The Fault Feature Extraction of Rolling Bearing Based on EMD and Difference Spectrum of Singular Value

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Te Han

2016-01-01

Full Text Available Nowadays, the fault diagnosis of rolling bearing in aeroengines is based on the vibration signal measured on casing, instead of bearing block. However, the vibration signal of the bearing is often covered by a series of complex components caused by other structures (rotor, gears. Therefore, when bearings cause failure, it is still not certain that the fault feature can be extracted from the vibration signal on casing. In order to solve this problem, a novel fault feature extraction method for rolling bearing based on empirical mode decomposition (EMD and the difference spectrum of singular value is proposed in this paper. Firstly, the vibration signal is decomposed by EMD. Next, the difference spectrum of singular value method is applied. The study finds that each peak on the difference spectrum corresponds to each component in the original signal. According to the peaks on the difference spectrum, the component signal of the bearing fault can be reconstructed. To validate the proposed method, the bearing fault data collected on the casing are analyzed. The results indicate that the proposed rolling bearing diagnosis method can accurately extract the fault feature that is submerged in other component signals and noise.

On the singular Sturm-Liouville problems that have the same spectrum

Energy Technology Data Exchange (ETDEWEB)

Gulsen, Tuba [Department of Mathematics, Firat University, 23119, Elazig (Turkey); Ulusoy, Ismail [Department of Mathematics, Adiyaman University, 02040,Adiyaman (Turkey)

2016-06-08

The problem of efficaciously constucting the potential q (x) and the numbers h and H was solved in [1]. Trubowitz [2] investigated the isospectrality problem which have the same spectrum with other same type of problems. Then Jodeit and Levitan [3] considered this problem with a different approach, based on transmutation operators and integral equation. In this work, we discussed this problem for singular Sturm-Liouville operator and obtained some important formulas for the number H, the potential q (x) and the norming constants α{sub n}.

Deep learning for classification of islanding and grid disturbance based on multi-resolution singular spectrum entropy

Science.gov (United States)

Li, Tie; He, Xiaoyang; Tang, Junci; Zeng, Hui; Zhou, Chunying; Zhang, Nan; Liu, Hui; Lu, Zhuoxin; Kong, Xiangrui; Yan, Zheng

2018-02-01

Forasmuch as the distinguishment of islanding is easy to be interfered by grid disturbance, island detection device may make misjudgment thus causing the consequence of photovoltaic out of service. The detection device must provide with the ability to differ islanding from grid disturbance. In this paper, the concept of deep learning is introduced into classification of islanding and grid disturbance for the first time. A novel deep learning framework is proposed to detect and classify islanding or grid disturbance. The framework is a hybrid of wavelet transformation, multi-resolution singular spectrum entropy, and deep learning architecture. As a signal processing method after wavelet transformation, multi-resolution singular spectrum entropy combines multi-resolution analysis and spectrum analysis with entropy as output, from which we can extract the intrinsic different features between islanding and grid disturbance. With the features extracted, deep learning is utilized to classify islanding and grid disturbance. Simulation results indicate that the method can achieve its goal while being highly accurate, so the photovoltaic system mistakenly withdrawing from power grids can be avoided.

Pattern Recognition of Gene Expression with Singular Spectrum Analysis

Directory of Open Access Journals (Sweden)

Hossein Hassani

2014-07-01

Full Text Available Drosophila segmentation as a model organism is one of the most highly studied. Among many maternal segmentation coordinate genes, bicoid protein pattern plays a significant role during Drosophila embryogenesis, since this gradient determines most aspects of head and thorax development. Despite the fact that several models have been proposed to describe the bicoid gradient, due to its association with considerable error, each can only partially explain bicoid characteristics. In this paper, a modified version of singular spectrum analysis is examined for filtering and extracting the bicoid gene expression signal. The results with strong evidence indicate that the proposed technique is able to remove noise more effectively and can be considered as a promising method for filtering gene expression measurements for other applications.

Embedding Dimension Selection for Adaptive Singular Spectrum Analysis of EEG Signal.

Science.gov (United States)

Xu, Shanzhi; Hu, Hai; Ji, Linhong; Wang, Peng

2018-02-26

The recorded electroencephalography (EEG) signal is often contaminated with different kinds of artifacts and noise. Singular spectrum analysis (SSA) is a powerful tool for extracting the brain rhythm from a noisy EEG signal. By analyzing the frequency characteristics of the reconstructed component (RC) and the change rate in the trace of the Toeplitz matrix, it is demonstrated that the embedding dimension is related to the frequency bandwidth of each reconstructed component, in consistence with the component mixing in the singular value decomposition step. A method for selecting the embedding dimension is thereby proposed and verified by simulated EEG signal based on the Markov Process Amplitude (MPA) EEG Model. Real EEG signal is also collected from the experimental subjects under both eyes-open and eyes-closed conditions. The experimental results show that based on the embedding dimension selection method, the alpha rhythm can be extracted from the real EEG signal by the adaptive SSA, which can be effectively utilized to distinguish between the eyes-open and eyes-closed states.

Embedding Dimension Selection for Adaptive Singular Spectrum Analysis of EEG Signal

Directory of Open Access Journals (Sweden)

Shanzhi Xu

2018-02-01

Full Text Available The recorded electroencephalography (EEG signal is often contaminated with different kinds of artifacts and noise. Singular spectrum analysis (SSA is a powerful tool for extracting the brain rhythm from a noisy EEG signal. By analyzing the frequency characteristics of the reconstructed component (RC and the change rate in the trace of the Toeplitz matrix, it is demonstrated that the embedding dimension is related to the frequency bandwidth of each reconstructed component, in consistence with the component mixing in the singular value decomposition step. A method for selecting the embedding dimension is thereby proposed and verified by simulated EEG signal based on the Markov Process Amplitude (MPA EEG Model. Real EEG signal is also collected from the experimental subjects under both eyes-open and eyes-closed conditions. The experimental results show that based on the embedding dimension selection method, the alpha rhythm can be extracted from the real EEG signal by the adaptive SSA, which can be effectively utilized to distinguish between the eyes-open and eyes-closed states.

A singularity extraction technique for computation of antenna aperture fields from singular plane wave spectra

DEFF Research Database (Denmark)

Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel

2008-01-01

An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...

A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular systems.

Science.gov (United States)

Zhang, Xuefeng; Chen, YangQuan

2017-11-01

The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

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Omar Abu Arqub

2012-01-01

Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

The Study of Radio Flux Density Variations of the Quasar OJ 287 by the Wavelet and the Singular Spectrum Methods

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Donskykh Ganna

2016-06-01

Full Text Available Flux density variations of the extragalactic radio source OJ 287 are studied by applying the wavelet and the singular spectrum methods to the long-term monitoring data at 14.5, 8.0 and 4.8 GHz acquired at the University of Michigan Radio Astronomy Observatory during 40 years. This monitoring significantly supplements the episodic VLBI data. The wavelet analysis at all three frequencies revealed the presence of quasiperiods within the intervals 6.0–7.4 and 1.2–1.8 years. The singular spectrum analysis revealed the presence of quasiperiods within the intervals 6–10 and 1.6–4.0 years. For each quasiperiod the time interval of its existence was determined.

Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

Science.gov (United States)

Kalantari, Mahdi; Yarmohammadi, Masoud; Hassani, Hossein; Silva, Emmanuel Sirimal

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the L1 norm-based version of Singular Spectrum Analysis (SSA), namely L1-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially L1-SSA can provide better imputation in comparison to other methods.

Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

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Songlin Wo

2018-01-01

Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

The spectrum of axisymmetric torsional Alfven waves

International Nuclear Information System (INIS)

Sy, W.N.

1977-03-01

The spectrum of axisymmetric torsional Alfven waves propagating in a cylindrical, non-uniform, resistive plasma waveguide has been analysed by a method of singular perturbations. A simple condition has been derived which predicts whether the spectrum is continuous or discrete under given physical conditions. Application of this result to resolve an apparent discrepancy in experimental observations is briefly discussed. (Author)

Multichannel singular spectrum analysis of the axial atmospheric angular momentum

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Leonid Zotov

2017-11-01

Full Text Available Earth's variable rotation is mainly produced by the variability of the AAM (atmospheric angular momentum. In particular, the axial AAM component χ3, which undergoes especially strong variations, induces changes in the Earth's rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the LOD (length of day were described. We applied MSSA (Multichannel Singular Spectrum Analysis jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-month, quasi-biennial, 5-year, and low-frequency oscillations. PCs (Principal components strongly related to ENSO (El Nino southern oscillation were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.

Plane waves with weak singularities

International Nuclear Information System (INIS)

David, Justin R.

2003-03-01

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

International Nuclear Information System (INIS)

Costa, O. L. V.; Dufour, F.

2011-01-01

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP’s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ n . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Timelike naked singularity

International Nuclear Information System (INIS)

Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis

2004-01-01

We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture

Transmutation of singularities in optical instruments

Energy Technology Data Exchange (ETDEWEB)

Tyc, Tomas [Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno (Czech Republic); Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom)], E-mail: tomtyc@physics.muni.cz

2008-11-15

We propose a method for eliminating a class of singularities in optical media where the refractive index goes to zero or infinity at one or more isolated points. Employing transformation optics, we find a refractive index distribution equivalent to the original one that is nonsingular but shows a slight anisotropy. In this way, the original singularity is 'transmuted' into another, weaker type of singularity where the permittivity and permeability tensors are discontinuous at one point. The method is likely to find applications in designing and improving optical devices by making them easier to implement or to operate in a broad band of the spectrum.

Naked singularities in higher dimensional Vaidya space-times

International Nuclear Information System (INIS)

Ghosh, S. G.; Dadhich, Naresh

2001-01-01

We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

Science.gov (United States)

Koslowski, Tim A.; Mercati, Flavio; Sloan, David

2018-03-01

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

Singular Spectrum Analysis for Astronomical Time Series: Constructing a Parsimonious Hypothesis Test

Science.gov (United States)

Greco, G.; Kondrashov, D.; Kobayashi, S.; Ghil, M.; Branchesi, M.; Guidorzi, C.; Stratta, G.; Ciszak, M.; Marino, F.; Ortolan, A.

We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with 1/f β power-law noise affected by photon counting statistics. Such noise process is simulated by a first-order autoregressive, AR(1) process corrupted by intrinsic Poisson noise. In doing so, we statistically estimate a basic stochastic variation of the source and the corresponding fluctuations due to the quantum nature of light. In addition, MC-SSA test retains its effectiveness even when a significant percentage of the signal falls below a certain level of detection, e.g., caused by the instrument sensitivity. The parsimonious approach presented here may be broadly applied, from the search for extrasolar planets to the extraction of low-intensity coherent phenomena probably hidden in high energy transients.

Coherent changes of multifractal properties of continuous acoustic emission at failure of heterogeneous materials

Science.gov (United States)

Panteleev, Ivan; Bayandin, Yuriy; Naimark, Oleg

2017-12-01

This work performs a correlation analysis of the statistical properties of continuous acoustic emission recorded in different parts of marble and fiberglass laminate samples under quasi-static deformation. A spectral coherent measure of time series, which is a generalization of the squared coherence spectrum on a multidimensional series, was chosen. The spectral coherent measure was estimated in a sliding time window for two parameters of the acoustic emission multifractal singularity spectrum: the spectrum width and the generalized Hurst exponent realizing the maximum of the singularity spectrum. It is shown that the preparation of the macrofracture focus is accompanied by the synchronization (coherent behavior) of the statistical properties of acoustic emission in allocated frequency intervals.

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

Science.gov (United States)

Vautard, R.; Ghil, M.

1989-01-01

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

USING THE METHODS OF WAVELET ANALYSIS AND SINGULAR SPECTRUM ANALYSIS IN THE STUDY OF RADIO SOURCE BL LAC

OpenAIRE

Donskykh, G. I.; Ryabov, M. I.; Sukharev, A. I.; Aller, M.

2014-01-01

We investigated the monitoring data of extragalactic source BL Lac. This monitoring was held withUniversityofMichigan26-meter radio  telescope. To study flux density of extragalactic source BL Lac at frequencies of 14.5, 8 and 4.8 GHz, the wavelet analysis and singular spectrum analysis were used. Calculating the integral wavelet spectra allowed revealing long-term  components  (~7-8 years) and short-term components (~ 1-4 years) in BL Lac. Studying of VLBI radio maps (by the program Mojave) ...

7 CFR 61.1 - Words in singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...

Microlocal study of S-matrix singularity structure

International Nuclear Information System (INIS)

Kawai, Takahiro; Kyoto Univ.; Stapp, H.P.

1975-01-01

Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.) [de

Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide

International Nuclear Information System (INIS)

Derguzov, V.I.

1986-01-01

One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide

Analytic continuation of quantum systems and their temporal evolution

International Nuclear Information System (INIS)

Sudarshan, E.C.G.; Chiu, C.B.

1993-01-01

The generalized vector space of quantum states is used to study the correspondence between the physical state space scrH and its continuation scrG. Consider the integral representation defined by the scalar product between an arbitrary vector in the dense subset of analytic vectors in scrH and its dual vector, where the integration is along the real axis. Keeping the scalar product fixed, the analytic vectors may be continued through the deformation of the integration contour. The deformed contour defines the generalized spectrum of the operator in the continued theory, which typically consists of a deformed contour in the fourth quadrant and the exposed singularities, if any, between the real axis and the deformed contour. Several models are studied with special attention to the unfolding of the generalized spectrum. The two-body models studied are the Lee model in the lowest sector and the Yamaguchi potential model, where the exposed singularities, if present, are simple poles. The three-body model studied is the cascade model, where the exposed singularities may be poles and the branch cuts associated with the quasi-two-body states. We demonstrate that the generalized spectrum obtained leads to the correct extended unitarity relation for the scattering amplitudes. The possibility of having mismatches between poles in the S matrix and the discrete states in the Hamiltonian, which exists in the scrH space, obtains also in the generalized scrG space. Finally, two distinct views on what constitutes an unstable particle are contrasted. One view is to identify it as a physical state of the system which ceases to exist as a discrete eigenstate in scrH. Here the survival amplitude of the unstable particle cannot be ever strictly exponential in time. The other view is to identify the unstable particle as a discrete state in the generalized space

7 CFR 1200.50 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

7 CFR 900.1 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.100 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.50 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

Terrestrial water storage changes over Xinjiang extracted by combining Gaussian filter and multichannel singular spectrum analysis from GRACE

Science.gov (United States)

Guo, Jinyun; Li, Wudong; Chang, Xiaotao; Zhu, Guangbin; Liu, Xin; Guo, Bin

2018-04-01

Water resource management is crucial for the economic and social development of Xinjiang, an arid area located in the Northwest China. In this paper, the time variations of gravity recovery and climate experiment (GRACE)-derived monthly gravity field models from 2003 January to 2013 December are analysed to study the terrestrial water storage (TWS) changes in Xinjiang using the multichannel singular spectrum analysis (MSSA) with a Gaussian smoothing radius of 400 km. As an extended singular spectrum analysis (SSA), MSSA is more flexible to deal with multivariate time-series in terms of estimating periodic components and trend, reducing noise and identifying patterns of similar spatiotemporal behaviour thanks to the data-adaptive nature of the base functions. Combining MSSA and Gaussian filter can not only obviously remove the north-south striping errors in the GRACE solutions but also reduce the leakage errors, which can increase the signal-to-noise ratio by comparing with the traditional procedure, that is, empirical decorrelation method followed with the Gaussian filtering. The spatiotemporal characteristics of TWS changes in Xinjiang were validated against the Global Land Dynamics Assimilation System, the Climate Prediction Center and in-situ precipitation data. The water storage in Xinjiang shows the relatively large fluctuation from 2003 January to 2013 December, with a drop from 2006 January to 2008 December due to the drought event and an obvious rise from 2009 January to 2010 December because of the high precipitation. Spatially, the TWS has been increasing in the south Xinjiang, but decreasing in the north Xinjiang. The minimum rate of water storage change is -4.4 mm yr-1 occurring in the central Tianshan Mountain.

7 CFR 900.20 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

7 CFR 900.36 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...

The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels

Energy Technology Data Exchange (ETDEWEB)

Bobodzhanov, A A; Safonov, V F [National Research University " Moscow Power Engineering Institute" , Moscow (Russian Federation)

2013-07-31

The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.

Holder continuity of bounded weak solutions to generalized parabolic p-Laplacian equations II: singular case

Directory of Open Access Journals (Sweden)

Sukjung Hwang

2015-11-01

Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1continuous with some degree of commonality between degenerate and singular types. By using geometric characters, our proof does not rely on any of alternatives which is based on the size of solutions.

Spectra of random operators with absolutely continuous integrated density of states

International Nuclear Information System (INIS)

Rio, Rafael del

2014-01-01

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic

Spectra of random operators with absolutely continuous integrated density of states

Energy Technology Data Exchange (ETDEWEB)

Rio, Rafael del, E-mail: delrio@iimas.unam.mx, E-mail: delriomagia@gmail.com [Departamento de Fisica Matematica, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510, México D.F. (Mexico)

2014-04-15

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic.

Numerical method of singular problems on singular integrals

International Nuclear Information System (INIS)

Zhao Huaiguo; Mou Zongze

1992-02-01

As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily

Rapid assessment of populations trends of invasive species: Singular Spectrum Analysis (SSA

Directory of Open Access Journals (Sweden)

DANA, ED

2010-01-01

Full Text Available Singular Spectrum Analysis (SSA is a powerful analytical approach for biodi-versity management. Its main advan-tages are due to its intuitive processing and visualization, since mathematical workflow is conceptually similar to the widely accepted Principal Components Analysis. Detailed analyses of popula-tion trends with mathematical tools are often difficult to achieve for managers by a number of reasons (large numbers or areas monitored, large number of species, insufficient statistics skills, strong knowledge level in demographic analyses, etc.. SSA has been used since the 1970’s in signal processing to clarify signal vs. noisy information, but it has also been used in climate change analy-sis and other developmental areas. Be-sides, SSA is a rapid-learning method for technicians and managers with medium level of mathematical knowledge. Free software in Unix environment is avail-able. Unfortunately, no free and friendly software is available for Win-dows SO. Although R package may offer solutions for really advanced users, it does not fit real work situations for managers of biological invasions. Cater-pillar (Gistat Group, Ltd is by now, the best option found by the author in terms of price, facility for results inter-pretation and time consumed in learn-ing. The main disadvantage is the poor content of tutorial files

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

Science.gov (United States)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

A new methodology for fault detection in rolling element bearings using singular spectrum analysis

Directory of Open Access Journals (Sweden)

Bugharbee Hussein Al

2018-01-01

Full Text Available This paper proposes a vibration-based methodology for fault detection in rolling element bearings, which is based on pure data analysis via singular spectrum method. The method suggests building a baseline space from feature vectors made of the signals measured in the healthy/baseline bearing condition. The feature vectors are made using the Euclidean norms of the first three PC’s found for the signals measured. Then, the lagged version of any new signal corresponding to a new (possibly faulty condition is projected onto this baseline feature space in order to assess its similarity to the baseline condition. The category of a new signal vector is determined based on the Mahalanobis distance (MD of its feature vector to the baseline space. A validation of the methodology is suggested based on the results from an experimental test rig. The results obtained confirm the effective performance of the suggested methodology. It is made of simple steps and is easy to apply with a perspective to make it automatic and suitable for commercial applications.

The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches

OpenAIRE

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-01-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 $\\mathcal{N}{=}2$ superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special K\\"ahler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the $\\rm\\, U(1)_R$ symmetry. A set of novel topological and ge...

Normal modes and continuous spectra

International Nuclear Information System (INIS)

Balmforth, N.J.; Morrison, P.J.

1994-12-01

The authors consider stability problems arising in fluids, plasmas and stellar systems that contain singularities resulting from wave-mean flow or wave-particle resonances. Such resonances lead to singularities in the differential equations determining the normal modes at the so-called critical points or layers. The locations of the singularities are determined by the eigenvalue of the problem, and as a result, the spectrum of eigenvalues forms a continuum. They outline a method to construct the singular eigenfunctions comprising the continuum for a variety of problems

On the omnipresent background gamma radiation of the continuous spectrum

Energy Technology Data Exchange (ETDEWEB)

Banjanac, R.; Maletić, D.; Joković, D., E-mail: yokovic@ipb.ac.rs; Veselinović, N.; Dragić, A.; Udovičić, V.; Aničin, I.

2014-05-01

The background spectrum of a germanium detector, shielded from the radiations arriving from the lower and open for the radiations arriving from the upper hemisphere, is studied by means of absorption measurements, both in a ground level and in an underground laboratory. The low-energy continuous portion of this background spectrum that peaks at around 100 keV, which is its most intense component, is found to be of very similar shape at the two locations. It is established that it is mostly due to the radiations of the real continuous spectrum, which is quite similar to the instrumental one. The intensity of this radiation is in our cases estimated to about 8000 photons/(m{sup 2}s·2π·srad) in the ground level laboratory, and to about 5000 photons/(m{sup 2}s·2π·srad) in the underground laboratory, at the depth of 25 m.w.e. Simulations by GEANT4 and CORSIKA demonstrate that this radiation is predominantly of terrestrial origin, due to environmental gamma radiations scattered off the materials that surround the detector (the “skyshine radiation”), and to a far less extent to cosmic rays of degraded energy. - Highlights: • We studied the low-energy part of continuous background spectra of germanium detectors. • The study was performed at the ground level and at the shallow underground sites. • The instrumental spectrum is due to radiations of the similar continuous spectrum. • The low-energy radiation is of both terrestrial and cosmic-ray origin. • In our study, we find that this radiation is of predominantly terrestrial origin.

Continuous Emission Spectrum Measurement for Electron Temperature Determination in Low-Temperature Collisional Plasmas

International Nuclear Information System (INIS)

Liu Qiuyan; Li Hong; Chen Zhipeng; Xie Jinlin; Liu Wandong

2011-01-01

Continuous emission spectrum measurement is applied for the inconvenient diagnostics of low-temperature collisional plasmas. According to the physical mechanism of continuous emission, a simplified model is presented to analyze the spectrum in low temperature plasma. The validity of this model is discussed in a wide range of discharge parameters, including electron temperature and ionization degree. Through the simplified model, the continuous emission spectrum in a collisional argon internal inductively coupled plasma is experimentally measured to determine the electron temperature distribution for different gas pressures and radio-frequency powers. The inverse Abel transform is also applied for a better spatially resoluted results. Meanwhile, the result of the continuous emission spectrum measurement is compared to that of the electrostatic double probes, which indicates the effectiveness of this method. (low temperature plasma)

Tolerance of continuous NFT spectrum to the optical fiber channel impairments

DEFF Research Database (Denmark)

Gaiarin, Simone; Da Ros, Francesco; Sørensen, Mads Peter

2016-01-01

The impact of launch power, additive white Gaussian noise and fiber loss on the nonlinear Fourier transform (NFT) continuous spectrum is investigated. NFT is shown to undergo lower spectral distortion than the discrete Fourier transform.......The impact of launch power, additive white Gaussian noise and fiber loss on the nonlinear Fourier transform (NFT) continuous spectrum is investigated. NFT is shown to undergo lower spectral distortion than the discrete Fourier transform....

Calculating the electron temperature in the lightning channel by continuous spectrum

Science.gov (United States)

Xiangcheng, DONG; Jianhong, CHEN; Xiufang, WEI; Ping, YUAN

2017-12-01

Based on the theory of plasma continuous radiation, the relationship between the emission intensity of bremsstrahlung and recombination radiation and the plasma electron temperature is obtained. During the development process of a return stroke of ground flash, the intensity of continuous radiation spectrum is separated on the basis of the spectrums with obviously different luminous intensity at two moments. The electron temperature of the lightning discharge channel is obtained through the curve fitting of the continuous spectrum intensity. It is found that electron temperature increases with the increase of wavelength and begins to reduce after the peak. The peak temperature of the two spectra is close to 25 000 K. To be compared with the result of discrete spectrum, the electron temperature is fitted by the O I line and N II line of the spectrum respectively. The comparison shows that the high temperature value is in good agreement with the temperature of the lightning core current channel obtained from the ion line information, and the low temperature at the high band closes to the calculation result of the atomic line, at a low band is lower than the calculation of the atomic line, which reflects the temperature of the luminous channel of the outer corona.

Connection conditions and the spectral family under singular potentials

International Nuclear Information System (INIS)

Tsutsui, Izumi; Fueloep, Tamas; Cheon, Taksu

2003-01-01

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wavefunctions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well defined even if the wavefunctions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential V(x)=-e 2 vertical bar x vertical bar and the harmonic oscillator with square inverse potential V(x)=(mω 2 /2)x 2 +g/x 2 , and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potential V(-x)=V(x), the spectrum is determined solely by the eigenvalues of the characteristic matrix U element of U(2)

7 CFR 1200.1 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...

Papapetrou's naked singularity is a strong curvature singularity

International Nuclear Information System (INIS)

Hollier, G.P.

1986-01-01

Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)

A Novel approach for predicting monthly water demand by combining singular spectrum analysis with neural networks

Science.gov (United States)

Zubaidi, Salah L.; Dooley, Jayne; Alkhaddar, Rafid M.; Abdellatif, Mawada; Al-Bugharbee, Hussein; Ortega-Martorell, Sandra

2018-06-01

Valid and dependable water demand prediction is a major element of the effective and sustainable expansion of municipal water infrastructures. This study provides a novel approach to quantifying water demand through the assessment of climatic factors, using a combination of a pretreatment signal technique, a hybrid particle swarm optimisation algorithm and an artificial neural network (PSO-ANN). The Singular Spectrum Analysis (SSA) technique was adopted to decompose and reconstruct water consumption in relation to six weather variables, to create a seasonal and stochastic time series. The results revealed that SSA is a powerful technique, capable of decomposing the original time series into many independent components including trend, oscillatory behaviours and noise. In addition, the PSO-ANN algorithm was shown to be a reliable prediction model, outperforming the hybrid Backtracking Search Algorithm BSA-ANN in terms of fitness function (RMSE). The findings of this study also support the view that water demand is driven by climatological variables.

Daily rainfall forecasting for one year in a single run using Singular Spectrum Analysis

Science.gov (United States)

Unnikrishnan, Poornima; Jothiprakash, V.

2018-06-01

Effective modelling and prediction of smaller time step rainfall is reported to be very difficult owing to its highly erratic nature. Accurate forecast of daily rainfall for longer duration (multi time step) may be exceptionally helpful in the efficient planning and management of water resources systems. Identification of inherent patterns in a rainfall time series is also important for an effective water resources planning and management system. In the present study, Singular Spectrum Analysis (SSA) is utilized to forecast the daily rainfall time series pertaining to Koyna watershed in Maharashtra, India, for 365 days after extracting various components of the rainfall time series such as trend, periodic component, noise and cyclic component. In order to forecast the time series for longer time step (365 days-one window length), the signal and noise components of the time series are forecasted separately and then added together. The results of the study show that the method of SSA could extract the various components of the time series effectively and could also forecast the daily rainfall time series for longer duration such as one year in a single run with reasonable accuracy.

The singularity structure of scale-invariant rank-2 Coulomb branches

Science.gov (United States)

Argyres, Philip C.; Long, Cody; Martone, Mario

2018-05-01

We compute the spectrum of scaling dimensions of Coulomb branch operators in 4d rank-2 N=2 superconformal field theories. Only a finite rational set of scaling dimensions is allowed. It is determined by using information about the global topology of the locus of metric singularities on the Coulomb branch, the special Kähler geometry near those singularities, and electric-magnetic duality monodromies along orbits of the U(1) R symmetry. A set of novel topological and geometric results are developed which promise to be useful for the study and classification of Coulomb branch geometries at all ranks.

Modeling the relationship between photosynthetically active radiation and global horizontal irradiance using singular spectrum analysis

International Nuclear Information System (INIS)

Zempila, Melina-Maria; Taylor, Michael; Bais, Alkiviadis; Kazadzis, Stelios

2016-01-01

We report on the construction of generic models to calculate photosynthetically active radiation (PAR) from global horizontal irradiance (GHI), and vice versa. Our study took place at stations of the Greek UV network (UVNET) and the Hellenic solar energy network (HNSE) with measurements from NILU-UV multi-filter radiometers and CM pyranometers, chosen due to their long (≈1 M record/site) high temporal resolution (≈1 min) record that captures a broad range of atmospheric environments and cloudiness conditions. The uncertainty of the PAR measurements is quantified to be ±6.5% while the uncertainty involved in GHI measurements is up to ≈±7% according to the manufacturer. We show how multi-linear regression and nonlinear neural network (NN) models, trained at a calibration site (Thessaloniki) can be made generic provided that the input–output time series are processed with multi-channel singular spectrum analysis (M-SSA). Without M-SSA, both linear and nonlinear models perform well only locally. M-SSA with 50 time-lags is found to be sufficient for identification of trend, periodic and noise components in aerosol, cloud parameters and irradiance, and to construct regularized noise models of PAR from GHI irradiances. Reconstructed PAR and GHI time series capture ≈95% of the variance of the cross-validated target measurements and have median absolute percentage errors <2%. The intra-site median absolute error of M-SSA processed models were ≈8.2±1.7 W/m"2 for PAR and ≈9.2±4.2 W/m"2 for GHI. When applying the models trained at Thessaloniki to other stations, the average absolute mean bias between the model estimates and measured values was found to be ≈1.2 W/m"2 for PAR and ≈0.8 W/m"2 for GHI. For the models, percentage errors are well within the uncertainty of the measurements at all sites. Generic NN models were found to perform marginally better than their linear counterparts. - Highlights: • Generic linear regression and nonlinear neural network

A novel singular pattern in the sine-Gordon equation

International Nuclear Information System (INIS)

Huang, Debin

2003-01-01

By the scatter problem and the Backlund transformation of the sine-Gordon equation, we find a novel solution with the singularity of jumping phenomenon, which displays pattern structure similar respectively to soliton, kink, anti-kink and double pole solution with the different choice of the purely imaginary spectrum of the sine-Gordon equation

On singular interaction potentials in classical statistical mechanics

International Nuclear Information System (INIS)

Zagrebnov, V.A.; Pastur, L.A.

1978-01-01

A classical system of particles with stable two-body interaction potential is considered. It is shown that for a certain class of highly singular stable two-body potentials a cut-off procedure preserves the stability of the potential. The thermodynamical potentials (pressure and free energy density) and correlation functions are proved to have the property of asymptotic independence with respect to the continuation of the interaction potentials near singularity

A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

Energy Technology Data Exchange (ETDEWEB)

Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)

2017-12-15

We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy

Science.gov (United States)

Perelman, Carlos Castro

2016-01-01

A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a spatial singularity at the origin r = 0 is found. These solutions are parametrized by a real valued parameter λ (ranging from 0 to 1) and such that the radial horizon's location is displaced continuously towards the singularity ( r = 0 ) as λ increases. In the extreme limit λ = 1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at r = 0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3.

The performance of one belt and one road exchange rate: Based on improved singular spectrum analysis

Science.gov (United States)

Lai, Lin; Guo, Kun

2017-10-01

;One Belt and One Road; strategy in China is on push of foreign trade openness at northwest, southwest and northeast, absorption of the excess capacity and new support for economic increase. However, the fluctuation in RMB exchange rate with the countries along the road is unstable so related Chinese enterprises will face high risk of exchange rate. Precise explanation or prediction for exchange rate has been the challengeable hop point in the international finance. This paper decomposed the One Belt One Road Exchange Rate Index (OBORR) and the RMB Effective Exchange Rate Index (CNYX) into trend term, market fluctuation term and noise term using improved singular spectrum analysis (SSA). It turns out that the increasing velocity of OBORR is greater than that of CNYX in the long term, and there is dynamic lead-lag structure in the medium term. In the short term, the fluctuation range and frequency of OBORR are greater than those of CNYX, which means there will be more exchange rate risks in One Belt and One Road countries.

Singular-value demodulation of phase-shifted holograms.

Science.gov (United States)

Lopes, Fernando; Atlan, Michael

2015-06-01

We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.

3D seismic data de-noising and reconstruction using Multichannel Time Slice Singular Spectrum Analysis

Science.gov (United States)

Rekapalli, Rajesh; Tiwari, R. K.; Sen, Mrinal K.; Vedanti, Nimisha

2017-05-01

Noises and data gaps complicate the seismic data processing and subsequently cause difficulties in the geological interpretation. We discuss a recent development and application of the Multi-channel Time Slice Singular Spectrum Analysis (MTSSSA) for 3D seismic data de-noising in time domain. In addition, L1 norm based simultaneous data gap filling of 3D seismic data using MTSSSA also discussed. We discriminated the noises from single individual time slices of 3D volumes by analyzing Eigen triplets of the trajectory matrix. We first tested the efficacy of the method on 3D synthetic seismic data contaminated with noise and then applied to the post stack seismic reflection data acquired from the Sleipner CO2 storage site (pre and post CO2 injection) from Norway. Our analysis suggests that the MTSSSA algorithm is efficient to enhance the S/N for better identification of amplitude anomalies along with simultaneous data gap filling. The bright spots identified in the de-noised data indicate upward migration of CO2 towards the top of the Utsira formation. The reflections identified applying MTSSSA to pre and post injection data correlate well with the geology of the Southern Viking Graben (SVG).

Bound states embedded into continuous spectrum as 'gathered' (compactified) scattering waves

International Nuclear Information System (INIS)

Zakhar'ev, B.N.; Chabanov, V.M.

1995-01-01

It is shown that states of continuous spectrum (the half-line case) can be considered as bound states normalized by unity but distributed on the infinite interval with vanishing density. Then the algorithms of shifting the range of primary localization of a chosen bound state in potential well of finite width appear to be applicable to scattering functions. The potential perturbations of the same type (but now on half-axis) concentrate the scattering wave in near vicinity of the origin, which leads to creation of bound state embedded into continuous spectrum. (author). 8 refs., 7 figs

Papapetrou's naked singularity is a strong curvature singularity

Energy Technology Data Exchange (ETDEWEB)

Hollier, G.P.

1986-11-01

Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.

The nature of the essential spectrum in curved quantum waveguides

International Nuclear Information System (INIS)

Krejcirik, David; Aldecoa, Rafael Tiedra de

2004-01-01

We study the nature of the essential spectrum of the Dirichlet Laplacian in tubes about infinite curves embedded in Euclidean spaces. Under suitable assumptions about the decay of curvatures at infinity, we prove the absence of singular continuous spectrum and state properties of possible embedded eigenvalues. The argument is based on the Mourre conjugate operator method developed for acoustic multistratified domains by Benbernou (1998 J. Math. Anal. Appl. 225 440-60) and Dermenjian et al (1998 Commun. Partial Differ. Equ. 23 141-69). As a technical preliminary, we carry out a spectral analysis for Schroedinger-type operators in straight Dirichlet tubes. We also apply the result to the strips embedded in abstract surfaces

From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport

International Nuclear Information System (INIS)

Ganapol, B.D.

2001-01-01

A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm

Naked singularities are not singular in distorted gravity

Energy Technology Data Exchange (ETDEWEB)

Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)

2014-07-15

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Naked singularities are not singular in distorted gravity

Science.gov (United States)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Naked singularities are not singular in distorted gravity

International Nuclear Information System (INIS)

Garattini, Remo; Majumder, Barun

2014-01-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity

Purely absolutely continuous spectrum for almost Mathieu operators

International Nuclear Information System (INIS)

Chulaevsky, V.; Delyon, F.

1989-01-01

Using a recent result of Sinai, the authors prove that the almost Mathieu operators acting on l 2 (Z), (H αλ Psi)(n) = Ψ(n + 1) + Ψ(n - 1) + λ cos(ωn + α) Ψ(n), have a purely absolutely continuous spectrum for almost all α provided that ω is a good irrational and λ is sufficiently small. Furthermore, the generalized eigenfunctions are quasiperiodic

Signal discrimination of ULF electromagnetic data with using singular spectrum analysis – an attempt to detect train noise

Directory of Open Access Journals (Sweden)

S. Saito

2011-07-01

Full Text Available Electromagnetic phenomena associated with crustal activities have been reported in a wide frequency range (DC-HF. In particular, ULF electromagnetic phenomena are the most promising among them because of the deeper skin depth. However, ULF geoelctromagnetic data are a superposition of signals of different origins. They originated from interactions between the geomagnetic field and the solar wind, leak current by a DC-driven train (train noise, precipitation, and so on. In general, the intensity of electromagnetic signals associated with crustal activity is smaller than the above variations. Therefore, in order to detect a smaller signal, signal discrimination such as noise reduction or identification of noises is very important. In this paper, the singular spectrum analysis (SSA has been performed to detect the DC-driven train noise in geoelectric potential difference data. The aim of this paper is to develop an effective algorithm for the DC-driven train noise detection.

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

Science.gov (United States)

Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni

2016-09-01

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

Multichannel features of the continuous spectrum of the 6He

International Nuclear Information System (INIS)

Filippov, G.F.; Mokhov, S.V.

2000-01-01

It is shown that the continuous spectrum of the nucleus 6 He right above the threshold of its decay to α-particle and two neutrons has a number of features extrinsic for continuous spectrum of binary systems. Multiplicity of degeneration of this spectrum is infinite and, hence, there is an infinite number of channels of decay, even if to fix their angular moment and parity. With increase of hyper radius potential energy of 6 He in states with certain hyper momentum decreases in inverse proportion to a cube of hyper radius, that is reflected on behaviour of elements of the three-in-three scattering S-matrix for energies slightly above the threshold. At last, the influence of the Pauli principle causes hyper momentum, in general, ceases to be a convenient quantum number for enumeration of decay channels and the arising standard situation needs to consider a superposition of states with different hyper momentum. Within the framework of the three-cluster hyper harmonics method and the asymptotical potential approximation, the calculations of phases of the scattering matrix is performed, and the regularities of behaviour of these phases with respect to energy are discovered [ru

Improved Tensor-Based Singular Spectrum Analysis Based on Single Channel Blind Source Separation Algorithm and Its Application to Fault Diagnosis

Directory of Open Access Journals (Sweden)

Dan Yang

2017-04-01

Full Text Available To solve the problem of multi-fault blind source separation (BSS in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS based on the improved tensor-based singular spectrum analysis (TSSA is proposed. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, TSSA method can be employed to extract the multi-fault features from the measured single-channel vibration signal. However, SCBSS based on TSSA still has some limitations, mainly including unsatisfactory convergence of TSSA in many cases and the number of source signals is hard to accurately estimate. Therefore, the improved TSSA algorithm based on canonical decomposition and parallel factors (CANDECOMP/PARAFAC weighted optimization, namely CP-WOPT, is proposed in this paper. CP-WOPT algorithm is applied to process the factor matrix using a first-order optimization approach instead of the original least square method in TSSA, so as to improve the convergence of this algorithm. In order to accurately estimate the number of the source signals in BSS, EMD-SVD-BIC (empirical mode decomposition—singular value decomposition—Bayesian information criterion method, instead of the SVD in the conventional TSSA, is introduced. To validate the proposed method, we applied it to the analysis of the numerical simulation signal and the multi-fault rolling bearing signals.

Computation at a coordinate singularity

Science.gov (United States)

Prusa, Joseph M.

2018-05-01

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar

Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

Directory of Open Access Journals (Sweden)

Omar Eldwaik

2018-01-01

Full Text Available Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.

Singular value decomposition and artificial neutral network for analyzing bonner sphere data

International Nuclear Information System (INIS)

Zhu, Qingjun; Song, Gang; Song, Fengquan; Guo, Qian; Wu, Yican

2012-01-01

The objective of this study was to build an effective and reliable method based on the artificial neural network (ANN) model for unfolding neutron spectrum. The number of counts measured by 15 Bonner spheres and 281 neutron spectra were selected as the database. After singular value decomposition was used to determine the relationship between Bonner spheres, 11 Bonner spheres were chosen as input descriptors. The three-layer feedforward neural networks (11-5-1) were employed to predict the spectrum in each energy bin. Using information entropy theory and the results of the ANN calculations, the sensitivity of each sphere to the entropy of the spectrum was quantitatively analyzed. The spectra results were compared with the results obtained using the maximum entropy method (MEM). The averaged root mean-square-error (MSE) of the MEM output and the desired spectra was 0.012; the averaged MSE of the ANN calculations was 0.006. The MSE results indicate that the 11-5-1 ANN models are able to accurately and reliably predict neutron spectra. The ANN model developed in this study to unfold neutron spectra from the counts measured by 11 Bonner spheres provides an alternative method for unfolding spectrum. The singular value decomposition is an effective method for the analysis of data obtained from Bonner spheres and the neutron spectra.

Application of local singularity in prospecting potential oil/gas Targets

Directory of Open Access Journals (Sweden)

Zhengyu Bao

2007-06-01

Full Text Available Together with generalized self-similarity and the fractal spectrum, local singularity analysis has been introduced as one part of the new 3S principle and technique for mineral resource assessment based on multifractal modeling, which has been demonstrated to be useful for anomaly delineation. Local singularity is used in this paper to characterize the property of multifractal distribution patterns of geochemical indexes to delineate potential areas for oil/gas exploration using the advanced GeoDAS GIS technology. Geochemical data of four oil/gas indexes, consisting of acid-extracted methane (SC1, ethane (SC2, propane (SC3, and secondary carbonate (ΔC, from 9637 soil samples amassed within a large area of 11.2×104 km2 in the Songpan-Aba district, Sichuan Province, southwestern China, were analyzed. By eliminating the interference of geochemical oil/gas data with the method of media-modification and Kriging, the prospecting area defined by the local singularity model is better identified and the results show that the subareas with higher singularity exponents for the four oil/gas indexes are potential targets for oil/gas exploration. These areas in the shape of rings or half-rings are spatially associated with the location of the known producing drilling well in this area. The spatial relationship between the anomalies delineated by oil/gas geochemical data and distribution patterns of local singularity exponents is confirmed by using the stable isotope of δ13C.

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

International Nuclear Information System (INIS)

Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

2012-08-01

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A n type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A k singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

Energy Technology Data Exchange (ETDEWEB)

Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

2012-08-15

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

International Nuclear Information System (INIS)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo; Martinet, Philippe

2008-01-01

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

Damped least square based genetic algorithm with Gaussian distribution of damping factor for singularity-robust inverse kinematics

Energy Technology Data Exchange (ETDEWEB)

Phuoc, Le Minh; Lee, Suk Han; Kim, Hun Mo [Sungkyunkwan University, Suwon (Korea, Republic of); Martinet, Philippe [Blaise Pascal University, Clermont-Ferrand Cedex (France)

2008-07-15

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot

Generalized Parton Distributions and their Singularities

Energy Technology Data Exchange (ETDEWEB)

Anatoly Radyushkin

2011-04-01

A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\\beta)/\\beta$ rather than with the usual parton density $f(\\beta)$. This results in a non-integrable singularity at $\\beta=0$ exaggerated by the fact that $f(\\beta)$'s, on their own, have a singular $\\beta^{-a}$ Regge behavior for small $\\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x,\\xi)$ that are finite and continuous at the "border point'' $x=\\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\\beta, \\alpha)$ into the "plus'' part $[f(\\beta,\\alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x,x)$ with the $D$-term function $D(\\alpha)$.

Algorithms in Singular

Directory of Open Access Journals (Sweden)

Hans Schonemann

1996-12-01

Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].

Multichannel Singular Spectrum Analysis in the Estimates of Common Environmental Effects Affecting GPS Observations

Science.gov (United States)

Gruszczynska, Marta; Rosat, Severine; Klos, Anna; Gruszczynski, Maciej; Bogusz, Janusz

2018-03-01

We described a spatio-temporal analysis of environmental loading models: atmospheric, continental hydrology, and non-tidal ocean changes, based on multichannel singular spectrum analysis (MSSA). We extracted the common annual signal for 16 different sections related to climate zones: equatorial, arid, warm, snow, polar and continents. We used the loading models estimated for a set of 229 ITRF2014 (International Terrestrial Reference Frame) International GNSS Service (IGS) stations and discussed the amount of variance explained by individual modes, proving that the common annual signal accounts for 16, 24 and 68% of the total variance of non-tidal ocean, atmospheric and hydrological loading models, respectively. Having removed the common environmental MSSA seasonal curve from the corresponding GPS position time series, we found that the residual station-specific annual curve modelled with the least-squares estimation has the amplitude of maximum 2 mm. This means that the environmental loading models underestimate the seasonalities observed by the GPS system. The remaining signal present in the seasonal frequency band arises from the systematic errors which are not of common environmental or geophysical origin. Using common mode error (CME) estimates, we showed that the direct removal of environmental loading models from the GPS series causes an artificial loss in the CME power spectra between 10 and 80 cycles per year. When environmental effect is removed from GPS series with MSSA curves, no influence on the character of spectra of CME estimates was noticed.

River flow prediction using hybrid models of support vector regression with the wavelet transform, singular spectrum analysis and chaotic approach

Science.gov (United States)

Baydaroğlu, Özlem; Koçak, Kasım; Duran, Kemal

2018-06-01

Prediction of water amount that will enter the reservoirs in the following month is of vital importance especially for semi-arid countries like Turkey. Climate projections emphasize that water scarcity will be one of the serious problems in the future. This study presents a methodology for predicting river flow for the subsequent month based on the time series of observed monthly river flow with hybrid models of support vector regression (SVR). Monthly river flow over the period 1940-2012 observed for the Kızılırmak River in Turkey has been used for training the method, which then has been applied for predictions over a period of 3 years. SVR is a specific implementation of support vector machines (SVMs), which transforms the observed input data time series into a high-dimensional feature space (input matrix) by way of a kernel function and performs a linear regression in this space. SVR requires a special input matrix. The input matrix was produced by wavelet transforms (WT), singular spectrum analysis (SSA), and a chaotic approach (CA) applied to the input time series. WT convolutes the original time series into a series of wavelets, and SSA decomposes the time series into a trend, an oscillatory and a noise component by singular value decomposition. CA uses a phase space formed by trajectories, which represent the dynamics producing the time series. These three methods for producing the input matrix for the SVR proved successful, while the SVR-WT combination resulted in the highest coefficient of determination and the lowest mean absolute error.

How far is it to a sudden future singularity of pressure?

International Nuclear Information System (INIS)

DaPbrowski, Mariusz P.; Denkiewicz, Tomasz; Hendry, Martin A.

2007-01-01

We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within 10x10 6 years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompleteness, which means that the evolution of the universe may eventually be continued throughout until another 'more serious' singularity such as a big crunch or big rip

Singularities of robot mechanisms numerical computation and avoidance path planning

CERN Document Server

Bohigas, Oriol; Ros, Lluís

2017-01-01

This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves...

Introduction to singularities

CERN Document Server

Ishii, Shihoko

2014-01-01

This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...

Surface Plasmon Singularities

Directory of Open Access Journals (Sweden)

Gabriel Martínez-Niconoff

2012-01-01

Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

OpenAIRE

Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane; Natarajan, S.; Rabczuk, T.

2013-01-01

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient ...

Pressure fluctuations induced by fluid flow in singular points of industrial circuits

International Nuclear Information System (INIS)

Gibert, R.J.; Villard, B.

1977-01-01

Flow singularities (enlargements, bards, valves, tees,...) generate in the circuits of industrial plants wall pressure fluctuations which are the main cause of vibration. Two types of pressure fluctuations can be considered. - 'Local ' fluctuations: They are associated to the unsteadiness downstream from the singularity. These fluctuations may be characterized by frequency spectra, correlation length and phase lags. These parameters are used to calculate forces on the walls of the circuit. - 'Acoustic' fluctuations: The singularity acts as an acoustical source; its frequency spectrum and the acoustical transfer function of the circuit are needed to evaluate the acoustical level at any point. A methodical study of the most current singularities has been performed at C.E.A./D.E.M.T.: - On one hand a theory of noise generation by unsteady flow in internal acoustics has been developed. This theory uses the basic idea initiated by LIGHTILL. As a result it is shown that the plane wave propagation is a valid assumption and that a singularity can be acoustically modelled by a pressure and a mass-flow-rate discontinuities. Both are random functions of time, the spectra of which are determined from the local fluctuations characteristics. - On the other hand, characteristics of several singularities have been measured: (i) Intercorrelation spectra of local pressure fluctuations. (ii) Autocorrelation spectra of associated acoustical sources (the measure of the acoustical pressures in the experimental circuit are interpreted by using the D.E.M.T. computer code VIBRAPHONE which gives the acoustical response of a complex circuit). (Auth.)

Quantum evolution across singularities

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg

2008-01-01

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space)

Study on a kind of ϕ-Laplacian Liénard equation with attractive and repulsive singularities.

Science.gov (United States)

Xin, Yun; Cheng, Zhibo

2017-01-01

In this paper, by application of the Manasevich-Mawhin continuation theorem, we investigate the existence of a positive periodic solution for a kind of ϕ -Laplacian singular Liénard equation with attractive and repulsive singularities.

Analytic Evolution of Singular Distribution Amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Radyushkin, Anatoly V. [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Tandogan Kunkel, Asli [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

2014-03-01

We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

Science.gov (United States)

Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

2018-05-01

A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

Loop quantum cosmology and singularities.

Science.gov (United States)

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

Singularity-free interpretation of the thermodynamics of supercooled water

International Nuclear Information System (INIS)

Sastry, S.; Debenedetti, P.G.; Sciortino, F.; Stanley, H.E.

1996-01-01

The pronounced increases in isothermal compressibility, isobaric heat capacity, and in the magnitude of the thermal expansion coefficient of liquid water upon supercooling have been interpreted either in terms of a continuous, retracing spinodal curve bounding the superheated, stretched, and supercooled states of liquid water, or in terms of a metastable, low-temperature critical point. Common to these two scenarios is the existence of singularities associated with diverging density fluctuations at low temperature. We show that the increase in compressibility upon lowering the temperature of a liquid that expands on cooling, like water, is not contingent on any singular behavior, but rather is a thermodynamic necessity. We perform a thermodynamic analysis for an anomalous liquid (i.e., one that expands when cooled) in the absence of a retracing spinodal and show that one may in general expect a locus of compressibility extrema in the anomalous regime. Our analysis suggests that the simplest interpretation of the behavior of supercooled water consistent with experimental observations is free of singularities. We then develop a waterlike lattice model that exhibits no singular behavior, while capturing qualitative aspects of the thermodynamics of water. copyright 1996 The American Physical Society

A Hybrid Short-Term Traffic Flow Prediction Model Based on Singular Spectrum Analysis and Kernel Extreme Learning Machine.

Directory of Open Access Journals (Sweden)

Qiang Shang

Full Text Available Short-term traffic flow prediction is one of the most important issues in the field of intelligent transport system (ITS. Because of the uncertainty and nonlinearity, short-term traffic flow prediction is a challenging task. In order to improve the accuracy of short-time traffic flow prediction, a hybrid model (SSA-KELM is proposed based on singular spectrum analysis (SSA and kernel extreme learning machine (KELM. SSA is used to filter out the noise of traffic flow time series. Then, the filtered traffic flow data is used to train KELM model, the optimal input form of the proposed model is determined by phase space reconstruction, and parameters of the model are optimized by gravitational search algorithm (GSA. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. And the SSA-KELM model is compared with several well-known prediction models, including support vector machine, extreme learning machine, and single KLEM model. The experimental results demonstrate that performance of the proposed model is superior to that of the comparison models. Apart from accuracy improvement, the proposed model is more robust.

Study on sampling of continuous linear system based on generalized Fourier transform

Science.gov (United States)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

Singularities in minimax optimization of networks

DEFF Research Database (Denmark)

Madsen, Kaj; Schjær-Jacobsen, Hans

1976-01-01

A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the li......A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used...

Coupled singular and non singular thermoelastic system and double lapalce decomposition methods

OpenAIRE

Hassan Gadain; Hassan Gadain

2016-01-01

In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples

Naked singularity, firewall, and Hawking radiation.

Science.gov (United States)

Zhang, Hongsheng

2017-06-21

Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

EDITORIAL: The plurality of optical singularities

Science.gov (United States)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

in a rapidly and inhomogeneously flowing material, horizons can develop, analogous to those surrounding black holes in general relativity, and these new optical singularities can be regarded as wave catastrophes, and new associated quantum effects anticipated. Three decades after wave dislocations were introduced as ‘a new concept in ... wave theory’, these phase singularities have been extensively explored and are now familiar. New ideas—in addition to those described in this special issue—continue to emerge. For example, x-ray vortices were observed recently; there is a proposal to create lenses to form atomic beams containing vortices; and astrophysical applications have been suggested for both photon orbital angular momentum and optical vortices. We can safely assume that the science of wave singularities will develop further, and diffuse into new areas of physics.

Finite-time future singularities in modified Gauss-Bonnet and F(R,G) gravity and singularity avoidance

International Nuclear Information System (INIS)

Bamba, Kazuharu; Odintsov, Sergei D.; Sebastiani, Lorenzo; Zerbini, Sergio

2010-01-01

We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from F(R,G)-gravity, where R and G are the Ricci scalar and the Gauss-Bonnet invariant, respectively. As an explicit example of F(R,G)-gravity, we also investigate modified Gauss-Bonnet gravity, so-called F(G)-gravity. In particular, we reconstruct the F(G)-gravity and F(R,G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F(G)-gravity and F(R,G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss-Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory a non-singular one as well. (orig.)

Are naked singularities really visible

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; De Felice, F [Alberta Univ., Edmonton (Canada); Nobili, L [Padua Univ. (Italy). Ist. di Fisica

1978-12-09

The question whether a Kerr naked singularity is actually visible from infinity is investigated; it is shown that in fact any signal which could be emitted from the singularity is infinitely red-shifted. This implies that naked singularities would be indistinguishable from a black hole.

Singular problems in shell theory. Computing and asymptotics

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM

2010-07-01

It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)

Residues and duality for singularity categories of isolated Gorenstein singularities

OpenAIRE

Murfet, Daniel

2009-01-01

We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.

The role of the generalized Phillips' spectrum in wave turbulence

International Nuclear Information System (INIS)

Newell, A.C.; Zakharov, V.E.

2008-01-01

We suggest the generalized Phillips' spectrum, which we define as that spectrum for which the statistical properties of wave turbulence inherit the symmetries of the original governing equations, is, in many circumstances, the spectrum which obtains in those regions of wavenumber space in which the Kolmogorov-Zakharov (KZ) spectra are no longer valid. This spectrum has many very special properties. We discuss its connection with the singularities which are associated with the whitecap events observed in windblown seas

String theory and cosmological singularities

Indian Academy of Sciences (India)

Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.

Pseudo-differential operators on manifolds with singularities

CERN Document Server

Schulze, B-W

1991-01-01

The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Multidimensional singular integrals and integral equations

CERN Document Server

Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S

1965-01-01

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals

Holographic complexity and spacetime singularities

Energy Technology Data Exchange (ETDEWEB)

Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)

2016-01-15

We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

Holographic complexity and spacetime singularities

International Nuclear Information System (INIS)

Barbón, José L.F.; Rabinovici, Eliezer

2016-01-01

We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.

On the singularities of solutions to singular perturbation problems

International Nuclear Information System (INIS)

Fruchard, A; Schaefke, R

2005-01-01

We consider a singularly perturbed complex first order ODE εu ' Φ(x, u, a, ε), x, u element of C, ε > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot

Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions

International Nuclear Information System (INIS)

Otani, H.; Ogawa, T.

1996-01-01

Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the x -1 type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, λ e and λ h , of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (λ e h max[λ e ,λ h ]/v F . Corresponding optical spectrum near the Fermi edge (within an energy range of ℎv F /max[λ e ,λ h ]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the x -1 type (i.e., λ e →∞ and/or λ h →∞), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity

Semicontinuity of 4d N=2 spectrum under renormalization group flow

International Nuclear Information System (INIS)

Xie, Dan; Yau, Shing-Tung

2016-01-01

We study renormalization group flow of four dimensional N=2 SCFTs defined by isolated hypersurface three-fold singularities. We define the spectrum of N=2 theory as the set of scaling dimensions of the parameters on the Coulomb branch, which include Coulomb branch moduli, mass parameters and coupling constants. We prove that the spectrum of those theories is semicontinous under the RG flow on the Coulomb branch using the mathematical result about the singularity spectra under deformation. The semicontinuity behavior of N=2 spectrum implies a theorem under relevant and Coulomb branch moduli deformation, the absence of dangerous irrelevant deformations and can be taken as the necessary condition for the ending point of a RG flow. This behavior is also true for (c,c) ring deformation of two dimensional Landau-Ginzburg model with (2,2) supersymmetry.

On solutions of neutral stochastic delay Volterra equations with singular kernels

Directory of Open Access Journals (Sweden)

Xiaotai Wu

2012-08-01

Full Text Available In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

Singularities in four-body final-state amplitudes

International Nuclear Information System (INIS)

Adhikari, S.K.

1978-01-01

Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering

Local and nonlocal space-time singularities

International Nuclear Information System (INIS)

Konstantinov, M.Yu.

1985-01-01

The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established

Shaped 3D Singular Spectrum Analysis for Quantifying Gene Expression, with Application to the Early Zebrafish Embryo

Directory of Open Access Journals (Sweden)

Alex Shlemov

2015-01-01

Full Text Available Recent progress in microscopy technologies, biological markers, and automated processing methods is making possible the development of gene expression atlases at cellular-level resolution over whole embryos. Raw data on gene expression is usually very noisy. This noise comes from both experimental (technical/methodological and true biological sources (from stochastic biochemical processes. In addition, the cells or nuclei being imaged are irregularly arranged in 3D space. This makes the processing, extraction, and study of expression signals and intrinsic biological noise a serious challenge for 3D data, requiring new computational approaches. Here, we present a new approach for studying gene expression in nuclei located in a thick layer around a spherical surface. The method includes depth equalization on the sphere, flattening, interpolation to a regular grid, pattern extraction by Shaped 3D singular spectrum analysis (SSA, and interpolation back to original nuclear positions. The approach is demonstrated on several examples of gene expression in the zebrafish egg (a model system in vertebrate development. The method is tested on several different data geometries (e.g., nuclear positions and different forms of gene expression patterns. Fully 3D datasets for developmental gene expression are becoming increasingly available; we discuss the prospects of applying 3D-SSA to data processing and analysis in this growing field.

The Geometry of Black Hole Singularities

Directory of Open Access Journals (Sweden)

Ovidiu Cristinel Stoica

2014-01-01

Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

On the singularities of solutions to singular perturbation problems

Energy Technology Data Exchange (ETDEWEB)

Fruchard, A [Laboratoire de Mathematiques, Informatique et Applications, Faculte des Sciences et Techniques, Universite de Haute Alsace, 4 rue des Freres Lumiere, 68093 Mulhouse cedex (France); Schaefke, R [Departement de Mathematiques, Universite Louis Pasteur, 7 rue Rene-Descartes, 67084 Strasbourg cedex (France)

2005-01-01

We consider a singularly perturbed complex first order ODE {epsilon}u ' {phi}(x, u, a, {epsilon}), x, u element of C, {epsilon} > 0 is a small complex parameter and a element of C is a control parameter. It is proven that the singularities of some solutions are regularly spaced and that they move from one to the next as a runs about a loop of index one around a value of overstability. This gives a positive answer to a question of J. L. Callot.

Tuning of tunneling current noise spectra singularities by localized states charging

OpenAIRE

Mantsevich, V. N.; Maslova, N. S.

2008-01-01

We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage. Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that switching "on" and "off" of Coulomb interaction of conduction electrons with two charged localized states results in power law singularity of low-frequency tunneling current noise spectrum ($1/f^{\\alpha}$) and also results on high frequency com...

Singularity kinematics principle and position-singularity analyses of the 6-3 Stewart-Gough parallel manipulators

International Nuclear Information System (INIS)

Cao, Yi; Zhou, Hui; Li, Baokun; Shen, Long

2011-01-01

This paper presents a new principle and method of kinematics to analyze the singularity of Stewart-Gough parallel manipulators and addresses the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulators for special orientations. Based on the kinematic relationship of a rigid body, a necessary and sufficient condition that three velocities of three non-collinear points in a moving rigid body can determine a screw motion is addressed and some typical singular configurations of the 6-3 Stewart-Gough parallel manipulators are also addressed in detail. With the above-mentioned condition, a symbolic analytical polynomial expression of degree three in the moving platform position parameters, representing the position-singularity locus of the 6-3 Stewart-Gough manipulators for special orientations, is derived: and the property identification of the position-singularity loci of the 6-3 Stewart-Gough manipulator for these special orientations is investigated at length. It is shown that position-singularity loci of the 6-3 Stewart-Gough parallel manipulator for these special orientations will be a plane and a hyperbolic paraboloid, even three intersecting planes

On important precursor of singular optics (tutorial)

Science.gov (United States)

Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.

2018-01-01

The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].

Properties of kinematic singularities

Energy Technology Data Exchange (ETDEWEB)

Coley, A A [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada); Hervik, S [Department of Mathematics and Natural Sciences, University of Stavanger, N-4036 Stavanger (Norway); Lim, W C [Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); MacCallum, M A H, E-mail: aac@mathstat.dal.c, E-mail: sigbjorn.hervik@uis.n, E-mail: wclim@aei.mpg.d, E-mail: m.a.h.maccallum@qmul.ac.u [School of Mathematical Sciences, Queen Mary University of London, E1 4NS (United Kingdom)

2009-11-07

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.

Analytic Evolution of Singular Distribution Amplitudes in QCD

Energy Technology Data Exchange (ETDEWEB)

Tandogan Kunkel, Asli [Old Dominion Univ., Norfolk, VA (United States)

2014-08-01

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.

3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities

CERN Document Server

Neto, Aurélio; Mond, David; Saia, Marcelo; Snoussi, Jawad; BMMS 2/NBMS 3; ENSINO; Singularities and foliations geometry, topology and applications

2018-01-01

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

Characterization of high-energy photoionization in terms of the singularities of the atomic potential. I. Photoionization of the ground state of a two-electron atom

International Nuclear Information System (INIS)

Suric, T.; Drukarev, E.G.; Pratt, R.H.

2003-01-01

We describe single and double photoionization of two-electron atoms by photoabsorption at high incident photon energies ω (but still ω 2 ) using a unified approach based on asymptotic Fourier transform (AFT) theory modified by Coulombic interactions. Within this approach the matrix elements for photoabsorption processes at high energies can be understood in terms of the singularities of the many-body Coulomb potential. These singularities (e-e and e-N) result in the singularities of the wave functions and the singularities of the e-γ interaction, which determine the asymptotic behavior of the matrix element. Within our unified approach we explain the dominant contributions, including both the dominant contributions to the total cross section for single ionization and for ionization with excitation, and the dominant contributions to the double ionization spectrum, as a Fourier transform asymptotic in a single large momentum (dependent on the process and the region of the spectrum). These dominant contributions are connected, through AFT, with either the e-N singularity or the e-e singularity. The AFT results are modified by Coulombic interactions. We include these modifications, for the cases of single ionization and of double ionization in the shake-off region at high energies, and extract a slowly convergent factor (Stobbe factor). In this way we obtain rapid convergence of the cross sections to their high-energy behaviors. This also allows us to discuss the convergence of ratios of cross sections

Topological resolution of gauge theory singularities

Science.gov (United States)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-01

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

Topological resolution of gauge theory singularities

Energy Technology Data Exchange (ETDEWEB)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

Singularities of Type-Q ABS Equations

Directory of Open Access Journals (Sweden)

James Atkinson

2011-07-01

Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.

The geometry of warped product singularities

Science.gov (United States)

Stoica, Ovidiu Cristinel

In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

The Big Bang Singularity

Science.gov (United States)

Ling, Eric

The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

On a Monge-Amp\\`ere operator for plurisubharmonic functions with analytic singularities

OpenAIRE

Andersson, Mats; Błocki, Zbigniew; Wulcan, Elizabeth

2017-01-01

We study continuity properties of generalized Monge-Amp\\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a formula for the total mass of the Monge-Amp\\`ere measure of such a function on a compact K\\"ahler manifold.

On local invariants of singular symplectic forms

Science.gov (United States)

Domitrz, Wojciech

2017-04-01

We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.

Spacetime averaging of exotic singularity universes

International Nuclear Information System (INIS)

Dabrowski, Mariusz P.

2011-01-01

Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.

Continuous relaxation time spectrum of α-process in glass-like B2O3

International Nuclear Information System (INIS)

Bartenev, G.M.; Lomovskij, V.A.

1991-01-01

α-process of relaxation of glass-like B 2 O 3 was investigated in a wide temperature range. Continuous spectrum of relaxation times H(τ) for this process was constructed, using data of dynamic methods of investigation. It is shown that increase of temperature of α-process investigation leads to change of glass-like BaO 3 structure in such a way, that H(τ) spectrum tends to the maxwell one with a unit relaxation time

The Semantics of Plurals: A Defense of Singularism

Science.gov (United States)

Florio, Salvatore

2010-01-01

In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

The accuracy comparison between ARFIMA and singular spectrum analysis for forecasting the sales volume of motorcycle in Indonesia

Science.gov (United States)

Sitohang, Yosep Oktavianus; Darmawan, Gumgum

2017-08-01

This research attempts to compare between two forecasting models in time series analysis for predicting the sales volume of motorcycle in Indonesia. The first forecasting model used in this paper is Autoregressive Fractionally Integrated Moving Average (ARFIMA). ARFIMA can handle non-stationary data and has a better performance than ARIMA in forecasting accuracy on long memory data. This is because the fractional difference parameter can explain correlation structure in data that has short memory, long memory, and even both structures simultaneously. The second forecasting model is Singular spectrum analysis (SSA). The advantage of the technique is that it is able to decompose time series data into the classic components i.e. trend, cyclical, seasonal and noise components. This makes the forecasting accuracy of this technique significantly better. Furthermore, SSA is a model-free technique, so it is likely to have a very wide range in its application. Selection of the best model is based on the value of the lowest MAPE. Based on the calculation, it is obtained the best model for ARFIMA is ARFIMA (3, d = 0, 63, 0) with MAPE value of 22.95 percent. For SSA with a window length of 53 and 4 group of reconstructed data, resulting MAPE value of 13.57 percent. Based on these results it is concluded that SSA produces better forecasting accuracy.

Quantum cosmology and late-time singularities

International Nuclear Information System (INIS)

Kamenshchik, A Yu

2013-01-01

The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behavior of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born–Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)

One dimensional systems with singular perturbations

International Nuclear Information System (INIS)

Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P

2011-01-01

This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.

Minimal solution for inconsistent singular fuzzy matrix equations

Directory of Open Access Journals (Sweden)

M. Nikuie

2013-10-01

Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps with prescribed singular fibers

OpenAIRE

Kalmar, Boldizsar

2006-01-01

We give a Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of -1 codimensional stable maps with prescribed singular fibers.

Singularities in FLRW spacetimes

Science.gov (United States)

het Lam, Huibert; Prokopec, Tomislav

2017-12-01

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.

The theory of singular perturbations

CERN Document Server

De Jager, E M

1996-01-01

The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

Singular potentials in quantum mechanics

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Koo, E. Ley

1995-10-01

This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs

Analysis of singularity in redundant manipulators

International Nuclear Information System (INIS)

Watanabe, Koichi

2000-03-01

In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)

Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side

Science.gov (United States)

Amirjanyan, A. A.; Sahakyan, A. V.

2017-08-01

A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.

An Exact Solution of the Binary Singular Problem

Directory of Open Access Journals (Sweden)

Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

Biclustering via Sparse Singular Value Decomposition

KAUST Repository

Lee, Mihee

2010-02-16

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.

Sensitivity analysis of automatic flight control systems using singular value concepts

Science.gov (United States)

Herrera-Vaillard, A.; Paduano, J.; Downing, D.

1985-01-01

A sensitivity analysis is presented that can be used to judge the impact of vehicle dynamic model variations on the relative stability of multivariable continuous closed-loop control systems. The sensitivity analysis uses and extends the singular-value concept by developing expressions for the gradients of the singular value with respect to variations in the vehicle dynamic model and the controller design. Combined with a priori estimates of the accuracy of the model, the gradients are used to identify the elements in the vehicle dynamic model and controller that could severely impact the system's relative stability. The technique is demonstrated for a yaw/roll damper stability augmentation designed for a business jet.

Noncrossing timelike singularities of irrotational dust collapse

International Nuclear Information System (INIS)

Liang, E.P.T.

1979-01-01

Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)

The dominant balance at cosmological singularities

International Nuclear Information System (INIS)

Cotsakis, Spiros; Barrow, John D

2007-01-01

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity

Dressing up a Kerr naked singularity

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Nobili, L [Padua Univ. (Italy). Ist. di Fisica

1979-06-11

The evolution of a naked singularity surrounded by an accreting disk of matter is studied; two kinds of disks are considered: the standard thin-disk model and the thick barytropic model, for several initial conditions. It is shown that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. The final mass, the luminosity and the time of evolution of the singularity are evaluated.

A new two-photon mechanism of the formation of a continuous spectrum of photons emitted by secondary emission products of atomic particles

International Nuclear Information System (INIS)

Veksler, V.I.

1986-01-01

A two-photon mechanism of the formation of a continuous spectrum of photons emitted by products of metal sputtering is considered. The following process of the two-photon mechanism is considered: the continuous spectrum is formed under quadrupole two-photon transitions in sputtered excited atoms having vacancies at the d level in atoms of transition metals or at the of level in lanthanides found against the filled conduction band. It is shown that the suggested mechanism should play an essential role in the formation of the continuous spectrum of optical radiation

Daily Average Wind Power Interval Forecasts Based on an Optimal Adaptive-Network-Based Fuzzy Inference System and Singular Spectrum Analysis

Directory of Open Access Journals (Sweden)

Zhongrong Zhang

2016-01-01

Full Text Available Wind energy has increasingly played a vital role in mitigating conventional resource shortages. Nevertheless, the stochastic nature of wind poses a great challenge when attempting to find an accurate forecasting model for wind power. Therefore, precise wind power forecasts are of primary importance to solve operational, planning and economic problems in the growing wind power scenario. Previous research has focused efforts on the deterministic forecast of wind power values, but less attention has been paid to providing information about wind energy. Based on an optimal Adaptive-Network-Based Fuzzy Inference System (ANFIS and Singular Spectrum Analysis (SSA, this paper develops a hybrid uncertainty forecasting model, IFASF (Interval Forecast-ANFIS-SSA-Firefly Alogorithm, to obtain the upper and lower bounds of daily average wind power, which is beneficial for the practical operation of both the grid company and independent power producers. To strengthen the practical ability of this developed model, this paper presents a comparison between IFASF and other benchmarks, which provides a general reference for this aspect for statistical or artificially intelligent interval forecast methods. The comparison results show that the developed model outperforms eight benchmarks and has a satisfactory forecasting effectiveness in three different wind farms with two time horizons.

Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

Science.gov (United States)

Ciuonzo, Domenico; Rossi, Pierluigi Salvo

2017-04-01

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario and several TR-MUSIC variants are here investigated. The analysis builds upon the 1st-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the 2nd order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.

Singularities in cosmologies with interacting fluids

International Nuclear Information System (INIS)

Cotsakis, Spiros; Kittou, Georgia

2012-01-01

We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for ‘phantom’ matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding to a logarithmic branch point that resembles a cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.

Observational constraints on cosmological future singularities

International Nuclear Information System (INIS)

Beltran Jimenez, Jose; Lazkoz, Ruth; Saez-Gomez, Diego; Salzano, Vincenzo

2016-01-01

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)

Observational constraints on cosmological future singularities

Energy Technology Data Exchange (ETDEWEB)

Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)

2016-11-15

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)

Non-singular string-cosmologies from exact conformal field theories

International Nuclear Information System (INIS)

Vega, H.J. de; Larsen, A.L.; Sanchez, N.

2001-01-01

Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular space-times with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation

Asymptotic safety, singularities, and gravitational collapse

International Nuclear Information System (INIS)

Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz

2011-01-01

Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.

Singularity resolution in quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity

Singular values of the Rogers-Ramanujan continued fraction

NARCIS (Netherlands)

Gee, A.C.P.; Honsbeek, M

1999-01-01

Let $z\\in\\C$ be imaginary quadratic in the upper half plane.Then the Rogers-Ramanujan continued fraction evaluated at $q=e^{2\\pi i z}$ is contained in a class field of $\\Q(z)$. Ramanujan showed that for certain values of $z$, one can write these continued fractions as nested radicals. We use the

On the continuity of the stationary state distribution of DPCM

Science.gov (United States)

Naraghi-Pour, Morteza; Neuhoff, David L.

1990-03-01

Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e., delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediciton coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e., it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e., either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions.

Compatibility conditions of a singular hypersurface in the relativistic mechanics of the continuous media

International Nuclear Information System (INIS)

Maugin, G.A.

1976-01-01

In this work the compatibility conditions verified by the discontinuities of relativistic fields and of their space-time and time-like derivatives up to be second order are systematically constructed in terms of the local geometry of the wave front (singular hypersurface). A new time-like derivative that generalizes Thomas' delta-derivative of classical continuum mechanics is thus introduced in the relativistic frame. It allows to formulate these conditions in compact forms. It is thus expected that the relativistic analogue of T.Y. Thomas' (1957) classical theory is produced [fr

Quantum dress for a naked singularity

Directory of Open Access Journals (Sweden)

Marc Casals

2016-09-01

Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.

Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

Science.gov (United States)

Pan, Supriya

2018-01-01

Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

Connection conditions and the spectral family under singular potentials 03.65.Ge Solutions of wave equations: bound states; 03.65.-w Quantum mechanics;

CERN Document Server

Tsutsui, I; Cheon, T

2003-01-01

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wavefunctions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well defined even if the wavefunctions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential V(x)=-e sup 2 vertical bar x vertical bar and the harmonic oscillator with square inverse potential V(x)=(m omega sup 2 /2)x sup 2 +g/x sup 2 , and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potential V(-x)=V(x), the spectrum is determined solely by the eigenvalues of ...

Singular multiparameter dynamic equations with distributional ...

African Journals Online (AJOL)

Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.

Is the cosmological singularity compulsory

International Nuclear Information System (INIS)

Bekenstein, J.D.; Meisels, A.

1980-01-01

The cosmological singularity is inherent in all conventional general relativistic cosmological models. There can be no question that it is an unphysical feature; yet there does not seem to be any convervative way of eliminating it. Here we present singularity-free isotropic cosmological models which are indistinguishable from general relativistic ones at late times. They are based on the general theory of variable rest masses that we developed recently. Outside cosmology this theory simulates general relativity well. Thus it provides a framework incorporating those features which have made geneal relativity so sucessful while providing a way out of singularity dilemma. The cosmological models can be made to incorporate Dirac's large numbers hypothesis. G(now)/G(0)approx.10 -38

São Carlos Workshop on Real and Complex Singularities

CERN Document Server

Ruas, Maria

2007-01-01

The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19–23, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...

Analytic continuation in perturbative QCD

International Nuclear Information System (INIS)

Caprini, Irinel

2002-01-01

We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)

Accuracy evaluation of Fourier series analysis and singular spectrum analysis for predicting the volume of motorcycle sales in Indonesia

Science.gov (United States)

Sasmita, Yoga; Darmawan, Gumgum

2017-08-01

This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.

Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type.

Science.gov (United States)

Xin, Yun; Liu, Hongmin; Cheng, Zhibo

2018-01-01

In this paper, we consider a kind of p -Laplacian neutral Rayleigh equation with singularity of attractive type, [Formula: see text] By applications of an extension of Mawhin's continuation theorem, sufficient conditions for the existence of periodic solution are established.

Discrete variable representation for singular Hamiltonians

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2004-01-01

We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...

Topological Signals of Singularities in Ricci Flow

Directory of Open Access Journals (Sweden)

Paul M. Alsing

2017-08-01

Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.

Singularities of affine fibrations in the regularity theory of Fourier integral operators

International Nuclear Information System (INIS)

Ruzhansky, M V

2000-01-01

We consider regularity properties of Fourier integral operators in various function spaces. The most interesting case is the L p spaces, for which survey of recent results is given. For example, sharp orders are known for operators satisfying the so-called smooth factorization condition. Here this condition is analyzed in both real and complex settings. In the letter case, conditions for the continuity of Fourier integral operators are related to singularities of affine fibrations in C n (or subsets of C n ) specified by the kernels of Jacobi matrices of holomorphic maps. Singularities of such fibrations are analyzed in this paper in the general case. In particular, it is shown that if the dimension n or the rank of the Jacobi matrix is small, then all singularities of an affine fibration are removable. The fibration associated with a Fourier integral operator is given by the kernels of the Hessian of the phase function of the operator. On the basis of an analysis of singularities for operators commuting with translations we show in a number of cases that the factorization condition is satisfied, which leads to L p estimates for operators. In other cases, examples are given in which the factorization condition fails. The results are applied to deriving L p estimates for solutions of the Cauchy problem for hyperbolic partial differential operators

Reasons for singularity in robot teleoperation

DEFF Research Database (Denmark)

Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth

2014-01-01

In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and dela...

Identification of discrete chaotic maps with singular points

Directory of Open Access Journals (Sweden)

P. G. Akishin

2001-01-01

Full Text Available We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.

Continuous optical measurement system of hemolysis during a photosensitization reaction using absorption spectrum

Science.gov (United States)

Hamada, R.; Ogawa, E.; Arai, T.

2018-02-01

To investigate hemolysis phenomena during a photosensitization reaction with the reaction condition continuously and simultaneously for a safety assessment of hemolysis side effect, we constructed an optical system to measure blood sample absorption spectrum during the reaction. Hemolysis degree might be under estimated in general evaluation methods because there is a constant oxygen pressure assumption in spite of oxygen depression take place. By investigating hemoglobin oxidation and oxygen desorption dynamics obtained from the contribution of the visible absorption spectrum and multiple regression analysis, both the hemolysis phenomena and its oxygen environment might be obtained with time. A 664 nm wavelength laser beam for the reaction excitation and 475-650 nm light beam for measuring the absorbance spectrum were arranged perpendicularly crossing. A quartz glass cuvette with 1×10 mm in dimensions for the spectrum measurement was located at this crossing point. A red blood cells suspension medium was arranged with low hematocrit containing 30 μg/ml talaporfin sodium. This medium was irradiated up to 40 J/cm2 . The met-hemoglobin, oxygenatedhemoglobin, and deoxygenated-hemoglobin concentrations were calculated by a multiple regression analysis from the measured spectra. We confirmed the met-hemoglobin concentration increased and oxygen saturation decreased with the irradiation time, which seems to indicate the hemolysis progression and oxygen consumption, respectively. By using our measuring system, the hemolysis progression seems to be obtained with oxygen environment information.

7 CFR 46.1 - Words in singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...

Stable computation of generalized singular values

Energy Technology Data Exchange (ETDEWEB)

Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)

1996-12-31

We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.

Singularly perturbed Burger-Huxley equation: Analytical solution ...

African Journals Online (AJOL)

user

solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.

Observer-dependent sign inversions of polarization singularities.

Science.gov (United States)

Freund, Isaac

2014-10-15

We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

Generalized teleparallel cosmology and initial singularity crossing

Energy Technology Data Exchange (ETDEWEB)

Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg [Center for Theoretical Physics, the British University in Egypt, Suez Desert Road, Sherouk City 11837 (Egypt)

2017-02-01

We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.

Cosmologies with quasiregular singularities. II. Stability considerations

International Nuclear Information System (INIS)

Konkowski, D.A.; Helliwell, T.M.

1985-01-01

The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R 1 x T 3 and R 3 x S 1 flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added

Exact solutions and singularities in string theory

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail

Technological Singularity: What Do We Really Know?

Directory of Open Access Journals (Sweden)

Alexey Potapov

2018-04-01

Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.

Quantum healing of classical singularities in power-law spacetimes

Energy Technology Data Exchange (ETDEWEB)

Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)

2007-07-07

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.

Singularities in the nonisotropic Boltzmann equation

International Nuclear Information System (INIS)

Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

1987-09-01

We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

Science.gov (United States)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

International Nuclear Information System (INIS)

Wu, Sheng-Jhih; Chu, Moody T

2017-01-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing–Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations. (paper)

Normal forms of Hopf-zero singularity

International Nuclear Information System (INIS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)

Normal forms of Hopf-zero singularity

Science.gov (United States)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

Radioanatomy of the singular nerve canal

Energy Technology Data Exchange (ETDEWEB)

Muren, C. [Dept. of Diagnostic Radiology, Sabbatsbergs Hospital, Stockholm (Sweden); Wadin, K. [University Hospital, Uppsala (Sweden); Dimopoulos, P. [University Hospital, Uppsala (Sweden)

1991-08-01

The singular canal conveys vestibular nerve fibers from the ampulla of the posterior semicircular canal to the posteroinferior border of the internal auditory meatus. Radiographic identification of this anatomic structure helps to distinguish it from a fracture. It is also a landmark in certain surgical procedures. Computed tomography (CT) examinations of deep-frozen temporal bone specimens were compared with subsequently prepared plastic casts of these bones, showing good correlation between the anatomy and the images. The singular canal and its variable anatomy were studied in CT examinations of 107 patients. The singular canal could be identified, in both the axial and in the coronal planes. Its point of entry into the internal auditory meatus varied considerably. (orig.)

Singularities in the delta = 3 Tomimatsu-Sato space-time

Energy Technology Data Exchange (ETDEWEB)

Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Turolla, R [International School for Advanced Studies, Trieste (Italy)

1980-08-02

The existence of singularities outside the equatorial plane is investigated. We show that when the specific angular momentum a exceeds the mass m of the source, there are six ring singularities, while when asingularities lie only in the equatorial plane.

Complexity, Analysis and Control of Singular Biological Systems

CERN Document Server

Zhang, Qingling; Zhang, Xue

2012-01-01

Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling  the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...

Can non-commutativity resolve the big-bang singularity?

Energy Technology Data Exchange (ETDEWEB)

Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)

2004-08-01

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)

Remarks on gauge variables and singular Lagrangians

International Nuclear Information System (INIS)

Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.

1977-01-01

The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)

Tangled nonlinear driven chain reactions of all optical singularities

Science.gov (United States)

Vasil'ev, V. I.; Soskin, M. S.

2012-03-01

Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

Workshop on Singularities in Geometry, Topology, Foliations and Dynamics

CERN Document Server

Lê, Dung; Oka, Mutsuo; Snoussi, Jawad

2017-01-01

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Cusp singularities in f(R) gravity: pros and cons

International Nuclear Information System (INIS)

Chen, Pisin; Yeom, Dong-han

2015-01-01

We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvature singularity that can be interpreted by a firewall

Naked singularities and cosmic censorship: comment on the current situation

International Nuclear Information System (INIS)

Seifert, H.J.

1979-01-01

The current discussion is mainly concerned with how, or indeed, whether space-times possessing naked singularities can be ruled out as being too unrealistic or not being singular at all. The present position is summarized, with references, under the following headings: the Hawking-Penrose existence theorems, hydrodynamical singularities and the strength of naked singularities. (UK)

Numerical investigation of stress singularities in cracked bimaterial body

Czech Academy of Sciences Publication Activity Database

Náhlík, Luboš; Šestáková, Lucie; Hutař, Pavel

2008-01-01

Roč. 385-387, - (2008), s. 125-128 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics /7./. Seoul, 09.09.2008-11.09.2008] R&D Projects: GA AV ČR(CZ) KJB200410803; GA ČR GP106/06/P239; GA ČR GA106/08/1409 Institutional research plan: CEZ:AV0Z20410507 Keywords : bimaterial interface * stress singularity exponent * corner singularity * vertex singularity * general singular stress concentrator Subject RIV: JL - Materials Fatigue, Friction Mechanics

[An automatic peak detection method for LIBS spectrum based on continuous wavelet transform].

Science.gov (United States)

Chen, Peng-Fei; Tian, Di; Qiao, Shu-Jun; Yang, Guang

2014-07-01

Spectrum peak detection in the laser-induced breakdown spectroscopy (LIBS) is an essential step, but the presence of background and noise seriously disturb the accuracy of peak position. The present paper proposed a method applied to automatic peak detection for LIBS spectrum in order to enhance the ability of overlapping peaks searching and adaptivity. We introduced the ridge peak detection method based on continuous wavelet transform to LIBS, and discussed the choice of the mother wavelet and optimized the scale factor and the shift factor. This method also improved the ridge peak detection method with a correcting ridge method. The experimental results show that compared with other peak detection methods (the direct comparison method, derivative method and ridge peak search method), our method had a significant advantage on the ability to distinguish overlapping peaks and the precision of peak detection, and could be be applied to data processing in LIBS.

Singularly perturbed volterra integro-differential equations | Bijura ...

African Journals Online (AJOL)

Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

On the nature of naked singularities in Vaidya spacetimes

Energy Technology Data Exchange (ETDEWEB)

Dwivedi, I.H. (Aligarh Muslim Univ. (India). Dept. of Physics); Joshi, P.S. (Tata Inst. of Fundamental Research, Bombay (India))

1989-11-01

The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author).

On the nature of naked singularities in Vaidya spacetimes

International Nuclear Information System (INIS)

Dwivedi, I.H.

1989-01-01

The Vaidya-Papapetrou model containing a naked singularity is analysed for outgoing causal geodesics joining the singularity. The curvature growth along these trajectories is examined to show that this is a strong curvature singularity, providing a counter-example to certain forms of cosmic censorship hypotheses. (author)

Ambient cosmology and spacetime singularities

CERN Document Server

Antoniadis, Ignatios

2015-01-01

We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.

Naked singularities in self-similar spherical gravitational collapse

International Nuclear Information System (INIS)

Ori, A.; Piran, T.

1987-01-01

We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (Γ-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

Science.gov (United States)

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Building Reproducible Science with Singularity Containers

CERN Multimedia

CERN. Geneva

2018-01-01

Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...

Phantom cosmology without Big Rip singularity

Energy Technology Data Exchange (ETDEWEB)

Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)

2012-03-23

We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

Phantom cosmology without Big Rip singularity

International Nuclear Information System (INIS)

Astashenok, Artyom V.; Nojiri, Shin'ichi; Odintsov, Sergei D.; Yurov, Artyom V.

2012-01-01

We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers

Science.gov (United States)

Prybol, Cameron J.; Kurtzer, Gregory M.

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub’s primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers. PMID:29186161

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.

Directory of Open Access Journals (Sweden)

Vanessa V Sochat

Full Text Available Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

Science.gov (United States)

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Curing Black Hole Singularities with Local Scale Invariance

Directory of Open Access Journals (Sweden)

Predrag Dominis Prester

2016-01-01

Full Text Available We show that Weyl-invariant dilaton gravity provides a description of black holes without classical space-time singularities. Singularities appear due to the ill behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are as follows: (1 singularities signal a phase transition from broken to unbroken phase of Weyl symmetry; (2 instead of a singularity, there is a “baby universe” or a white hole inside a black hole; (3 in the baby universe scenario, there is a critical mass after which reducing mass makes the black hole larger as viewed by outside observers; (4 if a black hole could be connected with white hole through the “singularity,” this would require breakdown of (classical geometric description; (5 the singularity of Schwarzschild BH solution is nongeneric and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information loss puzzle. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point.

Simpson's neutrino and the singular see-saw

International Nuclear Information System (INIS)

Allen, T.J.; Johnson, R.; Ranfone, S.; Schechter, J.; Walle, J.W.F.

1991-01-01

The authors of this paper derive explicit forms for the neutrino and lepton mixing-matrices which describe the generic singular see-saw model. The dependence on the hierarchy parameter is contrasted with the non-singular case. Application is made to Simpson's 17 keV neutrino

Supersymmetric quantum mechanics under point singularities

International Nuclear Information System (INIS)

Uchino, Takashi; Tsutsui, Izumi

2003-01-01

We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

Ambient cosmology and spacetime singularities

International Nuclear Information System (INIS)

Antoniadis, Ignatios; Cotsakis, Spiros

2015-01-01

We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)

Singular moduli and Arakelov intersection

International Nuclear Information System (INIS)

Weng Lin.

1994-05-01

The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs

Solutions of dissimilar material singularity and contact problems

International Nuclear Information System (INIS)

Yang, Y.

2003-09-01

Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)

Metric dimensional reduction at singularities with implications to Quantum Gravity

International Nuclear Information System (INIS)

Stoica, Ovidiu Cristinel

2014-01-01

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained

Beyond the singularity of the 2-D charged black hole

International Nuclear Information System (INIS)

Giveon, Amit; Rabinovici, Eliezer; Sever, Amit

2003-01-01

Two dimensional charged black holes in string theory can be obtained as exact SL(2,R) x U(1)/U(1) quotient CFTs. The geometry of the quotient is induced from that of the group, and in particular includes regions beyond the black hole singularities. Moreover, wavefunctions in such black holes are obtained from gauge invariant vertex operators in the SL(2,R) CFT, hence their behavior beyond the singularity is determined. When the black hole is charged we find that the wavefunctions are smooth at the singularities. Unlike the uncharged case, scattering waves prepared beyond the singularity are not fully reflected; part of the wave is transmitted through the singularity. Hence, the physics outside the horizon of a charged black hole is sensitive to conditions set behind the past singularity. (author)

THE EXT RACORPOREAL FERTILIZATION TECHNOLOGIES AND THE SINGULARITY PROBLEMS

Directory of Open Access Journals (Sweden)

S. V. Denysenko

2013-05-01

Full Text Available The peculiarities of modern medicine development connected with the technological and informative singularity are analyzed. The risks of realization of extracorporeal fertilization are examined from positions of development of informative singularity. The warning problems of origin of singularity are discussed on t h e base of t h e newest technologies development.

M theory and singularities of exceptional holonomy manifolds

International Nuclear Information System (INIS)

Acharya, Bobby S.; Gukov, Sergei

2004-12-01

M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)

Model of a black hole gas submitted to background gravitational field for active galaxy nuclei with application to calculating the continuous emission spectra of massless particles (Photons: neutrinos and gravitons)

International Nuclear Information System (INIS)

Pinto Neto, A.

1987-01-01

A new theoretical model for active galaxy nuclei which describes the continuous spectrum of rest massless particles (photons, neutrinos and gravitons) in the frequency range from radiofrequency to gamma ray frequency, is presented. The model consists in a black hole gas interacting with a background gravitacional field. The previously models proposed for active galaxy nuclei are exposured. Whole theoretical fundaments based on Einstein general relativity theory for defining and studying singularity properties (black holes) are also presented. (M.C.K.) [pt

Enveloping branes and brane-world singularities

Energy Technology Data Exchange (ETDEWEB)

Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)

2014-12-01

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)

Holographic subregion complexity for singular surfaces

Energy Technology Data Exchange (ETDEWEB)

Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)

2017-10-15

Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

Science.gov (United States)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

The cosmological singularity

CERN Document Server

Belinski, Vladimir

2018-01-01

Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...

Quantum gravitational collapse: non-singularity and non-locality

International Nuclear Information System (INIS)

Greenwood, Eric; Stojkovic, Dejan

2008-01-01

We investigate gravitational collapse in the context of quantum mechanics. We take primary interest in the behavior of the collapse near the horizon and near the origin (classical singularity) from the point of view of an infalling observer. In the absence of radiation, quantum effects near the horizon do not change the classical conclusions for an infalling observer, meaning the horizon is not an obstacle for him. However, quantum effects are able to remove the classical singularity at the origin, since the wave function is non-singular at the origin. Also, near the classical singularity, some non-local effects become important. In the Schrodinger equation describing behavior near the origin, derivatives of the wave function at one point are related to the value of the wave function at some other distant point.

7 CFR 900.80 - Words in the singular form.

Science.gov (United States)

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...

A spin-liquid with pinch-line singularities on the pyrochlore lattice.

Science.gov (United States)

Benton, Owen; Jaubert, L D C; Yan, Han; Shannon, Nic

2016-05-26

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.

An investigation of singular Lagrangians as field systems

International Nuclear Information System (INIS)

Rabei, E.M.

1995-07-01

The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs

Fundamental solutions of singular SPDEs

International Nuclear Information System (INIS)

Selesi, Dora

2011-01-01

Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

Singularities: the Brieskorn anniversary volume

National Research Council Canada - National Science Library

Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M

1998-01-01

...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

International Nuclear Information System (INIS)

Baker, G.; Siegel, M.; Tanveer, S.

1995-01-01

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. The situation is disastrous for numerical computation, as small roundoff errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out. 47 refs., 10 figs., 1 tab

Singularities in geodesic surface congruence

International Nuclear Information System (INIS)

Cho, Yong Seung; Hong, Soon-Tae

2008-01-01

In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.

Singularity Theory and its Applications

CERN Document Server

Stewart, Ian; Mond, David; Montaldi, James

1991-01-01

A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

Preventing singularities in the Einstein-Cartan cosmology

International Nuclear Information System (INIS)

Kuchowicz, B.

1977-01-01

The singularity in expanding cosmological models is an undesirable consequence of general relativity. It may be removed in the Einstein-Cartan theory of gravitation which is an extension of general relativity (''general relativity with spin''). In the Einstein-Cartan theory there appears a characteristic spin-spin interaction which counteracts the contraction of matter above a certain critical density, and thus prevents any singularity. Generalizations of homogeneous cosmological models may contain either locally aligned spins (along an asymmetry axis) or randomly distributed spins (and then only the mean spin density square is macroscopically meaningful). In both cases the singularity can be removed, if only the spin density does increase at a sufficiently fast rate with the contraction of matter. (author)

Initial singularity and pure geometric field theories

Science.gov (United States)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Singularity hypotheses a scientific and philosophical assessment

CERN Document Server

Moor, James; Søraker, Johnny; Steinhart, Eric

2012-01-01

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.

Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

Directory of Open Access Journals (Sweden)

Akira Shirai

2015-01-01

Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.

Signaling on the continuous spectrum of nonlinear optical fiber.

Science.gov (United States)

Tavakkolnia, Iman; Safari, Majid

2017-08-07

This paper studies different signaling techniques on the continuous spectrum (CS) of nonlinear optical fiber defined by nonlinear Fourier transform. Three different signaling techniques are proposed and analyzed based on the statistics of the noise added to CS after propagation along the nonlinear optical fiber. The proposed methods are compared in terms of error performance, distance reach, and complexity. Furthermore, the effect of chromatic dispersion on the data rate and noise in nonlinear spectral domain is investigated. It is demonstrated that, for a given sequence of CS symbols, an optimal bandwidth (or symbol rate) can be determined so that the temporal duration of the propagated signal at the end of the fiber is minimized. In effect, the required guard interval between the subsequently transmitted data packets in time is minimized and the effective data rate is significantly enhanced. Moreover, by selecting the proper signaling method and design criteria a distance reach of 7100 km is reported by only singling on CS at a rate of 9.6 Gbps.

Evidence of emerging Griffiths singularity in La{sub 0.5} Sr{sub 0.5} MnO{sub 3} nanocrystalline probed by magnetization and electron paramagnetic resonance

Energy Technology Data Exchange (ETDEWEB)

Zhang, Xiyuan [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Fan, Jiyu, E-mail: jiyufan@nuaa.edu.cn [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Xu, Lisa [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Tong, Wei [High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031 (China); Hu, Dazhi [Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); He, Xun [College of Environmental Science and Engineering, Hunan University, Changsha 410082 (China); Zhang, Lei; Pi, Li; Zhang, Yuheng [High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031 (China)

2016-06-01

We present an investigation of Griffiths singularity in La{sub 0.5} Sr{sub 0.5} MnO{sub 3} nanocrystalline by means of magnetic susceptibility and electron paramagnetic resonance (EPR). An unusual platform was found in paramagnetic region. Based on the analysis of EPR spectrum and magnetization variation across the whole temperature range of phase transition, we confirm it is due to the presence of Griffiths singularity rather than a superparamagnetic state in the nanocrystalline system. Such a singularity phase is constituted with some correlated ferromagnetic clusters which embed in paramagnetic matrix. Although they form ferromagnetic spin correlation, the system do not yield any spontaneous magnetization. According to core–shell model, the emergence of Griffiths singularity can be considered due to the presence of local ferromagnetic fluctuations originated from surface spin disorder as the sample size is confined to nanoscale. - Highlights: • Griffiths singularity rather than superparamagnetism occurs in La{sub 0.5}Sr{sub 0.5}MnO{sub 3} nanoparticals. • The sample’s size reduced to nanoscale results in the short-range ferromagnetic interaction. • The core-shell model is used to understand the formation of Griffiths phase in nanometer La{sub 0.5}Sr{sub 0.5}MnO{sub 3}.

Finger image quality based on singular point localization

DEFF Research Database (Denmark)

Wang, Jinghua; Olsen, Martin A.; Busch, Christoph

2014-01-01

Singular points are important global features of fingerprints and singular point localization is a crucial step in biometric recognition. Moreover the presence and position of the core point in a captured fingerprint sample can reflect whether the finger is placed properly on the sensor. Therefore...... and analyze the importance of singular points on biometric accuracy. The experiment is based on large scale databases and conducted by relating the measured quality of a fingerprint sample, given by the positions of core points, to the biometric performance. The experimental results show the positions of core...

Repulsive and attractive timelike singularities in vacuum cosmologies

International Nuclear Information System (INIS)

Miller, B.D.

1979-01-01

Spherically symmetric cosmologies whose big bang is partially spacelike and partially timelike are constrained to occur only in the presence of certain types of matter, and in such cosmologies the timelike part of the big bang is a negative-mass singularity. In this paper examples are given of cylindrically symmetric cosmologies whose big bang is partially spacelike and partially timelike. These cosmologies are vacuum. In some of them, the timelike part of the big bang is clearly a (generalized) negative-mass singularity, while in others it is a (generalized) positive-mass singularity

Singularity theorems from weakened energy conditions

International Nuclear Information System (INIS)

Fewster, Christopher J; Galloway, Gregory J

2011-01-01

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.

Managing focal fields of vector beams with multiple polarization singularities.

Science.gov (United States)

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Evidence for a continuous spectrum of equatorial waves in the Indian Ocean

Science.gov (United States)

Eriksen, Charles C.

1980-06-01

Seven-month records of current and temperature measurements from a moored array centered at 53°E on the equator in the Indian Ocean are consistent with a continuous spectrum of equatorially trapped internal inertial-gravity, mixed Rossby-gravity, and Kelvin waves. A model spectrum of free linear waves analogous to those for mid-latitude internal gravity waves is used to compute spectra of observed quantities at depths greater than about 2000 m. Model parameters are adjusted to fit general patterns in the observed spectra over periods from roughly 2 days to 1 month. Measurements at shallower depths presumably include forced motions which we have not attempted to model. This `straw-person' spectrum is consistent with the limited data available. The model spectru Ē (n, m, ω) = K · B(m) · C(n, ω), where Ē is an average local energy density in the equatorial wave guide which has amplitude K, wave number shape B(m) ∝ (1 + m/m*)-3, where m is vertical mode number and the bandwidth parameter m* is between 4 and 8, and frequency shape C(n, ω) ∝ [(2n + 1 + s2)½ · σ3]-1 where n is meridional mode number, and s and σ are dimensionless zonal wave number and frequency related by the usual dispersion relation. The scales are (β/cm)½ and (β · cm)½ for horizontal wave number and frequency, where cm is the Kelvin wave speed of the vertical mode m. At each frequency and vertical wave number, energy is partitioned equally among the available inertial gravity modes so that the field tends toward horizontal isotropy at high frequency. The transition between Kelvin and mixed Rossby-gravity motion at low frequency and inertial-gravity motion at high frequency occurs at a period of roughly 1 week. At periods in the range 1-3 weeks, the model spectrum which fits the observations suggests that mixed Rossby-gravity motion dominates; at shorter periods gravity motion dominates. The model results are consistent with the low vertical coherence lengths observed (roughly 80 m

Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-strips

Energy Technology Data Exchange (ETDEWEB)

Sadel, Christian, E-mail: Christian.Sadel@ist.ac.at [University of British Columbia, Mathematics Department (Canada)

2014-12-15

We consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.

Singular perturbation theory for interacting fermions in two dimensions

International Nuclear Information System (INIS)

Chubukov, A.V.; Maslov, D.L.; Gangadharaiah, S.; Glazman, L.I.

2004-11-01

We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a nonperturbative effect: an interaction with the zero-sound mode. Resuming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, C(T) ∝T 2 . It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in C(T) due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of C(T). We also obtain a general form of the non-analytic term in C(T), valid for the case of a generic Fermi liquid, i.e., beyond the perturbation theory. (author)

The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

International Nuclear Information System (INIS)

Chen Yong; Chen Xi; Qian Minping

2006-01-01

A general form of the Green-Kubo formula, which describes the fluctuations pertaining to all the steady states whether equilibrium or non-equilibrium, for a system driven by a finite Markov chain with continuous time (briefly, MC) {ξ t }, is shown. The equivalence of different forms of the Green-Kubo formula is exploited. We also look at the differences in terms of the autocorrelation function and the fluctuation spectrum between the equilibrium state and the non-equilibrium steady state. Also, if the MC is in the non-equilibrium steady state, we can always find a complex function ψ, such that the fluctuation spectrum of {φ(ξ t )} is non-monotonous in [0, + ∞)

Nonlinear singular elliptic equations

International Nuclear Information System (INIS)

Dong Minh Duc.

1988-09-01

We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

Transmutations between singular and subsingular vectors of the N = 2 superconformal algebras

International Nuclear Information System (INIS)

Doerrzapf, Matthias; Gato-Rivera, Beatriz

1999-01-01

We present subsingular vectors of the N = 2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the topological algebra become subsingular vectors of the antiperiodic NS algebra under the topological untwistings. These classes consist of BRST-invariant singular vectors with relative charges q = -2, -1 and zero conformal weight, and nolabel singular vectors with q = 0, -1. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2

Infinite derivative gravity : non-singular cosmology & blackhole solutions

NARCIS (Netherlands)

Mazumdar, Anupam

2017-01-01

Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and

Consideration on Singularities in Learning Theory and the Learning Coefficient

Directory of Open Access Journals (Sweden)

Miki Aoyagi

2013-09-01

Full Text Available We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy in learning theory.

Singular trajectories: space-time domain topology of developing speckle fields

Science.gov (United States)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Singularities in Free Surface Flows

Science.gov (United States)

Thete, Sumeet Suresh

Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental

The continuous spectrum and the effect of parametric resonance. The case of bounded operators

International Nuclear Information System (INIS)

Skazka, V V

2014-01-01

The paper is concerned with the Mathieu-type differential equation u ″ =−A 2 u+εB(t)u in a Hilbert space H. It is assumed that A is a bounded self-adjoint operator which only has an absolutely continuous spectrum and B(t) is almost periodic operator-valued function. Sufficient conditions are obtained under which the Cauchy problem for this equation is stable for small ε and hence free of parametric resonance. Bibliography: 10 titles

Singular vectors of Malikov-Fagin-Fux in topological theories

International Nuclear Information System (INIS)

Semikhatov, A.M.

1993-01-01

Coincidence of singular vectors in relation to the sl(2) Katza-Mudi algebra and the algebra of the N=2 (twisted) supersymmetry is established. On the base of the Kazama-Suzuki simplest model is obtained a representation for the sl(2) currents in terms of an interacting with mater gravitation. From the Malikov-Fagin-Fux formulae for the sl(2) singular currents is obtained the general expression for singular vectors in topological theories

Transmutation of planar media singularities in a conformal cloak.

Science.gov (United States)

Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K

2013-11-01

Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.

Quantum no-singularity theorem from geometric flows

Science.gov (United States)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Global embeddings for branes at toric singularities

CERN Document Server

Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki

2012-01-01

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

Boundary singularities produced by the motion of soap films.

Science.gov (United States)

Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

2014-06-10

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

Fold points and singularity induced bifurcation in inviscid transonic flow

International Nuclear Information System (INIS)

Marszalek, Wieslaw

2012-01-01

Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.

On the singular perturbations for fractional differential equation.

Science.gov (United States)

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Singular perturbation of simple eigenvalues

International Nuclear Information System (INIS)

Greenlee, W.M.

1976-01-01

Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

The connection between cluster and collective quadrupole channels in 20 Ne and E 2-transition probabilities between the bound and continuous spectrum states

International Nuclear Information System (INIS)

Bystrenko, A.V.; Okhrimenko, I.P.

1993-01-01

The E 2-transition probabilities between the discrete and continuous spectrum states in 20 Ne are investigated using the two-channel version (making allowance for the connection between cluster and quadrupole channels) of the consistent microscopic approach,an algebraic version of the resonating-group method. The correctness of the approximation of the continuous spectrum by the discrete states, which is usual in collective models, the quadrupole sum rule and the giant quadrupole resonance phenomenon are considered. (author). 2 tab., 12 figs

Non-perturbative string theories and singular surfaces

International Nuclear Information System (INIS)

Bochicchio, M.

1990-01-01

Singular surfaces are shown to be dense in the Teichmueller space of all Riemann surfaces and in the grasmannian. This happens because a regular surface of genus h, obtained identifying 2h disks in pairs, can be approximated by a very large genus singular surface with punctures dense in the 2h disks. A scale ε is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius ε. The non-perturbative partition function is proposed to be a scaling limit of the partition function on such infinite genus singular surfaces with a weight which is the coupling constant g raised to the approximate genus. For a gaussian model in any space-time dimension the regularized partition function on singular surfaces of infinite genus is the partition function of a two-dimensional lattice gas of charges and monopoles. It is shown that modular invariance of the partition function implies a version of the Dirac quantization condition for the values of the e/m charges. Before the scaling limit the phases of the lattice gas may be classified according to the 't Hooft criteria for the condensation of e/m operators. (orig.)

On the variably-charged black holes in general relativity: Hawking's radiation and naked singularities

International Nuclear Information System (INIS)

Ibohal, Ng

2002-01-01

In this paper variably-charged non-rotating Reissner-Nordstrom and rotating Kerr-Newman black holes are discussed. Such a variable charge e with respect to the polar coordinate r in the field equations is referred to as an electrical radiation of the black hole. It is shown that every electrical radiation e(r) of the non-rotating black hole leads to a reduction in its mass M by some quantity. If one considers such electrical radiation taking place continuously for a long time, then a continuous reduction of the mass may take place in the black-hole body and the original mass of the black hole may be evaporated completely. At that stage, the gravity of the object may depend only on the electromagnetic field, not on the mass. Immediately after the complete evaporation of the mass, if the next radiation continues, there may be creation of a new mass leading to the formation of a negative mass naked singularity. It appears that this new mass of the naked singularity would never decrease, but might increase gradually as the radiation continues forever. A similar investigation is also discussed in the case of a variably-charged rotating Kerr-Newman black hole. Thus, it has been shown by incorporating Hawking's evaporation of radiating black holes in the form of spacetime metrics, every electrical radiation of variably-charged rotating and non-rotating black holes may produce a change in the mass of the body without affecting the Maxwell scalar

Dark energy and dark matter perturbations in singular universes

International Nuclear Information System (INIS)

Denkiewicz, Tomasz

2015-01-01

We discuss the evolution of density perturbations of dark matter and dark energy in cosmological models which admit future singularities in a finite time. Up to now geometrical tests of the evolution of the universe do not differentiate between singular universes and ΛCDM scenario. We solve perturbation equations using the gauge invariant formalism. The analysis shows that the detailed reconstruction of the evolution of perturbations within singular cosmologies, in the dark sector, can exhibit important differences between the singular universes models and the ΛCDM cosmology. This is encouraging for further examination and gives hope for discriminating between those models with future galaxy weak lensing experiments like the Dark Energy Survey (DES) and Euclid or CMB observations like PRISM and CoRE

CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

International Nuclear Information System (INIS)

Benzley, S.E.; Beisinger, Z.E.

1981-01-01

1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

Directory of Open Access Journals (Sweden)

Kelong Cheng

2014-01-01

Full Text Available Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.

Light-like big bang singularities in string and matrix theories

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg

2011-01-01

Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.

Deficiency indices and singular boundary conditions in quantum mechanics

International Nuclear Information System (INIS)

Bulla, W.

1984-01-01

We consider Schroedinger operators H in L 2 (Rsup(n)), n from IN, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions

The road to singularities, and the roses on the way

International Nuclear Information System (INIS)

Collins, C.B.

1978-01-01

A survey of current investigations of space-time singularities is given. The different approaches adopted by various research schools is discussed, and an analogy is drawn between this study and the mounting of an expedition that sets out on a long trail of discovery. A heuristic discussion is given of the latest classification of singularities and some brief comments are made on how physically relevant each type of singularity is. Roughly speaking, it seems that the milder types (at which quantities remain well behaved) are pathological cases, whereas the crude 'big-bang' type of singularity is more generic. (author)

The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

Energy Technology Data Exchange (ETDEWEB)

Chen Yong; Chen Xi; Qian Minping [School of Mathematical Sciences, Peking University, Beijing 100871 (China)

2006-03-17

A general form of the Green-Kubo formula, which describes the fluctuations pertaining to all the steady states whether equilibrium or non-equilibrium, for a system driven by a finite Markov chain with continuous time (briefly, MC) {l_brace}{xi}{sub t}{r_brace}, is shown. The equivalence of different forms of the Green-Kubo formula is exploited. We also look at the differences in terms of the autocorrelation function and the fluctuation spectrum between the equilibrium state and the non-equilibrium steady state. Also, if the MC is in the non-equilibrium steady state, we can always find a complex function {psi}, such that the fluctuation spectrum of {l_brace}{phi}({xi}{sub t}){r_brace} is non-monotonous in [0, + {infinity})

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Habib Mâagli

2014-01-01

fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+⁡x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.

On the Singular Perturbations for Fractional Differential Equation

Directory of Open Access Journals (Sweden)

Abdon Atangana

2014-01-01

Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Singularities and the geometry of spacetime

Science.gov (United States)

Hawking, Stephen

2014-11-01

The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

Periodic solutions to second-order indefinite singular equations

Czech Academy of Sciences Publication Activity Database

Hakl, Robert; Zamora, M.

2017-01-01

Roč. 263, č. 1 (2017), s. 451-469 ISSN 0022-0396 Institutional support: RVO:67985840 Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039617301134

Segmentation of singularity maps in the context of soil porosity

Science.gov (United States)

Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.

2016-04-01

Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in

Singular vectors, predictability and ensemble forecasting for weather and climate

International Nuclear Information System (INIS)

Palmer, T N; Zanna, Laure

2013-01-01

The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system’s predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean–atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (review)

Quantum propagation across cosmological singularities

Science.gov (United States)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium

International Nuclear Information System (INIS)

Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho

2004-01-01

Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)

Virtual Singular Scattering of Electromagnetic Waves in Transformation Media Concept

Directory of Open Access Journals (Sweden)

M. Y. Barabanenkov

2012-07-01

Full Text Available If a scatterer and an observation point (receive both approach the so-called near field zone of a source of electromagnetic waves, the scattering process becomes singular one which is mathematically attributed to the spatial singularity of the free space Green function at the origin. Starting from less well known property of left-handed material slab to transfer the singularity of the free space Green function by implementing coordinate transformation, we present a phenomenon of virtual singular scattering of electromagnetic wave on an inhomogeneity located in the volume of left – handed material slab. Virtual singular scattering means that a scatterer is situated only virtually in the near field zone of a source, being, in fact, positioned in the far field zone. Such a situation is realized if a scatterer is embedded into a flat Veselago’s lens and approaches the lens’s inner focus because a slab of Veselago medium produces virtual sources inside and behind the slab and virtual scatterer (as a source of secondary waves from both slab sides. Considering a line-like dielectric scatterer we demonstrate that the scattering efficiency is proportional to product of singular quasistatic parts of two empty space Green functions that means a multiplicative quasistatic singularity of the Green function for a slab of inhomogeneous Veselago medium. We calculate a resonance value of the scattering amplitude in the regime similar to the known Mie resonance scattering.

A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

On Borel singularities in quantum field theory

International Nuclear Information System (INIS)

Chadha, S.; Olesen, P.

1977-10-01

The authors consider the effective one-loop Lagrangian in a constant electric field. It is shown that perturbation theory behaves as n factorial giving rise to singularities in the Borel plane. Comparing with the known exact result it is shown how to integrate these singularities. It is suggested that renormalons in QED and QCD should be integrated in a similar way. A speculation is made on a possible interpretation of this integration. (Auth.)

Five-dimensional null-cone structure of big bang singularity

Energy Technology Data Exchange (ETDEWEB)

Lauro, S.; Schucking, E.L.

1985-04-01

The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space MV is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in MV there is a motion of MV such that F'= F. The big bang singularity is the vertex of a null half-cone in MV. Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group.

Five-dimensional null-cone structure of big bang singularity

International Nuclear Information System (INIS)

Lauro, S.; Schucking, E.L.

1985-01-01

The Friedmann model PHI of positive space curvature, vanishing pressure and cosmological constant when isometrically imbedded as a hypersurface in five-dimensional Minkowski space M 5 is globally rigid: if F(PHI) and F'(PHI) are isometric embeddings in M 5 there is a motion π of M 5 such that F'=π 0 F. The big bang singularity is the vertex of a null half-cone in M 5 . Global rigidity leads to an invariant characterization of the singularity. The structure of matter at the singularity is governed by the de Sitter group. (author)

Logarithmic of mass singularities theorem in non massive quantum electrodynamics

International Nuclear Information System (INIS)

Mares G, R.; Luna, H.

1997-01-01

We give an explicit example of the use of dimensional regularization to calculate in a unified approach, all the ultraviolet, infrared and mass singularities, by considering the LMS (logarithms of mass singularities) theorem in the frame of massless QED (Quantum electrodynamics). In the calculation of the divergent part of the cross section, all singularities are found to cancel provided soft and hard photon emission are both taken into account. (Author)

The analysis of optimal singular controls for SEIR model of tuberculosis

Science.gov (United States)

Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.

2014-12-01

The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.

Singularities of elastic scattering amplitude by long-range potentials

International Nuclear Information System (INIS)

Kvitsinsky, A.A.; Komarov, I.V.; Merkuriev, S.P.

1982-01-01

The angular peculiarities and the zero energy singularities of the elastic scattering amplitude by a long-range potential are described. The singularities of the elastic (2 → 2) scattering amplitude for a system of three Coulomb particles are considered [ru

Influence of the non-singular stress on the crack extension and fatigue life

International Nuclear Information System (INIS)

Cheng, C.Z.; Recho, N.; Niu, Z.R.

2012-01-01

Highlights: ► BEM is combined by characteristic analysis to calculate the singular stress field. ► A new method is proposed to evaluate the full stress field at crack tip region. ► Effect of non-singular stress on the propagation direction of the fatigue crack is analyzed. ► The influence of non-singular stress on the fatigue crack life is evaluated. - Abstract: The complete elasticity stress field at a crack tip region can be presented by the sum of the singular stress and several non-singular stress terms according to the Williams asymptotic expansion theory. The non-singular stress has a non-negligible influence on the prediction of the crack extension direction and crack growth rate under the fatigue loading. A novel method combining the boundary element method and the singularity characteristic analysis is proposed here to evaluate the complete stress field at a crack tip region. In this new method, any non-singular stress term in the Williams series expansion can be evaluated according to the computational accuracy requirement. Then, a modified Paris law is introduced to predict the crack propagation under the mixed-mode loading for exploring the influence of the non-singular stress on the fatigue life duration. By comparing with the existed experimental results, the predicted crack fatigue life when the non-singular stress is taken into consideration is more accurate than the predicted ones only considering the singular stress.

Pseudospherical surfaces with singularities

DEFF Research Database (Denmark)

Brander, David

2017-01-01

We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...

Branes at Singularities in Type 0 String Theory

OpenAIRE

Alishahiha, M; Brandhuber, A; Oz, Y

1999-01-01

We consider Type 0B D3-branes placed at conical singularities and analyze in detail the conifold singularity. We study the non supersymmetric gauge theories on their worldvolume and their conjectured dual gravity descriptions. In the ultraviolet the solutions exhibit a logarithmic running of the gauge coupling. In the infrared we find confining solutions and IR fixed points.

One Critical Case in Singularly Perturbed Control Problems

Science.gov (United States)

Sobolev, Vladimir

2017-02-01

The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.

Quantization rules for point singularities in superfluid 3He and liquid crystals

International Nuclear Information System (INIS)

Blaha, S.

1976-01-01

It is shown that pointlike singularities can exist in superfluid 3 He. Integer quantum numbers are associated with these singularities. The quantization rules follow from the single valuedness of the order parameter and quantities derived from it. The results are also easily extended to the quantization of point singularities in nematic liquid crystals. The pointlike singularities in 3 He-A are experimentally accessible analogs of the magnetic monopole

Endpoint singularities in unintegrated parton distributions

CERN Document Server

Hautmann, F

2007-01-01

We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare this with the cut-off regularization method. The counterterms for the distributions with subtractive regularization are given in coordinate space by compact all-order expressions in terms of eikonal-line operators. We carry out an explicit calculation at one loop for the unintegrated quark distribution. We discuss the relation of the unintegrated parton distributions in subtractive regularization with the ordinary parton distributions.

A Note on Inclusion Intervals of Matrix Singular Values

Directory of Open Access Journals (Sweden)

Shu-Yu Cui

2012-01-01

Full Text Available We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.

Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity

Directory of Open Access Journals (Sweden)

Alberto Lastra

2018-02-01

Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.

Singularities in x-ray spectra of metals

International Nuclear Information System (INIS)

Mahan, G.D.

1987-08-01

The x-ray spectroscopies discussed are absorption, emission, and photoemission. The singularities show up in each of them in a different manner. In absorption and emission they show up as power law singularities at the thresholds frequencies. This review will emphasize two themes. First a simple model is proposed to describe this phenomena, which is now called the MND model after MAHAN-NOZIERES-DeDOMINICIS. Exact analytical solutions are now available for this model for the three spectroscopies discussed above. These analytical models can be evaluated numerically in a simple way. The second theme of this review is that great care must be used when comparing the theory to experiment. A number of factors influence the edge shapes in x-ray spectroscopy. The edge singularities play an important role, and are observed in many matals. Quantitative fits of the theory to experiment require the consideration of other factors. 51 refs

Hidden singularities in non-abelian gauge fields

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

1978-01-01

It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt

Physics of singularities in pressure-impulse theory

Science.gov (United States)

Krechetnikov, R.

2018-05-01

The classical solution in the pressure-impulse theory for the inviscid, incompressible, and zero-surface-tension water impact of a flat plate at zero dead-rise angle exhibits both singular-in-time initial fluid acceleration, ∂v /∂ t |t =0˜δ (t ) , and a near-plate-edge spatial singularity in the velocity distribution, v ˜r-1 /2 , where r is the distance from the plate edge. The latter velocity divergence also leads to the interface being stretched infinitely right after the impact, which is another nonphysical artifact. From the point of view of matched asymptotic analysis, this classical solution is a singular limit when three physical quantities achieve limiting values: sound speed c0→∞ , fluid kinematic viscosity ν →0 , and surface tension σ →0 . This leaves open a question on how to resolve these singularities mathematically by including the neglected physical effects—compressibility, viscosity, and surface tension—first one by one and then culminating in the local compressible viscous solution valid for t →0 and r →0 , demonstrating a nontrivial flow structure that changes with the degree of the bulk compressibility. In the course of this study, by starting with the general physically relevant formulation of compressible viscous flow, we clarify the parameter range(s) of validity of the key analytical solutions including classical ones (inviscid incompressible and compressible, etc.) and understand the solution structure, its intermediate asymptotics nature, characteristics influencing physical processes, and the role of potential and rotational flow components. In particular, it is pointed out that sufficiently close to the plate edge surface tension must be taken into account. Overall, the idea is to highlight the interesting physics behind the singularities in the pressure-impulse theory.

Topological regularizations of the triple collision singularity in the 3-vortex problem

International Nuclear Information System (INIS)

Hiraoka, Yasuaki

2008-01-01

The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail

Start-up Strategy for Continuous Bioreactors

Directory of Open Access Journals (Sweden)

A.C. da Costa

1997-06-01

Full Text Available Abstract - The start-up of continuous bioreactors is solved as an optimal control problem. The choice of the dilution rate as the control variable reduces the dimension of the system by making the use of the global balance equation unnecessary for the solution of the optimization problem. Therefore, for systems described by four or less mass balance equations, it is always possible to obtain an analytical expression for the singular arc as a function of only the state variables. The steady state conditions are shown to satisfy the singular arc expression and, based on this knowledge, a feeding strategy is proposed which leads the reactor from an initial state to the steady state of maximum productivity

Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams

Science.gov (United States)

Haitao, Chen; Gao, Zenghui; Wang, Wanqing

2017-06-01

The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.

Deformations of surface singularities

CERN Document Server

Szilárd, ágnes

2013-01-01

The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry.  This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...

Recollection is a continuous process: Evidence from plurality memory receiver operating characteristics.

Science.gov (United States)

Slotnick, Scott D; Jeye, Brittany M; Dodson, Chad S

2016-01-01

Is recollection a continuous/graded process or a threshold/all-or-none process? Receiver operating characteristic (ROC) analysis can answer this question as the continuous model and the threshold model predict curved and linear recollection ROCs, respectively. As memory for plurality, an item's previous singular or plural form, is assumed to rely on recollection, the nature of recollection can be investigated by evaluating plurality memory ROCs. The present study consisted of four experiments. During encoding, words (singular or plural) or objects (single/singular or duplicate/plural) were presented. During retrieval, old items with the same plurality or different plurality were presented. For each item, participants made a confidence rating ranging from "very sure old", which was correct for same plurality items, to "very sure new", which was correct for different plurality items. Each plurality memory ROC was the proportion of same versus different plurality items classified as "old" (i.e., hits versus false alarms). Chi-squared analysis revealed that all of the plurality memory ROCs were adequately fit by the continuous unequal variance model, whereas none of the ROCs were adequately fit by the two-high threshold model. These plurality memory ROC results indicate recollection is a continuous process, which complements previous source memory and associative memory ROC findings.

Singularity, initial conditions and quantum tunneling in modern cosmology

International Nuclear Information System (INIS)

Khalatnikov, I M; Kamenshchik, A Yu

1998-01-01

The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties. (special issue)

Supersymmetry in singular spaces

NARCIS (Netherlands)

Bergshoeff, Eric

2002-01-01

We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a

Non-singular cosmologies in the conformally invariant gravitation theory

International Nuclear Information System (INIS)

Kembhavi, A.K.

1976-01-01

It is shown that in the framework of a conformally invariant gravitation theory, the singularity which is present in some anisotropic universes in general relativity is due to a wrong choice of conformal frame. Frames exist in which these models can be made singularity free. (author)

Singular instantons in Eddington-inspired-Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Arroja, Frederico; Chen, Che-Yu; Chen, Pisin; Yeom, Dong-han, E-mail: arroja@phys.ntu.edu.tw, E-mail: b97202056@gmail.com, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan (China)

2017-03-01

In this work, we investigate O (4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.

Well logging method and apparatus using a continuous energy spectrum photon source

International Nuclear Information System (INIS)

Turcotte, R.E.

1976-01-01

In accordance with an illustrative embodiment of the present invention, a method and apparatus for logging an earth formation of interest is disclosed in which repetitive bursts of a continuous energy spectrum of photons are emitted that penetrate the media surrounding a borehole traversing the earth formation. Thereafter, indications of photons resulting from the interaction of the emitted photons and the surrounding media are obtained, each indication being obtained at a different separation from the source along the axis of the borehole. Finally, the indications are compared to determine representations of a characteristic of the media surrounding the borehole. According to one aspect of the present invention, at least one of the indications is the result of annihilation photons produced by the interaction of the emitted photons and the surrounding media

Controllability of non-linear systems: generic singularities and their stability

International Nuclear Information System (INIS)

Davydov, Alexey A; Zakalyukin, Vladimir M

2012-01-01

This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.

Boundary element analysis of stress singularity in dissimilar metals by friction welding

International Nuclear Information System (INIS)

Chung, N. Y.; Park, C. H.

2012-01-01

Friction welded dissimilar metals are widely applied in automobiles, rolling stocks, machine tools, and various engineering fields. Dissimilar metals have several advantages over homogeneous metals, including high strength, material property, fatigue endurance, impact absorption, high reliability, and vibration reduction. Due to the increased use of these metals, understanding their behavior under stress conditions is necessary, especially the analysis of stress singularity on the interface of friction-welded dissimilar metals. To establish a strength evaluation method and a fracture criterion, it is necessary to analyze stress singularity on the interface of dissimilar metals with welded flashes by friction welding under various loads and temperature conditions. In this paper, a method analyzing stress singularity for the specimens with and without flashes set in friction welded dissimilar metals is introduced using the boundary element method. The stress singularity index (λ) and the stress singularity factor (Γ) at the interface edge are computed from the stress analysis results. The shape and flash thickness, interface length, residual stress, and load are considered in the computation. Based on these results, the variations of interface length (c) and the ratio of flash thickness (t2 t1) greatly influence the stress singularity factors at the interface edge of friction welded dissimilar metals. The stress singularity factors will be a useful fracture parameter that considers stress singularity on the interface of dissimilar metals

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

Science.gov (United States)

Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.

2015-09-01

We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.

Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities

Energy Technology Data Exchange (ETDEWEB)

Stuchlik, Z.; Pugliese, D.; Schee, J.; Kucakova, H. [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Opava (Czech Republic)

2015-09-15

We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Horava quantum gravity, characterized by a dimensionless parameter ωM{sup 2}, combining the gravitational mass parameter M of the spacetime with the Horava parameter ω, reflecting the role of the quantum corrections. In dependence on the value of ωM{sup 2}, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an @gantigravity@h sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l = const. In the K-S naked singularity spacetimes with ωM{sup 2} > 0.2811, doubled tori with the same l = const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ωM{sup 2} < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics. (orig.)

On the formation of continuous spectrum and emission line profiles of P Cygni

International Nuclear Information System (INIS)

Nugis, T.; Kolka, I.; Lund, L.

1979-01-01

The attempts to interpret the values of the observed radio and infrared fluxes of P Cygni via simple mass outflow models lead to a strong discrepancy between the observed and the calculated values. Barlow and Cohen (1977) found also that constant velocity or usual radiative acceleration outflow models cannot explain the observed continuous spectra. They concluded that a more 'extended' acceleration law is needed to fit the observed and the calculated ratio and IR fluxes - a law by which the acceleration of matter takes place also at a comparatively large distance from the star. The present authors analyze such types of expanding envelope models which can explain the shape of line profiles in the spectrum of P Cygni. (Auth.)

On the Ice Nucleation Spectrum

Science.gov (United States)

Barahona, D.

2012-01-01

This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be

On the collinear singularity problem of hot QCD

International Nuclear Information System (INIS)

Candelpergher, B.; Grandou, T.

2002-01-01

The collinear singularity problem of hot QCD is revisited within a perturbative resummation scheme (PR) of the leading thermal fluctuations. On the basis of actual calculations, new aspects are discovered concerning the origin of the singularity plaguing the soft real photon emission rate out of a quark-gluon plasma at thermal equilibrium, when the latter is calculated by means of the Resummation Program (RP)

Singularity: Raychaudhuri equation once again

Indian Academy of Sciences (India)

Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.

Singularities in FLRW Spacetimes

NARCIS (Netherlands)

Lam, Huibert het; Prokopec, Tom

2017-01-01

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept

Dyslexia singular brain

International Nuclear Information System (INIS)

Habis, M.; Robichon, F.; Demonet, J.F.

1996-01-01

Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.)

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

International Nuclear Information System (INIS)

Unver, O.; Gurtug, O.

2010-01-01

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.

Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

KAUST Repository

Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M.

2015-01-01

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

KAUST Repository

Paszyńska, Anna

2015-06-01

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

Characteristic classes, singular embeddings, and intersection homology.

Science.gov (United States)

Cappell, S E; Shaneson, J L

1987-06-01

This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.

Can noncommutativity resolve the Big-Bang singularity?

CERN Document Server

Maceda, M; Manousselis, P; Zoupanos, George

2004-01-01

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.

Geometric singular perturbation analysis of systems with friction

DEFF Research Database (Denmark)

Bossolini, Elena

This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter......, two mechanical problems with two different formulations of the friction force are introduced and analysed. The first mechanical problem is a one-dimensional spring-block model describing earthquake faulting. The dynamics of earthquakes is naturally a multiple timescale problem: the timescale...... scales. The action of friction is generally explained as the loss and restoration of linkages between the surface asperities at the molecular scale. However, the consequences of friction are noticeable at much larger scales, like hundreds of kilometers. By using geometric singular perturbation theory...

Solitary wave solution to a singularly perturbed generalized Gardner ...

Indian Academy of Sciences (India)

2017-03-24

Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...

Diagnostics of helium plasmas under special consideration of the continuous spectrum

International Nuclear Information System (INIS)

Einfeld, D.

1974-01-01

From measurements of the spectral beam density of the helium plasma in the region 290 nm to 650 nm, transition probabilities, Gaunt factors, line broadening parameters and deviations from the state of local thermodynamic equilibrium (L.T.E.) were determined and compared with theoretical data. Using the Gaunt factors experimentally secured in this work for the term n = 3, the electron density could be determined with an uncertainty of +-10% from the emission coefficients of the continuous spectrum. Assuming steady transition of the spectral emission coefficients over the series limit, a numerical method has been given according to which, amongst others, the Gaunt factors for the various series limits can be determined from the transition probabilities of these series. By determining the overpopulation factors of the ground states of the helium atom and the helium ion, a deviation from the L.T.E. state is experimentally detected and quantitatively described. (orig./LH) [de

Assessing the relationships between phylogenetic and functional singularities in sharks (Chondrichthyes).

Science.gov (United States)

Cachera, Marie; Le Loc'h, François

2017-08-01

The relationships between diversity and ecosystem functioning have become a major focus of science. A crucial issue is to estimate functional diversity, as it is intended to impact ecosystem dynamics and stability. However, depending on the ecosystem, it may be challenging or even impossible to directly measure ecological functions and thus functional diversity. Phylogenetic diversity was recently under consideration as a proxy for functional diversity. Phylogenetic diversity is indeed supposed to match functional diversity if functions are conservative traits along evolution. However, in case of adaptive radiation and/or evolutive convergence, a mismatch may appear between species phylogenetic and functional singularities. Using highly threatened taxa, sharks, this study aimed to explore the relationships between phylogenetic and functional diversities and singularities. Different statistical computations were used in order to test both methodological issue (phylogenetic reconstruction) and overall a theoretical questioning: the predictive power of phylogeny for function diversity. Despite these several methodological approaches, a mismatch between phylogeny and function was highlighted. This mismatch revealed that (i) functions are apparently nonconservative in shark species, and (ii) phylogenetic singularity is not a proxy for functional singularity. Functions appeared to be not conservative along the evolution of sharks, raising the conservational challenge to identify and protect both phylogenetic and functional singular species. Facing the current rate of species loss, it is indeed of major importance to target phylogenetically singular species to protect genetic diversity and also functionally singular species in order to maintain particular functions within ecosystem.

Charged singularities: repulsive effects

Energy Technology Data Exchange (ETDEWEB)

De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia

1980-07-01

The repulsive phenomena which a particle experiences in the vicinity of a naked singularity are investigated in the Kerr-Newman space-time. The aim is to extend the knowledge of this fact to charged solutions and to have a direct indication of how, in these situations, the gravitational and electrostatic interactions are competing.

Singular f-sum rule for superfluid 4He

International Nuclear Information System (INIS)

Wong, V.K.

1979-01-01

The validity and applicability to inelastic neutron scattering of a singular f-sum rule for superfluid helium, proposed by Griffin to explain the rhosub(s) dependence in S(k, ω) as observed by Woods and Svensson, are examined in the light of similar sum rules rigorously derived for anharmonic crystals and Bose liquids. It is concluded that the singular f-sum rules are only of microscopic interest. (Auth,)

Dimension counts for singular rational curves via semigroups

OpenAIRE

Cotterill, Ethan; Feital, Lia; Martins, Renato Vidal

2015-01-01

We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\\mb{P}^n$, holds whenever $g$ is small.

Some BMO estimates for vector-valued multilinear singular integral ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

the multilinear operator related to some singular integral operators is obtained. The main purpose of this paper is to establish the BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators. First, let us introduce some notations [10,16]. Throughout this paper, Q = Q(x,r).

Constructing Current Singularity in a 3D Line-tied Plasma

Science.gov (United States)

Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

2018-01-01

We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

Current singularities at finitely compressible three-dimensional magnetic null points

International Nuclear Information System (INIS)

Pontin, D.I.; Craig, I.J.D.

2005-01-01

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

Quantum fate of singularities in a dark-energy dominated universe

International Nuclear Information System (INIS)

Bouhmadi-Lopez, Mariam; Kiefer, Claus; Sandhoefer, Barbara; Moniz, Paulo Vargas

2009-01-01

Classical models for dark energy can exhibit a variety of singularities, many of which occur for scale factors much bigger than the Planck length. We address here the issue of whether some of these singularities, the big freeze and the big demarrage, can be avoided in quantum cosmology. We use the framework of quantum geometrodynamics. We restrict our attention to a class of models whose matter content can be described by a generalized Chaplygin gas and be represented by a scalar field with an appropriate potential. Employing the DeWitt criterion that the wave function be zero at the classical singularity, we show that a class of solutions to the Wheeler-DeWitt equation fulfilling this condition can be found. These solutions thus avoid the classical singularity. We discuss the reasons for the remaining ambiguity in fixing the solution.

Non-uniqueness of the source for singular gauge fields

International Nuclear Information System (INIS)

Lanyi, G.; Pappas, R.

1977-01-01

It is shown that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a 'smeared' potential or a 'smeared' field strength. (Auth.)

Invariant identification of naked singularities in spherically symmetric spacetimes

International Nuclear Information System (INIS)

Torres, R

2012-01-01

The study of generic naked singularities and their implications for the cosmic censorship conjecture is still an open issue in the framework of general relativity. One of the obstacles can be traced to the procedures for identifying naked singularities. Usually, the methods applied are not only model and coordinate dependent, but they very often rely in some strong assumptions on the degree of differentiability of the physical magnitudes of the model (such as the mass, density, etc) in the singularity. In this paper, we present a coordinate independent framework for identifying naked singularities based on invariants which is also devoid of strong differentiability requirements. The approach is intended to analyse whole families of models and to provide general results related to the cosmic censorship conjecture. Moreover, since the framework has a strict geometrical nature it can be used with alternative theories of gravitation as long as they assume the existence of a Lorentzian manifold. We exemplify its strength by applying it to the study of the collapse of radiation in radiative coordinates and the collapse of dust in comoving coordinates. (paper)

Fermi-edge singularity and the functional renormalization group

Science.gov (United States)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators

CERN Document Server

Eberle, Andreas

1999-01-01

This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.

Families of singular and subsingular vectors of the topological N=2 superconformal algebra

International Nuclear Information System (INIS)

Gato-Rivera, B.; Rosado, J.I.

1998-01-01

We analyze several issues concerning the singular vectors of the topological N=2 superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties, finding four different types in chiral Verma modules and twenty-nine different types in complete Verma modules. Then we study the family structure of the singular vectors, every member of a family being mapped to any other member by a chain of simple transformations involving the spectral flows. The families of singular vectors in chiral Verma modules follow a unique pattern (four vectors) and contain subsingular vectors. We write down these families until level 3, identifying the subsingular vectors. The families of singular vectors in complete Verma modules follow infinitely many different patterns, grouped roughly in five main kinds. We present a particularly interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the complete set of singular vectors at level 1 (twenty-eight different types). Finally we analyze the Doerrzapf conditions leading to two linearly independent singular vectors of the same type, at the same level in the same Verma module, and we write down four examples of those pairs of singular vectors, which belong to the same thirty-eight-member family. (orig.)

Body frames and frame singularities for three-atom systems

International Nuclear Information System (INIS)

Littlejohn, R.G.; Mitchell, K.A.; Aquilanti, V.; Cavalli, S.

1998-01-01

The subject of body frames and their singularities for three-particle systems is important not only for large-amplitude rovibrational coupling in molecular spectroscopy, but also for reactive scattering calculations. This paper presents a geometrical analysis of the meaning of body frame conventions and their singularities in three-particle systems. Special attention is devoted to the principal axis frame, a certain version of the Eckart frame, and the topological inevitability of frame singularities. The emphasis is on a geometrical picture, which is intended as a preliminary study for the more difficult case of four-particle systems, where one must work in higher-dimensional spaces. The analysis makes extensive use of kinematic rotations. copyright 1998 The American Physical Society

Polarization singularities of the object field of skin surface

International Nuclear Information System (INIS)

Angelsky, O V; Ushenko, A G; Ushenko, Yu A; Ushenko, Ye G

2006-01-01

The paper deals with the investigation of formation mechanisms of laser radiation polarization structure scattered by an optically thin surface layer of human skin in two registration zones: a boundary field and a far zone of Fraunhofer diffraction. The conditions of forming polarization singularities by such an object in the scattered radiation field have been defined. Statistical and fractal polarization structure of object fields of physiologically normal and pathologically changed skin has been studied. It has been shown that polarization singularities of radiation scattered by physiologically normal skin samples have a fractal coordinate structure. It is characteristic for fields of pathologically changed skin to have a statistical coordinate structure of polarization singularities in all diffraction zones

TRUST MODEL FOR SOCIAL NETWORK USING SINGULAR VALUE DECOMPOSITION

Directory of Open Access Journals (Sweden)

Davis Bundi Ntwiga

2016-06-01

Full Text Available For effective interactions to take place in a social network, trust is important. We model trust of agents using the peer to peer reputation ratings in the network that forms a real valued matrix. Singular value decomposition discounts the reputation ratings to estimate the trust levels as trust is the subjective probability of future expectations based on current reputation ratings. Reputation and trust are closely related and singular value decomposition can estimate trust using the real valued matrix of the reputation ratings of the agents in the network. Singular value decomposition is an ideal technique in error elimination when estimating trust from reputation ratings. Reputation estimation of trust is optimal at the discounting of 20 %.

Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

Directory of Open Access Journals (Sweden)

George N. Galanis

2005-10-01

Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0continuous function defined on the real line $mathbb{R}$ with $g(0=0$ and $ug(ugeq 0$. Our approach is a combination of Nonlinear Alternative of Leray-Schauder with the properties of the associated vector field at the $(u,u'$ plane. More precisely, we show that the solutions of the above boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

Directory of Open Access Journals (Sweden)

L.-P. Wang

2015-09-01

Full Text Available Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2 (Edinburgh, UK during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

Science.gov (United States)

Wang, L.-P.; Ochoa-Rodríguez, S.; Onof, C.; Willems, P.

2015-09-01

Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system

String theory and cosmological singularities

Indian Academy of Sciences (India)

recent times, string theory is providing new perspectives of such singularities which .... holes appear as stacks of a large number of D-branes wrapped in internal .... results into a well-known measure factor which makes the wave function into a.

Interval matrices: Regularity generates singularity

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří; Shary, S.P.

2018-01-01

Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

On reliability of singular-value decomposition in attractor reconstruction

International Nuclear Information System (INIS)

Palus, M.; Dvorak, I.

1990-12-01

Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs

Constraint theory, singular lagrangians and multitemporal dynamics

International Nuclear Information System (INIS)

Lusanna, L.

1988-01-01

Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Directory of Open Access Journals (Sweden)

Borbon Martin de

2017-02-01

Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

Asymptotic expansions close to the singularity in Gowdy spacetimes[04.20.Dw Singularities and cosmic censorship;

Energy Technology Data Exchange (ETDEWEB)

Ringstroem, Hans [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany)

2004-02-07

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In a paper by Grubisic and Moncrief, a formal expansion of solutions in the direction towards the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In a previous paper, we proved that one can put a condition on initial data that leads to asymptotic expansions. However, control of up to and including three derivatives in L{sup 2} was necessary, and the condition was rather technical. The main point of the present paper is to demonstrate the existence of certain monotone quantities and to illustrate how these can be used to weaken the assumptions to one derivative in the sup norm. Furthermore, we demonstrate that the false spikes do not appear in the disc model. Finally, we show that knowledge concerning the behaviour of the solution (as time tends to the singularity) for one fixed spatial point in some situations can be used to conclude that there are smooth expansions in the neighbourhood of that spatial point.

Double atom ionization by multicharged ions and strong electromagnetic field: correlation effects in a continuous spectrum

International Nuclear Information System (INIS)

Presnyakov, L.P.; Uskov, D.B.

1997-01-01

The nonstationary theory of double ionization of two-electron atoms in collisions with multicharged ions or under the impact of intensive electromagnetic field is developed. The approach, making it possible to study both problems by uniform method, is formulated. The two-electron wave function of continuous spectrum, accounting for interaction of electrons with atomic nucleus, external ionizer and between themselves is obtained. The calculation results on the helium atoms double ionization by multicharged ions is a good quantitative agreement with available experimental data

Singularity detection by wavelet approach: application to electrocardiogram signal

Science.gov (United States)

Jalil, Bushra; Beya, Ouadi; Fauvet, Eric; Laligant, Olivier

2010-01-01

In signal processing, the region of abrupt changes contains the most of the useful information about the nature of the signal. The region or the points where these changes occurred are often termed as singular point or singular region. The singularity is considered to be an important character of the signal, as it refers to the discontinuity and interruption present in the signal and the main purpose of the detection of such singular point is to identify the existence, location and size of those singularities. Electrocardiogram (ECG) signal is used to analyze the cardiovascular activity in the human body. However the presence of noise due to several reasons limits the doctor's decision and prevents accurate identification of different pathologies. In this work we attempt to analyze the ECG signal with energy based approach and some heuristic methods to segment and identify different signatures inside the signal. ECG signal has been initially denoised by empirical wavelet shrinkage approach based on Steins Unbiased Risk Estimate (SURE). At the second stage, the ECG signal has been analyzed by Mallat approach based on modulus maximas and Lipschitz exponent computation. The results from both approaches has been discussed and important aspects has been highlighted. In order to evaluate the algorithm, the analysis has been done on MIT-BIH Arrhythmia database; a set of ECG data records sampled at a rate of 360 Hz with 11 bit resolution over a 10mv range. The results have been examined and approved by medical doctors.

Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach

Directory of Open Access Journals (Sweden)

Ayman A. El-Badawy

2016-01-01

Full Text Available Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.

Mathematical models with singularities a zoo of singular creatures

CERN Document Server

Torres, Pedro J

2015-01-01

The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.

Experimental verification of free-space singular boundary conditions in an invisibility cloak

International Nuclear Information System (INIS)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Zhang, Baile; Chen, Huanyang

2016-01-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak. (paper)

Experimental verification of free-space singular boundary conditions in an invisibility cloak

Science.gov (United States)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

2016-04-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

Anomalous singularities in the complex Kohn variational principle of quantum scattering theory

International Nuclear Information System (INIS)

Lucchese, R.R.

1989-01-01

Variational principles for symmetric complex scattering matrices (e.g., the S matrix or the T matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied

Screw Theory Based Singularity Analysis of Lower-Mobility Parallel Robots considering the Motion/Force Transmissibility and Constrainability

Directory of Open Access Journals (Sweden)

Xiang Chen

2015-01-01

Full Text Available Singularity is an inherent characteristic of parallel robots and is also a typical mathematical problem in engineering application. In general, to identify singularity configuration, the singular solution in mathematics should be derived. This work introduces an alternative approach to the singularity identification of lower-mobility parallel robots considering the motion/force transmissibility and constrainability. The theory of screws is used as the mathematic tool to define the transmission and constraint indices of parallel robots. The singularity is hereby classified into four types concerning both input and output members of a parallel robot, that is, input transmission singularity, output transmission singularity, input constraint singularity, and output constraint singularity. Furthermore, we take several typical parallel robots as examples to illustrate the process of singularity analysis. Particularly, the input and output constraint singularities which are firstly proposed in this work are depicted in detail. The results demonstrate that the method can not only identify all possible singular configurations, but also explain their physical meanings. Therefore, the proposed approach is proved to be comprehensible and effective in solving singularity problems in parallel mechanisms.

Transmutation of singularities and zeros in graded index optical instruments: a methodology for designing practical devices.

Science.gov (United States)

Hooper, I R; Philbin, T G

2013-12-30

We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting in graded profiles that are all-dielectric, do not require materials with unrealistic values, and that are impedance matched to the bounding medium. This is achieved by transmuting the singularities (or zeros) using the formalism of transformation optics, but with an additional boundary condition requiring the gradient of the co-ordinate transformation be continuous. This additional boundary condition ensures that the device is impedance matched to the bounding medium when the spatially varying permittivity and permeability profiles are scaled to realizable values. We demonstrate the method in some detail for an Eaton lens, before describing the profiles for an "invisible disc" and "multipole" lenses.

Generic phase transitions and profit singularities in Arnol'd's model

International Nuclear Information System (INIS)

Davydov, Aleksei A; Matos, Helena Mena

2007-01-01

For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families. Bibliography: 16 titles.

Classical resolution of black hole singularities via wormholes

Energy Technology Data Exchange (ETDEWEB)

Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)

2016-03-15

In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)

Singularity confinement for maps with the Laurent property

International Nuclear Information System (INIS)

Hone, A.N.W.

2007-01-01

The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: The iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities

Energy conditions and spacetime singularities

International Nuclear Information System (INIS)

Tipler, F.J.

1978-01-01

In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete

Singular value correlation functions for products of Wishart random matrices

International Nuclear Information System (INIS)

Akemann, Gernot; Kieburg, Mario; Wei, Lu

2013-01-01

We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalizes the classical Wishart–Laguerre Gaussian unitary ensemble with M = 1. In this paper, we first compute the joint probability distribution for the singular values of the product matrix when the matrix size N and the number M are fixed but arbitrary. This leads to a determinantal point process which can be realized in two different ways. First, it can be written as a one-matrix singular value model with a non-standard Jacobian, or second, for M ⩾ 2, as a two-matrix singular value model with a set of auxiliary singular values and a weight proportional to the Meijer G-function. For both formulations, we determine all singular value correlation functions in terms of the kernels of biorthogonal polynomials which we explicitly construct. They are given in terms of the hypergeometric and Meijer G-functions, generalizing the Laguerre polynomials for M = 1. Our investigation was motivated from applications in telecommunication of multi-layered scattering multiple-input and multiple-output channels. We present the ergodic mutual information for finite-N for such a channel model with M − 1 layers of scatterers as an example. (paper)

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

Science.gov (United States)

Barker, L. K.; Houck, J. A.; Carzoo, S. W.

1984-01-01

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

Cosmic censorship and the strengths of singularities

International Nuclear Information System (INIS)

Newman, R.P.

1986-01-01

This paper considers the principal definitions concerning limiting curvature strength on geodesics, and on non-spacelike geodesics in particular. They are formulated in terms of focussing conditions. Two definitions suggest themselves, and these are given in terms of a concept of a generalized Jacobi field. An historical survey is presented on some important developments concerning examples of naked singularities. The historical context is recalled in which these models, and cosmic censorship in general, have arisen. It is the author's opinion that one can expect to obtain theoretical limitations on the strengths of any naked singularities which do occur

K3-fibered Calabi-Yau threefolds II, singular fibers

OpenAIRE

Hunt, Bruce

1999-01-01

In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur. This differs from previous work since the fibrations we discuss have constant modulus, and the singular fibers have torsion monodromy.

Cosmological singularities in electrovacuum spacetimes with two-parameter spacelike isometry groups

International Nuclear Information System (INIS)

Mansfield, P.A.

1989-01-01

The big bang singularities occurring in an infinite-dimensional class of solutions to the source-free Einstein-Maxwell equations are presented. These solutions are essentially Gowdy three-torus universes (not necessarily polarized) with electromagnetic radiation added. The problem is reformulated in terms of complex potentials analogous to those used by Ernst in the study of stationary axisymmetric metrics. It is shown that in these new variables the problem admits a harmonic map formulation. Its general solution is written as a perturbation series, where the background solutions being perturbed are a special class of real analytic functions obtained by evolving analytic data specified right at the singularity. The perturbation problem is solved to all orders, and terms which dominate as the singularity is approached are identified at each order. It is possible to sum the dominant terms, and thereby obtain explicit expressions representing the asymptotic structure of the singularities. This representation of asymptotic structure is developed into a simple geometric model. Specializing to the case of no electromagnetic fields, the model is then used to determine asymptotic metric and curvature properties in Gowdy spacetimes. The Gowdy metrics are Kasner-like near their singularity, which is generically a curvature singularity. Curvature-nonsingular solutions can be constructed, and extended into the past beyond a Cauchy horizon. However, such solutions are unstable, a fact which is consistent with Strong Cosmic Censorship

A computer program for estimating the power-density spectrum of advanced continuous simulation language generated time histories

Science.gov (United States)

Dunn, H. J.

1981-01-01

A computer program for performing frequency analysis of time history data is presented. The program uses circular convolution and the fast Fourier transform to calculate power density spectrum (PDS) of time history data. The program interfaces with the advanced continuous simulation language (ACSL) so that a frequency analysis may be performed on ACSL generated simulation variables. An example of the calculation of the PDS of a Van de Pol oscillator is presented.

Travelling wave solutions for a singularly perturbed Burgers–KdV ...

Indian Academy of Sciences (India)

This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

Friedmann-like cosmological models without singularity

International Nuclear Information System (INIS)

Kuchowicz, B.

1978-01-01

The Einstein-Cartan theory of gravitation ('general relativity with spin') provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in cosmological models. it is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a micro-physical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid. (author)

Non-Gaussian ground-state deformations near a black-hole singularity

Science.gov (United States)

Hofmann, Stefan; Schneider, Marc

2017-03-01

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows us to probe the spacelike singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The physical relevance of different completeness concepts for black holes is discussed.

Image Denoising Using Singular Value Difference in the Wavelet Domain

Directory of Open Access Journals (Sweden)

Min Wang

2018-01-01

Full Text Available Singular value (SV difference is the difference in the singular values between a noisy image and the original image; it varies regularly with noise intensity. This paper proposes an image denoising method using the singular value difference in the wavelet domain. First, the SV difference model is generated for different noise variances in the three directions of the wavelet transform and the noise variance of a new image is used to make the calculation by the diagonal part. Next, the single-level discrete 2-D wavelet transform is used to decompose each noisy image into its low-frequency and high-frequency parts. Then, singular value decomposition (SVD is used to obtain the SVs of the three high-frequency parts. Finally, the three denoised high-frequency parts are reconstructed by SVD from the SV difference, and the final denoised image is obtained using the inverse wavelet transform. Experiments show the effectiveness of this method compared with relevant existing methods.

Do sewn up singularities falsify the Palatini cosmology?

Energy Technology Data Exchange (ETDEWEB)

Szydlowski, Marek [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Krakow (Poland); Stachowski, Aleksander [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Borowiec, Andrzej [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Wojnar, Aneta [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Universita di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica, Naples (Italy)

2016-10-15

We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R + γR{sup 2} in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the Ω{sub γ} > 0 is favored by data only very small values of Ω{sub γ} parameter are allowed if we require agreement with the ΛCDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of Ω{sub γ} cannot be rejected. Therefore, observation data favor the universe without the ghost states (f{sup '}(R) > 0) and tachyons (f''(R) > 0). (orig.)

The method of rigged spaces in singular perturbation theory of self-adjoint operators

CERN Document Server

Koshmanenko, Volodymyr; Koshmanenko, Nataliia

2016-01-01

This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...

The exotic heat-trace asymptotics of a regular-singular operator revisited

OpenAIRE

Vertman, Boris

2013-01-01

We discuss the exotic properties of the heat-trace asymptotics for a regular-singular operator with general boundary conditions at the singular end, as observed by Falomir, Muschietti, Pisani and Seeley as well as by Kirsten, Loya and Park. We explain how their results alternatively follow from the general heat kernel construction by Mooers, a natural question that has not been addressed yet, as the latter work did not elaborate explicitly on the singular structure of the heat trace expansion...

Analytic continuation of dual Feynman amplitudes

International Nuclear Information System (INIS)

Bleher, P.M.

1981-01-01

A notion of dual Feynman amplitude is introduced and a theorem on the existence of analytic continuation of this amplitude from the convergence domain to the whole complex is proved. The case under consideration corresponds to massless power propagators and the analytic continuation is constructed on the propagators powers. Analytic continuation poles and singular set of external impulses are found explicitly. The proof of the theorem on the existence of analytic continuation is based on the introduction of α-representation for dual Feynman amplitudes. In proving, the so-called ''trees formula'' and ''trees-with-cycles formula'' are established that are dual by formulation to the trees and 2-trees formulae for usual Feynman amplitudes. (Auth.)

OVERGENERALIZATION IN SINGULAR/PLURAL NOUNS AND SUFFIXED NOUNS OF IELTS COURSE STUDENTS

Directory of Open Access Journals (Sweden)

Gharizi Matiini

2016-12-01

Full Text Available This study aims to investigate the morphological overgeneralization of IELTS students. It focuses on the singular/plural nouns and suffixed nouns that are overgeneralized by those students. Three students are chosen as the participants of the study by collecting their writing exercises. Three writing texts are gathered taken from several weeks and materials. The writings are analyzed by sorting the nouns they produced and categorizing them according to the singular/plural nouns and suffixed nouns. The results reveal that the students over extended the rules of singular/plural nouns and suffixed nouns. However, recovery occurs very varied in both singular/plural nouns and suffixed nouns. They tend to be better in mentioning singular/plural nouns, yet they are being selective and careful in writing suffixed nouns. In conclusion, even though the language learners can mark their overgeneralization, it is still difficult for them to recover their errors. It is recommended here that longitudinal study that has more time to examine students recovery from overgeneralization can be conducted for the further study to give more detail evidence in students’ overgeneralizations. Keywords: overgeneralization, singular/plural nouns, suffixed nouns

Quantum jump from singularity to outside of black hole

Energy Technology Data Exchange (ETDEWEB)

Dündar, Furkan Semih [Physics and Mathematics Departments, Sakarya University, 54050, Sakarya (Turkey); Hajian, Kamal [School of Physics, Institute for Research in Fundamental Sciences, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Department of Physics, Sharif University of Technology, P.O. Box 11365-8639, Tehran (Iran, Islamic Republic of)

2016-02-26

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

Quantum jump from singularity to outside of black hole

International Nuclear Information System (INIS)

Dündar, Furkan Semih; Hajian, Kamal

2016-01-01

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

Relating hard QCD processes through universality of mass singularities

International Nuclear Information System (INIS)

Amati, D.; Petronzio, R.; Veneziano, G.

1978-01-01

Hard QCD processes involving final jets are studied and compared by means of a simple approach to mass singularities. This is based on the Lee-Nauenberg-Kinoshita theorem and on a rather subtle use of gauge invariance in hard collinear gluon bremsstrahlung. One-loop results are easily derived for processes involving any number of initial quarks and/or currents. The method greatly simplifies the computation of higher-order loops at the leading log level and the preliminary results allow one to conclude that the crucial features encountered at the one-loop level will persist. The authors are thus able to relate different hard processes and to show that suitable ratios of cross sections, being free from mass singularities, can be computed perturbatively, as usually assumed in QCD-inspired parton models. It is also possible to relate the universal leading mass singularities to leading scaling violations and to extend therefor the results of the operator product expansion method to processes outside the range of the light-cone analysis. Some delicate points caused by confinement-related singularities (e.g. narrow resonance poles) are also discussed. (Auth.)

Classification of subsurface objects using singular values derived from signal frames

Science.gov (United States)

Chambers, David H; Paglieroni, David W

2014-05-06

The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.

On the discrete spectrum of non-self-adjoint Schroedinger differential equation with an operator coefficient

International Nuclear Information System (INIS)

Bayramoglu, Mehmet; Tasci, Fatih; Zeynalov, Djafar

2004-01-01

We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schroedinger boundary value problem -Δu+q(x)u=λ 2 u, u vertical bar ∂D =0, with a complex potential q(x) in an angular domain

Multiscale singularity trees

DEFF Research Database (Denmark)

Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter

2007-01-01

We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....

Dynamics of continuous medium in space with torsion

International Nuclear Information System (INIS)

Krechet, V.G.

1985-01-01

In frames of Einstein-Cartan gravitation theory general properties of continuous media dynamics using description formalism of continuous medium steam-line congruence geometry are investigated. Raichaudhuri type equations in space with torsion applied to study the problem of singularities in gravitation theory are derived. It is shown that space-time torsion tensor trace may immediately affect volumetric autoparallel divergence and torsion pseudo trace - rotation of continuous medium steam-line congruences. Using formalism considered metrics of homogeneous rotation nonstationary cosmological model is determined and investigated

Fractional charge and inter-Landau-level states at points of singular curvature.

Science.gov (United States)

Biswas, Rudro R; Son, Dam Thanh

2016-08-02

The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

Singularities and horizons in the collisions of gravitational waves

International Nuclear Information System (INIS)

Yurtsever, U.H.

1989-01-01

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and the generic initial data for the colliding plane waves always produce pure spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction. In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wave-fronts; i.e., it must leave behind tails in the spacetime region through which is passes

Perturbation theory for Alfven wave

International Nuclear Information System (INIS)

Yoshida, Z.; Mahajan, S.M.

1995-01-01

The Alfven wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfven wave propagation along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k parallel ) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfven wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfven resonance constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfven wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena

Singular ways to search for the Higgs boson

CERN Document Server

De Rújula, A

2012-01-01

The discovery or exclusion of the fundamental standard scalar is a hot topic, given the data of LEP, the Tevatron and the LHC, as well as the advanced status of the pertinent theoretical calculations. With the current statistics at the hadron colliders, the workhorse decay channel, at all relevant H masses, is H to WW, followed by W to light leptons. Using phase-space singularity techniques, we construct and study a plethora of "singularity variables" meant to facilitate the difficult tasks of separating signal and backgrounds and of measuring the mass of a putative signal. The simplest singularity variables are not invariant under boosts along the collider's axes and the simulation of their distributions requires a good understanding of parton distribution functions, perhaps not a serious shortcoming during the boson hunting season. The derivation of longitudinally boost-invariant variables, which are functions of the four charged-lepton observables that share this invariance, is quite elaborate. But their u...

Breakdown of predictability: an investigation on the nature of singularities

International Nuclear Information System (INIS)

Tahir Shah, K.

1980-12-01

When relations are extrapolated beyond their premises of discovery, the operation sometimes results in an undefined object, i.e., one which cannot be identified within the given structure. The thesis is put forth that the occurrence of singularities is due to ''incompleteness'' in knowledge. An intuitive answer on how to deal with singularities (in, for instance, the real number system, space-time, quantum field theory) is presented first. Then a quasi-formalistic approach, e.g. non-standard models in higher-order languages and Lawvere's axiomatic formulation of categories, is set out. The independence of singularity with respect to other primitive notions of the Universe of knowledge is noted

Singularities: the state of the art

International Nuclear Information System (INIS)

Clarke, C.J.S.; Schmidt, B.G.

1977-01-01

A brief, but precise and unified account is given of the results that have been rigorously established at the time of writing concerning the existence and nature of singularities in classical relativity. (author)

Shocks and finite-time singularities in Hele-Shaw flow

Energy Technology Data Exchange (ETDEWEB)

Teodorescu, Razvan [Los Alamos National Laboratory; Wiegmann, P [UNIV OF MONTREAL; Lee, S-y [UNIV OF CHICAGO

2008-01-01

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Conformally-flat, non-singular static metric in infinite derivative gravity

Science.gov (United States)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Is the shell-focusing singularity of Szekeres space-time visible?

International Nuclear Information System (INIS)

Nolan, Brien C; Debnath, Ujjal

2007-01-01

The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach

Surface singularities in Eddington-inspired Born-Infeld gravity.

Science.gov (United States)

Pani, Paolo; Sotiriou, Thomas P

2012-12-21

Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubt on its viability.

Algorithms for singularities and real structures of weak Del Pezzo surfaces

KAUST Repository

Lubbes, Niels

2014-08-01

In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc. 30 (1934) 453-491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides. © World Scientific Publishing Company.

Energy conditions of non-singular black hole spacetimes in conformal gravity

International Nuclear Information System (INIS)

Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Abdujabbarov, Ahmadjon; Stuchlik, Zdenek

2017-01-01

Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)

Energy conditions of non-singular black hole spacetimes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Toshmatov, Bobir [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic); Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany); Ahmedov, Bobomurat [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Abdujabbarov, Ahmadjon [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Tashkent University of Information Technologies, Tashkent (Uzbekistan); Stuchlik, Zdenek [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)

2017-08-15

Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)

Short time propagation of a singular wave function: Some surprising results

Science.gov (United States)

Marchewka, A.; Granot, E.; Schuss, Z.

2007-08-01

The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.

Singular tachyon kinks from regular profiles

International Nuclear Information System (INIS)

Copeland, E.J.; Saffin, P.M.; Steer, D.A.

2003-01-01

We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately

Conditions for the spectrum associated with an asymptotically straight leaky wire to comprise the interval (-∞, ∞)

International Nuclear Information System (INIS)

Brown, B M; Eastham, M S P; Wood, I G

2009-01-01

We consider a quantum (or leaky) wire in the plane, and the wire supports a singular attraction which becomes large at distant points on the wire. An analogous regular potential arises from the motion of a hydrogen atom in an electric field. We prove that, as in the regular case, the spectrum is the whole of (-∞, ∞)

Conditions for the spectrum associated with an asymptotically straight leaky wire to comprise the interval (-{infinity}, {infinity})

Energy Technology Data Exchange (ETDEWEB)

Brown, B M; Eastham, M S P [Department of Computer Science, Cardiff University, Cardiff, CF24 3XF (United Kingdom); Wood, I G [Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, SY23 3BZ (United Kingdom)], E-mail: malcolm@cs.cf.ac.uk, E-mail: mandh@chesilhay.fsnet.co.uk, E-mail: iww@aber.ac.uk

2009-02-06

We consider a quantum (or leaky) wire in the plane, and the wire supports a singular attraction which becomes large at distant points on the wire. An analogous regular potential arises from the motion of a hydrogen atom in an electric field. We prove that, as in the regular case, the spectrum is the whole of (-{infinity}, {infinity})

Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

Directory of Open Access Journals (Sweden)

J. Humberto Pérez-Cruz

2014-01-01

Full Text Available The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.

Absolutely continuous spectrum and spectral transition for some ...

Indian Academy of Sciences (India)

Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 243–255. c Indian ... we also know the existence of dense pure point spectrum for some disorder thus exhibit- ing spectral .... When β varies from 1 to 0, the growth behaviour of N(R) changes from ...... Student Texts 37 (Cambridge University Press) (1997).

Distribution of flux vacua around singular points in Calabi-Yau moduli space

International Nuclear Information System (INIS)

Eguchi, Tohru; Tachikawa, Yuji

2006-01-01

We study the distribution of type-IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P 1 , Argyres-Douglas point etc, using the Ashok-Douglas density det (R+ω). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in a compact Calabi-Yau manifold

Singularities of n-fold integrals of the Ising class and the theory of elliptic curves

International Nuclear Information System (INIS)

Boukraa, S; Hassani, S; Maillard, J-M; Zenine, N

2007-01-01

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the n-particle contributions χ (n) to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for n = 1, 2, 3, 4 and only modulo some primes for n = 5 and 6, thus providing a large set of (possible) new singularities of χ (n) . We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to n = 6) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a finite number of one-dimensional integrals. Among the singularities found, we underline the fact that the quadratic polynomial condition 1 + 3w + 4w 2 = 0, that occurs in the linear differential equation of χ (3) , actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves

Long Range Prospects of Education – from Now until Singularity

Directory of Open Access Journals (Sweden)

Vatroslav Zovko

2014-04-01

Full Text Available This work describes key characteristics and genesis of educational system today. As it is considered that we live in information society, presented are major goals of information society education and the school system in general in relation to the labour market. Briefly is described the concept of singularity and how it will make a quantum leap in the history of human development. Education is briefly put in the singularity framework and the concept of future society that is more technologically advanced. This paper also discusses the chronology of future technological development until the singularity age. It is argued that once we reach the singularity age the consequence will be the shift away from economic centered education and employment and toward humanities research. Ultimately, the goal of this paper is to open up a discussion about the different possible future scenarios of education, its long term perspective and the role in society rather than making a precise forecast about the education in mid-21st century.

Charged singularities: the causality violation

Energy Technology Data Exchange (ETDEWEB)

De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia

1980-12-01

A search is made for examples of particle trajectories which, approaching a naked singularity from infinity, make up for lost time before going back to infinity. In the Kerr-Newman metric a whole family of such trajectories is found showing that the causality violation is indeed a non-avoidable pathology.

Harnack's Inequality for Degenerate and Singular Parabolic Equations

CERN Document Server

DiBenedetto, Emmanuele; Vespri, Vincenzo

2012-01-01

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive

Three dimensional nilpotent singularity and Sil'nikov bifurcation

International Nuclear Information System (INIS)

Li Xindan; Liu Haifei

2007-01-01

In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions

Symposium on Singularities, Representation of Algebras, and Vector Bundles

CERN Document Server

Trautmann, Günther

1987-01-01

It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

International Nuclear Information System (INIS)

Levanony, Dana; Ori, Amos

2010-01-01

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

Science.gov (United States)

Levanony, Dana; Ori, Amos

2010-05-01

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

OpenAIRE

García Planas, María Isabel; Tarragona Romero, Sonia

2014-01-01

The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family

Hybrid direct and iterative solvers for h refined grids with singularities

KAUST Repository

Paszyński, Maciej R.

2015-04-27

This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to the standard algorithm performing static condensation over the entire mesh and executing the ILUPCG algorithm on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2], and the optimal refinements are selected using the projection based interpolation. The computational mesh is partitioned into sub-meshes with local point and edge singularities separated. This is done by using the following greedy algorithm.

Strong 'Quantum' Chaos in the Global Ballooning Mode Spectrum of Three-dimensional Plasmas

International Nuclear Information System (INIS)

Dewar, R. L.; Cuthbert, P.; Ball, R.

2000-01-01

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to ballooning-unstable plasma equilibria in the H-1NF helical axis stellarator and the Large Helical Device (LHD)

Singularity in the positive Hall coeffcient near pre-onset temperatures in high-Tc superconductors

Science.gov (United States)

Vezzoli, G. C.; Chen, M. F.; Craver, F.; Moon, B. M.; Safari, A.; Burke, T.; Stanley, W.

1990-10-01

Hall measurements using continuous extremely slow cooling and reheating rates as well as employing eqiulibrium point-by-point conventional techniques reveals a clear anomally in RH at pre-onset temperatures near Tc in polycrystalline samples Y1Ba2Cu3O7 and Bi2Sr2Ca2Cu3O10. The anomaly has the appearance of a singularity of Dirac-delta function which parallels earlier work on La1-xSrxCuO4. Recent single crystal work on the Bi-containing high-Tc superconductor is in accord with a clearcut anomaly. The singularity is tentatively interpreted to be associated (upon cooling) with initially the removal of positive holes from the hopping conduction system of the normal state such as from the increased concentration of bound virtual excitons due to increased exciton and hole lifetimes at low temperature. Subsequently the formation of Cooper pairs by mediation from these centers (bound-holes) and/or bound excitons) may cause an ionization of these bound virtual excitons thereby re-introducing holes and electrons into the conduction system at Tc.

Stochastic singular optics

CSIR Research Space (South Africa)

Roux, FS

2013-09-01

Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...

On the behaviour of Navier–Stokes equations near a possible singular point

International Nuclear Information System (INIS)

Kang, Kyungkeun; Lee, Jihoon

2010-01-01

We show that if a singularity of suitable weak solutions to Navier–Stokes equations occurs, then either p or at least two of ∂ i v i , i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂ r v r is not bounded both below and above near a singular point, if it exists

Quantum dynamics of classical stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Casati, G

1983-01-01

It is shown that one hand Quantum Mechanics introduces limitations to the manifestations of chaotic motion resulting, for the case of the periodically kicked rotator, in the limitation of energy growth; also, as it is confirmed by numerical experiments, phenomena like the exponential instability of orbits, inherent to strongly chaotic systems, are absent here and therefore Quantum Mechanics appear to be more stable and predictable than Classical Mechanics. On the other hand, we have seen that nonrecurrent behavior may arise in Quantum Systems and it is connected to the presence of singular continuous spectrum. We conjecture that the classical chaotic behavior is reflected, at least partially, in the nature of the spectrum and the singular-continuity of the latter may possess a self-similar structure typical of classical chaos.

Nature of protein family signatures: insights from singular value analysis of position-specific scoring matrices.

Directory of Open Access Journals (Sweden)

Akira R Kinjo

Full Text Available Position-specific scoring matrices (PSSMs are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.

Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

Directory of Open Access Journals (Sweden)

Rakowski Waldemar

2015-12-01

Full Text Available In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters associated with cubic box wavelets that are applied in implementing the discrete dyadic wavelet transform are defined. The filters and the algorithme à trous of the discrete dyadic wavelet transform are used in detecting signal singularities and in calculating the measures of signal singularities in the form of a Lipschitz exponent. The article presents examples illustrating the use of cubic box spline wavelets in the analysis of signal singularities.

A locally convergent Jacobi iteration for the tensor singular value problem

NARCIS (Netherlands)

Shekhawat, Hanumant Singh; Weiland, Siep

2018-01-01

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to

Removability of singularity for nonlinear elliptic equations with p(x-growth

Directory of Open Access Journals (Sweden)

Yongqiang Fu

2013-09-01

Full Text Available Using Moser's iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.

Further holographic investigations of big bang singularities

Energy Technology Data Exchange (ETDEWEB)

Engelhardt, Netta [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States); Hertog, Thomas [Institute for Theoretical Physics, KU Leuven,3001 Leuven (Belgium); Horowitz, Gary T. [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States)

2015-07-09

We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.

Further holographic investigations of big bang singularities

Science.gov (United States)

Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T.

2015-07-01

We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.

Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem

Directory of Open Access Journals (Sweden)

Lubomir Dechevski

2012-01-01

Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.

Non-singular bounce transitions in the multiverse

International Nuclear Information System (INIS)

Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun

2013-01-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ c . This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ c . We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua

Non-singular bounce transitions in the multiverse

Energy Technology Data Exchange (ETDEWEB)

Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, 08028, Barcelona (Spain); Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2013-11-01

According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.

The singular weapon. What remains from the atomic age?; Die Singulaere Waffe. Was bleibt vom Atomzeitalter?

Energy Technology Data Exchange (ETDEWEB)

Eisenbart, Constanze (ed.) [Forschungsstaette der Evangelischen Studiengemeinschaft (FEST), Heidelberg (Germany)

2012-07-01

The book contains the following contributions: Why do we talk about the atomic age? The language of the atomic myth - comments to a protestant debate. Nuclear singularity between fiction and reality. Only one can get through: military singularity of nuclear weapons. Physical singularity of nuclear weapons. Nuclear weapons test and fall-out. Quantitative disarmament and qualitative rearmament. Do mini nukes neutralize the singularity? The vulnerability of the industrial society by the nuclear electromagnetic momentum. Nuclear weapons as national status symbol - the example of India. The general regulations of international laws and the singularity of nuclear weapons. The construction of normative singularity - development and change of the nuclear taboo.

Simulation of generation and dynamics of polarization singularities with circular Airy beams.

Science.gov (United States)

Ye, Dong; Peng, Xinyu; Zhou, Muchun; Xin, Yu; Song, Minmin

2017-11-01

The generation and dynamics of polarization singularities have been underresearched for years, while the focusing property of the topological configuration has not been explored much. In this paper, we simulated the generation of low-order polarization singularities with a circular Airy beam and explored the focusing property of the synthetic light field during propagation due to the autofocusing of the component. Our work researched the focusing properties of the polarization singularity configuration, which may help to develop its application prospect.

Numerical static state feedback laws for closed-loop singular optimal control

NARCIS (Netherlands)

Graaf, de S.C.; Stigter, J.D.; Straten, van G.

2005-01-01

Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper,

On the C(R) stability of uncertain singularly perturbed systems

International Nuclear Information System (INIS)

Sun, Y.-J.

2009-01-01

In this paper, a simple criterion for the C(R) stability of uncertain singularly perturbed systems is proposed. Such a criterion can be easily checked by some algebraic inequality. The upper bound of the singular perturbation parameter ε is also given by estimating the unique positive zero of specific function. Finally, a numerical example is provided to illustrate the main result

Sparsity- and continuity-promoting seismic image recovery with curvelet frames

NARCIS (Netherlands)

Herrmann, Felix J.; Moghaddam, Peyman; Stolk, C.C.

2008-01-01

A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging

Propagation of singularities for linearised hybrid data impedance tomography

DEFF Research Database (Denmark)

Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim

2017-01-01

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con......For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...

Cosmic ray-modified stellar winds. I. Solution topologies and singularities

International Nuclear Information System (INIS)

Ko, C.M.; Webb, G.M.

1987-01-01

In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P/sub c/)-space, or a two-dimensional hypersurface of singularities in (r, u, P/sub c/, dP/sub c/dr)-space, where r, u, and P/sub c/ are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points. 64 references

Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems

CERN Document Server

Burban, Igor

2017-01-01

In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \\mathbb{k} x,y,z/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.

Logarithmic corrections in a quantization rule. The polaron spectrum

International Nuclear Information System (INIS)

Karasev, M.V.; Pereskokov, A.V.

1994-01-01

A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed. 18 refs., 1 tab

Tensor renormalization group with randomized singular value decomposition

Science.gov (United States)

Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai; Kawashima, Naoki

2018-03-01

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

Science.gov (United States)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

Directory of Open Access Journals (Sweden)

Ziheng Zhang

2014-01-01

Full Text Available We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS where -∞continuous bounded function, and the potential W:ℝN∖{ξ}→ℝ has a singularity at 0≠ξ∈ℝN, and Wuu is the gradient of W at u. The novelty of this paper is that, for the case that N≥3 and (HS is nonautonomous (neither periodic nor almost periodic, we show that (HS possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of W. Different from the cases that (HS is autonomous at≡1 or (HS is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS is nonautonomous and N≥3. Besides the usual conditions on W, we need the assumption that a′t<0 for all t∈ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

Singularity Analysis: a powerful image processing tool in remote sensing of the oceans

Science.gov (United States)

Turiel, A.; Umbert, M.; Hoareau, N.; Ballabrera-Poy, J.; Portabella, M.

2012-04-01

The study of fully developed turbulence has given rise to the development of new methods to describe real data of scalars submitted to the action of a turbulent flow. The application of this brand of methodologies (known as Microcanonical Multifractal Formalism, MMF) on remote sensing ocean maps open new ways to exploit those data for oceanographic purposes. The main technique in MMF is that of Singularity Analysis (SA). By means of SA a singularity exponents is assigned to each point of a given image. The singularity exponent of a given point is a dimensionless measure of the regularity or irregularity of the scalar at that point. Singularity exponents arrange in singularity lines, which accurately track the flow streamlines from any scalar, as we have verified with remote sensing and simulated data. Applications of SA include quality assessment of different products, the estimation of surface velocities, the development of fusion techniques for different types of scalars, comparison with measures of ocean mixing, and improvement in assimilation schemes.

Spacetime completeness of non-singular black holes in conformal gravity

Energy Technology Data Exchange (ETDEWEB)

Bambi, Cosimo; Rachwał, Lesław [Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai (China); Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com [Department of Physics, Southern University of Science and Technology, 1088 Xueyuan Road, Shenzhen 518055 (China)

2017-05-01

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.

Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space

DEFF Research Database (Denmark)

Brander, David

2011-01-01

We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space L-3. We show how to solve the singular Bjorling problem for such surfaces, which is stated as follows: given a real analytic null-curve f(0)(x), and a real analytic null vector...... field v(x) parallel to the tangent field of f(0), find a conformally parameterized (generalized) CMC H surface in L-3 which contains this curve as a singular set and such that the partial derivatives f(x) and f(y) are given by df(0)/dx and v along the curve. Within the class of generalized surfaces...

Singularities and n-dimensional black holes in torsion theories

Energy Technology Data Exchange (ETDEWEB)

Cembranos, J.A.R.; Valcarcel, J. Gigante; Torralba, F.J. Maldonado, E-mail: cembra@fis.ucm.es, E-mail: jorgegigante@ucm.es, E-mail: fmaldo01@ucm.es [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

2017-04-01

In this work we have studied the singular behaviour of gravitational theories with non symmetric connections. For this purpose we introduce a new criteria for the appearance of singularities based on the existence of black/white hole regions of arbitrary codimension defined inside a spacetime of arbitrary dimension. We discuss this prescription by increasing the complexity of the particular torsion theory under study. In this sense, we start with Teleparallel Gravity, then we analyse Einstein-Cartan theory, and finally dynamical torsion models.

Singularity theory and equivariant symplectic maps

CERN Document Server

Bridges, Thomas J

1993-01-01

The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate student...

Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

Directory of Open Access Journals (Sweden)

Ida de Bonis

2017-09-01

Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

Dirac operator on spaces with conical singularities

International Nuclear Information System (INIS)

Chou, A.W.

1982-01-01

The Dirac operator on compact spaces with conical singularities is studied via the separation of variables formula and the functional calculus of the Dirac Laplacian on the cone. A Bochner type vanishing theorem which gives topological obstructions to the existence of non-negative scalar curvature k greater than or equal to 0 in the singular case is proved. An index formula relating the index of the Dirac operator to the A-genus and Eta-invariant similar to that of Atiyah-Patodi-Singer is obtained. In an appendix, manifolds with boundary with non-negative scalar curvature k greater than or equal to 0 are studied, and several new results on constructing complete metrics with k greater than or equal to on them are obtained

Naked singularity formation in Brans-Dicke theory

Energy Technology Data Exchange (ETDEWEB)

Ziaie, Amir Hadi; Atazadeh, Khedmat [Department of Physics, Shahid Beheshti University, Evin, Tehran 19839 (Iran, Islamic Republic of); Tavakoli, Yaser, E-mail: am.ziaie@mail.sbu.ac.i, E-mail: k-atazadeh@sbu.ac.i, E-mail: tavakoli@ubi.p [Departamento de Fisica, Universidade da Beira Interior, Rua Marques d' Avila e Bolama, 6200 Covilha (Portugal)

2010-04-07

Gravitational collapse of the Brans-Dicke scalar field with non-zero potential in the presence of matter fluid obeying the barotropic equation of state, p = wrho, is studied. Utilizing the concept of the expansion parameter, it is seen that the cosmic censorship conjecture may be violated for w=-1/3 and w=-2/3 which correspond to the cosmic string and domain wall, respectively. We have shown that physically, it is the rate of collapse that governs the formation of a black hole or a naked singularity as the final fate of dynamical evolution and only for these two cases can the singularity be naked as the collapse end state. Also the weak energy condition is satisfied by the collapsing configuration.

Existence of localizing solutions in plasticity via the geometric singular perturbation theory

KAUST Repository

Lee, Min-Gi; Tzavaras, Athanasios

2017-01-01

system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré

Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I

Energy Technology Data Exchange (ETDEWEB)

Gaiotto, D. [Institute for Advanced Study (IAS), Princeton, NJ (United States); Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-03-15

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S{sup 4}. (orig.)

Correlation between topological structure and its properties in dynamic singular vector fields.

Science.gov (United States)

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 103  s order.

Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I

International Nuclear Information System (INIS)

Gaiotto, D.; Teschner, J.

2012-03-01

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S 4 . (orig.)

Identity and singularity: Metastability and morphogenesis in light of Deleuze

Directory of Open Access Journals (Sweden)

Barison Marcello

2015-01-01

Full Text Available The question of life is inextricably connected with the problem of identification and with the fact that each identification process includes the acquisition of a form. Nevertheless, it appears that at the biological level, that is, for what concerns a morphogenetic description of the status of the living being, the term singularity comes into play right there where you would expect to get into the notion of identity. According to Christian De Duve, the organic form has no identity, but it expresses - and is an expression of - a singularity. Given these observations, this is the object of the paper: to explain in a clear and consistent way how these terms - namely identity and singularity - differ and whether it is possible to ground their distinction in a coherent theoretical manner.

Method of mechanical quadratures for solving singular integral equations of various types

Science.gov (United States)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Analysis of jacobian and singularity of planar parallel robots using screw theory

Energy Technology Data Exchange (ETDEWEB)

Choi, Jung Hyun; Lee, Jeh Won; Lee, Hyuk Jin [Yeungnam Univ., Gyeongsan (Korea, Republic of)

2012-11-15

The Jacobian and singularity analysis of parallel robots is necessary to analyze robot motion. The derivations of the Jacobian matrix and singularity configuration are complicated and have no geometrical earning in the velocity form of the Jacobian matrix. In this study, the screw theory is used to derive the Jacobian of parallel robots. The statics form of the Jacobian has a geometrical meaning. In addition, singularity analysis can be performed by using the geometrical values. Furthermore, this study shows that the screw theory is applicable to redundantly actuated robots as well as non redundant robots.

The singular value filter: a general filter design strategy for PCA-based signal separation in medical ultrasound imaging.

Science.gov (United States)

Mauldin, F William; Lin, Dan; Hossack, John A

2011-11-01

A general filtering method, called the singular value filter (SVF), is presented as a framework for principal component analysis (PCA) based filter design in medical ultrasound imaging. The SVF approach operates by projecting the original data onto a new set of bases determined from PCA using singular value decomposition (SVD). The shape of the SVF weighting function, which relates the singular value spectrum of the input data to the filtering coefficients assigned to each basis function, is designed in accordance with a signal model and statistical assumptions regarding the underlying source signals. In this paper, we applied SVF for the specific application of clutter artifact rejection in diagnostic ultrasound imaging. SVF was compared to a conventional PCA-based filtering technique, which we refer to as the blind source separation (BSS) method, as well as a simple frequency-based finite impulse response (FIR) filter used as a baseline for comparison. The performance of each filter was quantified in simulated lesion images as well as experimental cardiac ultrasound data. SVF was demonstrated in both simulation and experimental results, over a wide range of imaging conditions, to outperform the BSS and FIR filtering methods in terms of contrast-to-noise ratio (CNR) and motion tracking performance. In experimental mouse heart data, SVF provided excellent artifact suppression with an average CNR improvement of 1.8 dB with over 40% reduction in displacement tracking error. It was further demonstrated from simulation and experimental results that SVF provided superior clutter rejection, as reflected in larger CNR values, when filtering was achieved using complex pulse-echo received data and non-binary filter coefficients.

Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure

Science.gov (United States)

Pestrenin, V. M.; Pestrenina, I. V.

2017-03-01

The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors' opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.

Resolving curvature singularities in holomorphic gravity

NARCIS (Netherlands)

Mantz, C.L.M.; Prokopec, T.

2011-01-01

We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature

The Notion of 'Singularity' in the Work of Gilles Deleuze

DEFF Research Database (Denmark)

Borum, Peter

2017-01-01

In Deleuze, singularity replaces generality in the economy of thought. A Deleuzian singularity is an event, but the notion comprises the effectuation of the event into form. The triptych émission–distribution–répartition itself distributes the dimensions of the passage from form-giving event to t......-drama-different/ciation’. The essay concludes that it is art that may let us consciously contemplate our pre-individual differences....

Constraints on the structure of naked singularities in classical general relativity

International Nuclear Information System (INIS)

Newman, R.P.A.; Joshi, P.S.

1988-01-01

The known examples of naked singularities in general relativity are, in a certain sense, either gravitationally or causally innocuous. A cosmic censorship theorem is formulated and proved to the effect that this behaviour is characteristic of naked singularities in general spacetimes which do not deviate too far from spherical symmetry. copyright 1988 Academic Press, Inc

A miniaturized near infrared spectrometer for non-invasive sensing of bio-markers as a wearable healthcare solution

Science.gov (United States)

Bae, Jungmok; Druzhin, Vladislav V.; Anikanov, Alexey G.; Afanasyev, Sergey V.; Shchekin, Alexey; Medvedev, Anton S.; Morozov, Alexander V.; Kim, Dongho; Kim, Sang Kyu; Moon, Hyunseok; Jang, Hyeongseok; Shim, Jaewook; Park, Jongae

2017-02-01

A novel miniaturized near-infrared spectrometer readily mountable to wearable devices for continuous monitoring of individual's key bio-markers was proposed. Spectrum is measured by sequential illuminations with LED's, having independent spectrum profiles and a continuous detection of light radiations from the skin tissue with a single cell PD. Based on Tikhonov regularization with singular value decomposition, a spectrum resolution less than 10nm was reconstructed based on experimentally measured LED profiles. A prototype covering first overtone band (1500-1800nm) where bio-markers have pronounced absorption peaks was fabricated and verified of its performance. Reconstructed spectrum shows that the novel concept of miniaturized spectrometer is valid.