite type structure is proposed (author) [French] Le travail presente dans cette these consiste en une etude experimentale essentiellement par microscopie electronique en transmission des differentes phases supraconductrices presentes dans les composes appartenant a la famille des cuprates de bismuth Bi{sub 2}Sr{sub 2}Ca{sub n-1}Cu{sub n}O{sub 2n+4}. Les obsevations de microscopie electronique a haute resolution ont permis de mettre en evidence les differentes modulations incommensurables realisees dans ces composes. Un modele de structure est propose et a permis d'obtenir des images simulees compatibles avec les observations. D'autre part, les observations de microscopie electronique en moyenne resolution sur ces composes, combinees avec les resultats de diffraction electronique, ont montre l'existence d'un regime multisoliton associe a des phases de Lock-in latentes de parametres compris entre 4b et 10b. Enfin, une description des differentes phases de ces composes en terme de surstructures derivees de structure perovskite desordonnee est exposee. (auteur)

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.

Study of the structure of the particles of channel black of phase-contrasting electron microscopy of high resolution

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.

Electron microscopy of nuclear zirconium alloys

International Nuclear Information System (INIS)

Versaci, R.A.; Ipohorski, Miguel

1986-01-01

Transmission electron microscopy observations of the microstructure of zirconium alloys used in fuel sheaths of nuclear power reactors are reported. Specimens were observed after different thermal and mechanical treatment, similar to those actually used during fabrication of the sheaths. Electron micrographs and electron diffraction patterns of second phase particles present in zircaloy-2 and zircaloy-4 were also obtained, as well as some characteristic parameters. Images of oxides and hydrides most commonly present in zirconium alloys are also shown. Finally, the structure of a Zr-2,5Nb alloy used in CANDU reactors pressure tubes, is observed by electron microscopy. (Author) [es

Multiscale phase mapping of LiFePO4-based electrodes by transmission electron microscopy and electron forward scattering diffraction.

Science.gov (United States)

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.

Wearable Sensor-Based Human Activity Recognition Method with Multi-Features Extracted from Hilbert-Huang Transform

Directory of Open Access Journals (Sweden)

Huile Xu

2016-12-01

Full Text Available Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT or wavelet transform (WT. However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA and instantaneous frequency (IF by means of empirical mode decomposition (EMD, as well as instantaneous energy density (IE and marginal spectrum (MS derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.

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

Chiral Floquet Phases of Many-Body Localized Bosons

Directory of Open Access Journals (Sweden)

Hoi Chun Po

2016-12-01

Full Text Available We construct and classify chiral topological phases in driven (Floquet systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

Use of atomic force microscopy and transmission electron microscopy for correlative studies of bacterial capsules.

Science.gov (United States)

Stukalov, Oleg; Korenevsky, Anton; Beveridge, Terry J; Dutcher, John R

2008-09-01

Bacteria can possess an outermost assembly of polysaccharide molecules, a capsule, which is attached to their cell wall. We have used two complementary, high-resolution microscopy techniques, atomic force microscopy (AFM) and transmission electron microscopy (TEM), to study bacterial capsules of four different gram-negative bacterial strains: Escherichia coli K30, Pseudomonas aeruginosa FRD1, Shewanella oneidensis MR-4, and Geobacter sulfurreducens PCA. TEM analysis of bacterial cells using different preparative techniques (whole-cell mounts, conventional embeddings, and freeze-substitution) revealed capsules for some but not all of the strains. In contrast, the use of AFM allowed the unambiguous identification of the presence of capsules on all strains used in the present study, including those that were shown by TEM to be not encapsulated. In addition, the use of AFM phase imaging allowed the visualization of the bacterial cell within the capsule, with a depth sensitivity that decreased with increasing tapping frequency.

Feature Extraction and Classification of EHG between Pregnancy and Labour Group Using Hilbert-Huang Transform and Extreme Learning Machine

Directory of Open Access Journals (Sweden)

Lili Chen

2017-01-01

Full Text Available Preterm birth (PTB is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT and extreme learning machine (ELM. For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs using empirical mode decomposition (EMD. Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

International Nuclear Information System (INIS)

Loubenets, Elena R.

2015-01-01

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)

Feature Extraction and Classification of EHG between Pregnancy and Labour Group Using Hilbert-Huang Transform and Extreme Learning Machine.

Science.gov (United States)

Chen, Lili; Hao, Yaru

2017-01-01

Preterm birth (PTB) is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG) related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT) and extreme learning machine (ELM). For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC) curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.

Stratum corneum lipid organization as observed by atomic force, confocal and two-photon excitation fluorescence microscopy

DEFF Research Database (Denmark)

Norlén, Lars; Plasencia Gil, Maria Inés; Bagatolli, Luis

2008-01-01

-related biophysical techniques (e.g. atomic force microscopy and confocal/two-photon excitation fluorescence microscopy), it was recently shown that reconstituted membranes composed of extracted decontaminated human stratum corneum lipids do not form a fluid phase, but exclusively a single-gel phase that segregates...

Berry phase and entangled systems: a proposal for an experimental realization with neutrons

International Nuclear Information System (INIS)

Bertlmann, R.A.; Durstberger, K.; Hiesmayr, B.C.; Hasegawa, Y.

2003-01-01

Full text: The Berry phase - a geometric object - is included into an entangled spin-1/2 system. We discuss the case, where only one part of the Hilbert space is affected by the geometric phase. We are able to cancel the effects of the dynamical phase by using the 'spin-echo' method. With this modified state we establish a CHSH-inequality to test locality and study how the geometry effects the entanglement. We suggest an experimental realization of the proposed set-up using neutron interferometry, which is an almost ideal tool to investigate the evolution of a two-level system, e.g., spin-1/2. We see that the theoretical predictions can be tested within this set-up, where we have to deal with contextuality rather than locality. (author)

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.

A Barcoding Strategy Enabling Higher-Throughput Library Screening by Microscopy.

Science.gov (United States)

Chen, Robert; Rishi, Harneet S; Potapov, Vladimir; Yamada, Masaki R; Yeh, Vincent J; Chow, Thomas; Cheung, Celia L; Jones, Austin T; Johnson, Terry D; Keating, Amy E; DeLoache, William C; Dueber, John E

2015-11-20

Dramatic progress has been made in the design and build phases of the design-build-test cycle for engineering cells. However, the test phase usually limits throughput, as many outputs of interest are not amenable to rapid analytical measurements. For example, phenotypes such as motility, morphology, and subcellular localization can be readily measured by microscopy, but analysis of these phenotypes is notoriously slow. To increase throughput, we developed microscopy-readable barcodes (MiCodes) composed of fluorescent proteins targeted to discernible organelles. In this system, a unique barcode can be genetically linked to each library member, making possible the parallel analysis of phenotypes of interest via microscopy. As a first demonstration, we MiCoded a set of synthetic coiled-coil leucine zipper proteins to allow an 8 × 8 matrix to be tested for specific interactions in micrographs consisting of mixed populations of cells. A novel microscopy-readable two-hybrid fluorescence localization assay for probing candidate interactions in the cytosol was also developed using a bait protein targeted to the peroxisome and a prey protein tagged with a fluorescent protein. This work introduces a generalizable, scalable platform for making microscopy amenable to higher-throughput library screening experiments, thereby coupling the power of imaging with the utility of combinatorial search paradigms.

French Society of Microscopies, 11. Colloquium. SFM Paris 2009. Compilation of summaries

International Nuclear Information System (INIS)

2009-06-01

The 11. conference of the SFM (French Society of Microscopies), held in Paris in 2009, was divided into 14 symposiums, 4 GN-MEBA symposiums, and 10 workshops. The titles of the symposiums are: homage to Nicolas Boisset, advanced microscopies, alternative microscopies, new optical and plasmonic imaging microscopies, dynamic and quantitative microscopy of the living matter, photonic and correlative electronic microscopy, near field microscopy, molecular and cellular electronic cryo-microscopy, cellular compartmentation and dynamics (CFPU), microscopy and materials, dynamical microscopy in materials science, minerals/bio-minerals and environment, structure and properties of nano-materials, sub-eV and sub-nm chemical bonds imaging. The titles of the GN-MEBA symposiums are: microscopy and metals, microscopy and minerals, microscopy and living beings, microscopy and new materials. The titles of the workshops are: Correlative Light and Electron Microscopy (CLEM), Cryo and electronic tomography in cellular biology, Cryo electronic microscopy of vitreous sections (CEMOVIS), Atomic Force Microscopy (AFM), ULTRASTEM, Digital Micrograph programming, Cryo-Microscopy and molecular tomography, Cryo-ultra-microtomy and immuno-marking, FIB, ASTAR(EBSD-MET) - rapid mapping of crystalline orientations and phases

Real-time observation of growth and orientation of Sm-Ba-Cu-O phases on a Sm-211 whisker substrate by high-temperature optical microscopy

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

Phase transition behaviors of the supported DPPC bilayer investigated by sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM).

Science.gov (United States)

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.

Study of NaCl:Mn2+ nanostructures in the Suzuki phase by optical spectroscopy and atomic force microscopy

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

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)

Exploring Neural Cell Dynamics with Digital Holographic Microscopy

KAUST Repository

Marquet, Pierre; Jourdain, Pascal; Boss, Daniel; Depeursinge, Christian D.; Magistretti, Pierre J.

2013-01-01

In this talk, I will present how digital holographic microscopy, as a powerful quantitative phase technique, can non-invasively measure cell dynamics and especially resolve local neuronal network activity through simultaneous multiple site optical recording.

Exploring Neural Cell Dynamics with Digital Holographic Microscopy

KAUST Repository

Marquet, Pierre

2013-04-21

In this talk, I will present how digital holographic microscopy, as a powerful quantitative phase technique, can non-invasively measure cell dynamics and especially resolve local neuronal network activity through simultaneous multiple site optical recording.

Polarized Light Microscopy

Science.gov (United States)

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

Hilbert-Huang transform analysis of long-term solar magnetic activity

Science.gov (United States)

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.

A High-Resolution Demodulation Algorithm for FBG-FP Static-Strain Sensors Based on the Hilbert Transform and Cross Third-Order Cumulant

Directory of Open Access Journals (Sweden)

Wenzhu Huang

2015-04-01

Full Text Available Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs. However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs. The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs’ reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method.

Liquid-phase sample preparation method for real-time monitoring of airborne asbestos fibers by dual-mode high-throughput microscopy.

Science.gov (United States)

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.

Scanning conductance microscopy investigations on fixed human chromosomes

DEFF Research Database (Denmark)

Clausen, Casper Hyttel; Lange, Jacob Moresco; Jensen, Linda Boye

2008-01-01

Scanning conductance microscopy investigations were carried out in air on human chromosomes fixed on pre-fabricated SiO2 surfaces with a backgate. The point of the investigation was to estimate the dielectric constant of fixed human chromosomes in order to use it for microfluidic device...... optimization. The phase shift caused by the electrostatic forces, together with geometrical measurements of the atomic force microscopy (AFM) cantilever and the chromosomes were used to estimate a value,for the dielectric constant of different human chromosomes....

A time-frequency analysis method to obtain stable estimates of magnetotelluric response function based on Hilbert-Huang transform

Science.gov (United States)

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.

The effect of phase constitution on the magnetic structure of nanophase NdFeB alloys observed by magnetic force microscopy

Science.gov (United States)

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.

Phase contrast scanning transmission electron microscopy imaging of light and heavy atoms at the limit of contrast and resolution.

Science.gov (United States)

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

Extraction of microseismic waveforms characteristics prior to rock burst using Hilbert-Huang transform

Science.gov (United States)

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.

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.

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.

[Realization of Heart Sound Envelope Extraction Implemented on LabVIEW Based on Hilbert-Huang Transform].

Science.gov (United States)

Tan, Zhixiang; Zhang, Yi; Zeng, Deping; Wang, Hua

2015-04-01

We proposed a research of a heart sound envelope extraction system in this paper. The system was implemented on LabVIEW based on the Hilbert-Huang transform (HHT). We firstly used the sound card to collect the heart sound, and then implemented the complete system program of signal acquisition, pretreatment and envelope extraction on LabVIEW based on the theory of HHT. Finally, we used a case to prove that the system could collect heart sound, preprocess and extract the envelope easily. The system was better to retain and show the characteristics of heart sound envelope, and its program and methods were important to other researches, such as those on the vibration and voice, etc.

Probing superconductors. Spectroscopic-imaging scanning tunneling microscopy

International Nuclear Information System (INIS)

Hanaguri, Tetsuo

2011-01-01

Discovery of high-temperature superconductivity in a cuprate triggered developments of various spectroscopic tools which have been utilized to elucidate electronic states of this mysterious compound. Particularly, angle-resolved photoemission spectroscopy and scanning-tunneling microscopy/spectroscopy are improved considerably. It is now possible to map the superconducting gap in both momentum and real spaces using these two techniques. Here we review spectroscopic-imaging scanning tunneling microscopy which is able to explore momentum-space phase structure of the superconducting gap, as well as real-space structure. Applications of this technique to a cuprate and an iron-based superconductor are discussed. (author)

On using the Hilbert transform for blind identification of complex modes: A practical approach

Science.gov (United States)

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

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.

Transmission Electron Microscopy Physics of Image Formation

CERN Document Server

Kohl, Helmut

2008-01-01

Transmission Electron Microscopy: Physics of Image Formation presents the theory of image and contrast formation, and the analytical modes in transmission electron microscopy. The principles of particle and wave optics of electrons are described. Electron-specimen interactions are discussed for evaluating the theory of scattering and phase contrast. Also discussed are the kinematical and dynamical theories of electron diffraction and their applications for crystal-structure analysis and imaging of lattices and their defects. X-ray microanalysis and electron energy-loss spectroscopy are treated as analytical methods. Specimen damage and contamination by electron irradiation limits the resolution for biological and some inorganic specimens. This fifth edition includes discussion of recent progress, especially in the area of aberration correction and energy filtering; moreover, the topics introduced in the fourth edition have been updated. Transmission Electron Microscopy: Physics of Image Formation is written f...

Automated classification of cell morphology by coherence-controlled holographic microscopy

Science.gov (United States)

Strbkova, Lenka; Zicha, Daniel; Vesely, Pavel; Chmelik, Radim

2017-08-01

In the last few years, classification of cells by machine learning has become frequently used in biology. However, most of the approaches are based on morphometric (MO) features, which are not quantitative in terms of cell mass. This may result in poor classification accuracy. Here, we study the potential contribution of coherence-controlled holographic microscopy enabling quantitative phase imaging for the classification of cell morphologies. We compare our approach with the commonly used method based on MO features. We tested both classification approaches in an experiment with nutritionally deprived cancer tissue cells, while employing several supervised machine learning algorithms. Most of the classifiers provided higher performance when quantitative phase features were employed. Based on the results, it can be concluded that the quantitative phase features played an important role in improving the performance of the classification. The methodology could be valuable help in refining the monitoring of live cells in an automated fashion. We believe that coherence-controlled holographic microscopy, as a tool for quantitative phase imaging, offers all preconditions for the accurate automated analysis of live cell behavior while enabling noninvasive label-free imaging with sufficient contrast and high-spatiotemporal phase sensitivity.

Determination of electrostatic force and its characteristics based on phase difference by amplitude modulation atomic force microscopy

Science.gov (United States)

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.

Electron microscopy characterization of Ni-Cr-B-Si-C laser deposited coatings.

Science.gov (United States)

Hemmati, I; Rao, J C; Ocelík, V; De Hosson, J Th M

2013-02-01

During laser deposition of Ni-Cr-B-Si-C alloys with high amounts of Cr and B, various microstructures and phases can be generated from the same chemical composition that results in heterogeneous properties in the clad layer. In this study, the microstructure and phase constitution of a high-alloy Ni-Cr-B-Si-C coating deposited by laser cladding were analyzed by a combination of several microscopy characterization techniques including scanning electron microscopy in secondary and backscatter imaging modes, energy dispersive spectroscopy (EDS), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM). The combination of EDS and EBSD allowed unequivocal identification of micron-sized precipitates as polycrystalline orthorhombic CrB, single crystal tetragonal Cr5B3, and single crystal hexagonal Cr7C3. In addition, TEM characterization showed various equilibrium and metastable Ni-B, Ni-Si, and Ni-Si-B eutectic products in the alloy matrix. The findings of this study can be used to explain the phase formation reactions and to tune the microstructure of Ni-Cr-B-Si-C coatings to obtain the desired properties.

Multiplexed phase-space imaging for 3D fluorescence microscopy.

Science.gov (United States)

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.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

Science.gov (United States)

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.

SOBRE EL CONTROL EN SISTEMAS DINÁMICOS DE DIMENSIÓN INFINITA EN ESPACIOS DE HILBERT Y DE FRECHÉT

OpenAIRE

Nancy López-Reyes

2017-01-01

Se revisa el Control sobre sistemas dinámicos lineales de dimensión infnita que evolucionan en espacios con propiedades geométrico-algebraicas diferentes. En un caso, sobre espacios de Hilbert, los cuales poseen una rica estructura geométrico-algebraica, muy útil para el tratamiento del control, desde el punto de vista del enfoque dominio-frecuencia y del enfoque espacio-estado. En el otro caso, sobre espacios de Frechét, en particular sobre H(D), cuyas propiedades geométricas implican un tra...

Duality, phase structures, and dilemmas in symmetric quantum games

International Nuclear Information System (INIS)

Ichikawa, Tsubasa; Tsutsui, Izumi

2007-01-01

Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD, and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of the players are provided

Chatter identification in milling of Inconel 625 based on recurrence plot technique and Hilbert vibration decomposition

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.

Classification of cyclic initial states and geometric phase for the spin-j system

Energy Technology Data Exchange (ETDEWEB)

Skrynnikov, N.R.; Zhou, J.; Sanctuary, B.C. [Dept. of Chem., McGill Univ., Montreal, PQ (Canada)

1994-09-21

Quantum states which evolve cyclically in their projective Hilbert space give rise to a geometric (or Aharonov-Anandan) phase. An aspect of primary interest is stable cyclic behaviour as realized under a periodic Hamiltonian. The problem has been handled by use of time-dependent transformations treated along the lines of Floquet's theory as well as in terms of exponential operators with a goal to examine the variety of initial states exhibiting cyclic behaviour. A particular case of special cyclic initial states is described which is shown to be important for nuclear magnetic resonance experiments aimed at the study of the effects of the geometric phase. An example of arbitrary spin j in a precessing magnetic field and spin j=1 subject to both axially symmetric quadrupolar interaction and a precessing magnetic field are presented. The invariant (Kobe's) geometric phase is calculated for special cyclic states. (author)

Analytical electron microscopy characterization of uranium-contaminated soils from the Fernald Site, FY1993 report

International Nuclear Information System (INIS)

Buck, E.C.; Cunnane, J.C.; Brown, N.R.; Dietz, N.L.

1994-10-01

A combination of optical microscopy, scanning electron microscopy with backscattered electron detection (SEM/BSE), and analytical electron microscopy (AEM) is being used to determine the nature of uranium in soils from the Fernald Environmental Management Project. The information gained from these studies is being used to develop and test remediation technologies. Investigations using SEM have shown that uranium is contained within particles that are typically 1 to 100 μm in diameter. Further analysis with AEM has shown that these uranium-rich regions are made up of discrete uranium-bearing phases. The distribution of these uranium phases was found to be inhomogeneous at the microscopic level

Characterization of multilayer nitride coatings by electron microscopy and modulus mapping

International Nuclear Information System (INIS)

Pemmasani, Sai Pramod; Rajulapati, Koteswararao V.; Ramakrishna, M.; Valleti, Krishna; Gundakaram, Ravi C.; Joshi, Shrikant V.

2013-01-01

This paper discusses multi-scale characterization of physical vapour deposited multilayer nitride coatings using a combination of electron microscopy and modulus mapping. Multilayer coatings with a triple layer structure based on TiAlN and nanocomposite nitrides with a nano-multilayered architecture were deposited by Cathodic arc deposition and detailed microstructural studies were carried out employing Energy Dispersive Spectroscopy, Electron Backscattered Diffraction, Focused Ion Beam and Cross sectional Transmission Electron Microscopy in order to identify the different phases and to study microstructural features of the various layers formed as a result of the deposition process. Modulus mapping was also performed to study the effect of varying composition on the moduli of the nano-multilayers within the triple layer coating by using a Scanning Probe Microscopy based technique. To the best of our knowledge, this is the first attempt on modulus mapping of cathodic arc deposited nitride multilayer coatings. This work demonstrates the application of Scanning Probe Microscopy based modulus mapping and electron microscopy for the study of coating properties and their relation to composition and microstructure. - Highlights: • Microstructure of a triple layer nitride coating studied at multiple length scales. • Phases identified by EDS, EBSD and SAED (TEM). • Nanolayered, nanocomposite structure of the coating studied using FIB and TEM. • Modulus mapping identified moduli variation even in a nani-multilayer architecture

High-resolution photoluminescence electro-modulation microscopy by scanning lock-in

Science.gov (United States)

Koopman, W.; Muccini, M.; Toffanin, S.

2018-04-01

Morphological inhomogeneities and structural defects in organic semiconductors crucially determine the charge accumulation and lateral transport in organic thin-film transistors. Photoluminescence Electro-Modulation (PLEM) microscopy is a laser-scanning microscopy technique that relies on the modulation of the thin-film fluorescence in the presence of charge-carriers to image the spatial distribution of charges within the active organic semiconductor. Here, we present a lock-in scheme based on a scanning beam approach for increasing the PLEM microscopy resolution and contrast. The charge density in the device is modulated by a sinusoidal electrical signal, phase-locked to the scanning beam of the excitation laser. The lock-in detection scheme is achieved by acquiring a series of images with different phases between the beam scan and the electrical modulation. Application of high resolution PLEM to an organic transistor in accumulation mode demonstrates its potential to image local variations in the charge accumulation. A diffraction-limited precision of sub-300 nm and a signal to noise ratio of 21.4 dB could be achieved.

Correlative Stochastic Optical Reconstruction Microscopy and Electron Microscopy

Science.gov (United States)

Kim, Doory; Deerinck, Thomas J.; Sigal, Yaron M.; Babcock, Hazen P.; Ellisman, Mark H.; Zhuang, Xiaowei

2015-01-01

Correlative fluorescence light microscopy and electron microscopy allows the imaging of spatial distributions of specific biomolecules in the context of cellular ultrastructure. Recent development of super-resolution fluorescence microscopy allows the location of molecules to be determined with nanometer-scale spatial resolution. However, correlative super-resolution fluorescence microscopy and electron microscopy (EM) still remains challenging because the optimal specimen preparation and imaging conditions for super-resolution fluorescence microscopy and EM are often not compatible. Here, we have developed several experiment protocols for correlative stochastic optical reconstruction microscopy (STORM) and EM methods, both for un-embedded samples by applying EM-specific sample preparations after STORM imaging and for embedded and sectioned samples by optimizing the fluorescence under EM fixation, staining and embedding conditions. We demonstrated these methods using a variety of cellular targets. PMID:25874453

Flexible Hilbert-Curve Loop Antenna Having a Triple-Band and Omnidirectional Pattern for WLAN/WiMAX Applications

Directory of Open Access Journals (Sweden)

Dang-Oh Kim

2012-01-01

Full Text Available A triple-band flexible loop antenna is proposed for WLAN/WiMAX applications in this paper. The proposed antenna is formed by the third-order Hilbert-curve and bending type structure which provides flexible characteristics. Even though the radius of the curvature for bending antennas is changed, a triple-band feature still remains in the proposed antenna. Moreover, the antenna exhibits the characteristics of omnidirectional radiation pattern and circular polarization. To verify the receiving performance of antenna, a simulation on the antenna factor was conducted by an EM simulator. Based on these results, the suggested antenna makes a noteworthy performance over typical loop antennas.

Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

Directory of Open Access Journals (Sweden)

Zhou Yinying

2014-01-01

Full Text Available We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009, Min and Chang (2012, Plubtieng and Punpaeng (2007, S. Takahashi and W. Takahashi (2007, Tada and Takahashi (2007, Gang and Changsong (2009, Ying (2013, Y. Yao and J. C. Yao (2007, and Yong-Cho and Kang (2012.

Preparation of ZiO2 specimens for transmission electron microscopy

International Nuclear Information System (INIS)

Bressiani, A.H.A.

1987-01-01

The determination of average grain size, of the presence of monoclinic, tetragonal and cubic phases, as well as their relative distributions are necessary for the study of several partially stabilized zirconia properties. However, the phase distributions can be changed during the preparation of specimens for transmission electron microscopy, yielding misleading results. In this work suitable preparation method is reported. (Author) [pt

Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection

Science.gov (United States)

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.

Determination of the positions and orientations of concentrated rod-like colloids from 3D microscopy data

International Nuclear Information System (INIS)

Besseling, T H; Hermes, M; Kuijk, A; De Nijs, B; Deng, T-S; Dijkstra, M; Imhof, A; Van Blaaderen, A

2015-01-01

Confocal microscopy in combination with real-space particle tracking has proven to be a powerful tool in scientific fields such as soft matter physics, materials science and cell biology. However, 3D tracking of anisotropic particles in concentrated phases remains not as optimized compared to algorithms for spherical particles. To address this problem, we developed a new particle-fitting algorithm that can extract the positions and orientations of fluorescent rod-like particles from three dimensional confocal microscopy data stacks. The algorithm is tailored to work even when the fluorescent signals of the particles overlap considerably and a threshold method and subsequent clusters analysis alone do not suffice. We demonstrate that our algorithm correctly identifies all five coordinates of uniaxial particles in both a concentrated disordered phase and a liquid-crystalline smectic-B phase. Apart from confocal microscopy images, we also demonstrate that the algorithm can be used to identify nanorods in 3D electron tomography reconstructions. Lastly, we determined the accuracy of the algorithm using both simulated and experimental confocal microscopy data-stacks of diffusing silica rods in a dilute suspension. This novel particle-fitting algorithm allows for the study of structure and dynamics in both dilute and dense liquid-crystalline phases (such as nematic, smectic and crystalline phases) as well as the study of the glass transition of rod-like particles in three dimensions on the single particle level. (paper)

Automated classification of cell morphology by coherence-controlled holographic microscopy.

Science.gov (United States)

Strbkova, Lenka; Zicha, Daniel; Vesely, Pavel; Chmelik, Radim

2017-08-01

In the last few years, classification of cells by machine learning has become frequently used in biology. However, most of the approaches are based on morphometric (MO) features, which are not quantitative in terms of cell mass. This may result in poor classification accuracy. Here, we study the potential contribution of coherence-controlled holographic microscopy enabling quantitative phase imaging for the classification of cell morphologies. We compare our approach with the commonly used method based on MO features. We tested both classification approaches in an experiment with nutritionally deprived cancer tissue cells, while employing several supervised machine learning algorithms. Most of the classifiers provided higher performance when quantitative phase features were employed. Based on the results, it can be concluded that the quantitative phase features played an important role in improving the performance of the classification. The methodology could be valuable help in refining the monitoring of live cells in an automated fashion. We believe that coherence-controlled holographic microscopy, as a tool for quantitative phase imaging, offers all preconditions for the accurate automated analysis of live cell behavior while enabling noninvasive label-free imaging with sufficient contrast and high-spatiotemporal phase sensitivity. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Three-dimensional motion-picture imaging of dynamic object by parallel-phase-shifting digital holographic microscopy using an inverted magnification optical system

Science.gov (United States)

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.

Fourier phase in Fourier-domain optical coherence tomography

Science.gov (United States)

Uttam, Shikhar; Liu, Yang

2015-01-01

Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383

Fourier phase in Fourier-domain optical coherence tomography.

Science.gov (United States)

Uttam, Shikhar; Liu, Yang

2015-12-01

Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.

Study of Perylenetetracarboxylic Acid Dimethylimide Films by Cyclic Thermal Desorption and Scanning Probe Microscopy

Science.gov (United States)

Pochtennyi, A. E.; Lappo, A. N.; Il'yushonok, I. P.

2018-02-01

Some results of studying the direct-current (DC) conductivity of perylenetetracarboxylic acid dimethylimide films by cyclic oxygen thermal desorption are presented. The microscopic parameters of hopping electron transport over localized impurity and intrinsic states were determined. The bandgap width and the sign of major current carriers were determined by scanning probe microscopy methods (atomic force microscopy, scanning probe spectroscopy, and photoassisted Kelvin probe force microscopy). The possibility of the application of photoassisted scanning tunneling microscopy for the nanoscale phase analysis of photoconductive films is discussed.

Characterization of konjac glucomannan-ethyl cellulose film formation via microscopy.

Science.gov (United States)

Xiao, Man; Wan, Li; Corke, Harold; Yan, Wenli; Ni, Xuewen; Fang, Yapeng; Jiang, Fatang

2016-04-01

Konjac glucomannan-ethyl cellulose (KGM-EC, 7:3, w/w) blended film shows good mechanical and moisture resistance properties. To better understand the basis for the KGM-EC film formation, optical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM) were used to observe the formation of the film from emulsion. Optical microscopy images showed that EC oil droplets were homogeneously dispersed in KGM water phase without obviously coalescence throughout the entire drying process. SEM images showed the surface and cross-sectional structures of samples maintained continuous and homogeneous appearance from the emulsion to dried film. AFM images indicated that KGM molecules entangled EC molecules in the emulsion. Interactions between KGM and EC improved the stability of KGM-EC emulsion, and contributed to uniformed structures of film formation. Based on these output information, a schematic model was built to elucidate KGM-EC film-forming process. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

Science.gov (United States)

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.

Atomic force microscopy studies of lateral phase separation in mixed monolayers of dipalmitoylphosphatidylcholine and dilauroylphosphatidylcholine

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.

Fluorescence microscopy.

Science.gov (United States)

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.