Singular continuous spectrum for palindromic Schroedinger operators
International Nuclear Information System (INIS)
Hof, A.; Knill, O.; Simon, B.
1995-01-01
We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)
Absence of singular continuous spectrum for certain self-adjoint operators
International Nuclear Information System (INIS)
Mourre, E.
1979-01-01
An adequate condition is given for a self-adjoint operator to show in the vinicity of a point E of its spectrum the following properties: its point spectrum is of finite size; its singular continuous spectrum is empty. In the way of new applications the absence of singular continuous spectrum is demonstrated in the following two cases: perturbations of pseudo-differential operators; Schroedinger operators of a three-body system [fr
Generic singular continuous spectrum for ergodic Schr\\"odinger operators
Avila, Artur; Damanik, David
2004-01-01
We consider Schr\\"odinger operators with ergodic potential $V_\\omega(n)=f(T^n(\\omega))$, $n \\in \\Z$, $\\omega \\in \\Omega$, where $T:\\Omega \\to \\Omega$ is a non-periodic homeomorphism. We show that for generic $f \\in C(\\Omega)$, the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani Theory.
Singularity spectrum of self-organized criticality
International Nuclear Information System (INIS)
Canessa, E.
1992-10-01
I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the theory the origin of self-organized critical phenomena is analysed in terms of a nonlinear singularity spectrum different form the typical convex shape due to multifractal measures. (author). 29 refs, 5 figs
Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type
International Nuclear Information System (INIS)
Iakovlev, Serguei I.
2006-01-01
In L 2 (R) we consider a family of self adjoint operators of the Friedrichs model: A m =|t| m +V. Here |t| m is the operator of multiplication by the corresponding function of the independent variable t element of R, and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel ν(t,x) satisfying some smoothness condition. These absolute type operators have one singular point of order m>0. Conditions on the kernel ν(t,x) are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity. The sharpness of these conditions is confirmed by counterexamples
Multifractal signal reconstruction based on singularity power spectrum
International Nuclear Information System (INIS)
Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
2016-01-01
Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.
Singular spectrum analysis of sleep EEG in insomnia.
Aydın, Serap; Saraoǧlu, Hamdi Melih; Kara, Sadık
2011-08-01
In the present study, the Singular Spectrum Analysis (SSA) is applied to sleep EEG segments collected from healthy volunteers and patients diagnosed by either psycho physiological insomnia or paradoxical insomnia. Then, the resulting singular spectra computed for both C3 and C4 recordings are assigned as the features to the Artificial Neural Network (ANN) architectures for EEG classification in diagnose. In tests, singular spectrum of particular sleep stages such as awake, REM, stage1 and stage2, are considered. Three clinical groups are successfully classified by using one hidden layer ANN architecture with respect to their singular spectra. The results show that the SSA can be applied to sleep EEG series to support the clinical findings in insomnia if ten trials are available for the specific sleep stages. In conclusion, the SSA can detect the oscillatory variations on sleep EEG. Therefore, different sleep stages meet different singular spectra. In addition, different healthy conditions generate different singular spectra for each sleep stage. In summary, the SSA can be proposed for EEG discrimination to support the clinical findings for psycho-psychological disorders.
SINGULAR SPECTRUM ANALYSIS: METHODOLOGY AND APPLICATION TO ECONOMICS DATA
Institute of Scientific and Technical Information of China (English)
Hossein HASSANI; Anatoly ZHIGLJAVSKY
2009-01-01
This paper describes the methodology of singular spectrum analysis (SSA) and demonstrate that it is a powerful method of time series analysis and forecasting, particulary for economic time series. The authors consider the application of SSA to the analysis and forecasting of the Iranian national accounts data as provided by the Central Bank of the Islamic Republic of lran.
Analysis of the essential spectrum of singular matrix differential operators
Czech Academy of Sciences Publication Activity Database
Ibrogimov, O. O.; Siegl, Petr; Tretter, C.
2016-01-01
Roč. 260, č. 4 (2016), s. 3881-3926 ISSN 0022-0396 Institutional support: RVO:61389005 Key words : essential spectrum * system of singular differential equations * operator matrix * Schur complement * magnetohydrodynamics * Stellar equilibrium model Subject RIV: BE - Theoretical Physics Impact factor: 1.988, year: 2016
Identifying secondary series for stepwise common singular spectrum ...
African Journals Online (AJOL)
Abstract. Common singular spectrum analysis is a technique which can be used to forecast a pri- mary time series by using the information from a secondary series. Not all secondary series, however, provide useful information. A first contribution in this paper is to point out the properties which a secondary series should ...
Singular spectrum analysis, Harmonic regression and El-Nino effect ...
Indian Academy of Sciences (India)
42
Keywords: Total ozone; Singular Spectrum Analysis; Spatial interpolation; Multivariate ENSO .... needed for a whole gamut of activities that contribute to the ultimate synthesis ..... −0.0009 3 + 0.0581 2 − 1.0123 + 7.3246, 2 = 0.53…
Special relativity with a discrete spectrum of singular velocities
International Nuclear Information System (INIS)
Gonzales Gascon, F.
1977-01-01
The introduction of real transformation formulae containing a whole discrete spectrum of singularities is suggested. Some phenomenological hypotheses are introduced and the group property is substituted by weaker conditions. The first singular speed (c 1 =c) is invariant with respect to the measures of it from subluminal frames, but the remaining speeds are not invariant. The proposed transformations do not form a closed set (for the superluminal speeds) and, therefore, the problem of having (within this framework) a principle of relativity valid for any velocity remains open
Geomechanical time series and its singularity spectrum analysis
Czech Academy of Sciences Publication Activity Database
Lyubushin, Alexei A.; Kaláb, Zdeněk; Lednická, Markéta
2012-01-01
Roč. 47, č. 1 (2012), s. 69-77 ISSN 1217-8977 R&D Projects: GA ČR GA105/09/0089 Institutional research plan: CEZ:AV0Z30860518 Keywords : geomechanical time series * singularity spectrum * time series segmentation * laser distance meter Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 0.347, year: 2012 http://www.akademiai.com/content/88v4027758382225/fulltext.pdf
On Absence of Pure Singular Spectrum of Random Perturbations and in Anderson Model at Low Disorde
Grinshpun, V
2006-01-01
Absence of singular component, with probability one, in the conductivity spectra of bounded random perturbations of multidimensional finite-difference Hamiltonians, is for the first time rigorously established under certain conditions ensuring either absence of pure point, or absence of pure absolutely continuous component in the corresponding regions of spectra. The main technical tool applied is the theory of rank-one perturbations of singular spectra. The respective new result (the non-mixing property) is applied to establish existence and bounds of the (non-empty) pure absolutely continuous component in the spectrum of the Anderson model with bounded random potential in dimension 2 at low disorder. The new (1999) result implies, via the trace-class perturbation analysis, the Anderson model with the unbounded potential to have only pure point spectrum (complete system of localized wave-functions) with probability one in arbitrary dimension. The new technics, based on the resolvent reduction formula, and ex...
Multichannel singular spectrum analysis of the axial atmospheric angular momentum
Directory of Open Access Journals (Sweden)
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.
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.
Discrimination of Earthquakes and Explosions using Multi-fractal Singularity Spectrums Properties
Czech Academy of Sciences Publication Activity Database
Lyubushin, A. A.; Kaláb, Zdeněk; Lednická, Markéta; Haggag, H. M.
2013-01-01
Roč. 17, č. 3 (2013), s. 975-983 ISSN 1383-4649 Institutional support: RVO:68145535 Keywords : multi- fractal parameters * singularity spectrum * seismic event discrimination Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.386, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs10950-013-9366-3.pdf
Directory of Open Access Journals (Sweden)
Leila Mebarki
2015-11-01
Full Text Available This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-A-K^{-1}K or K(lambda-A-K^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.
Singular values of the Rogers-Ramanujan continued fraction
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
Directory of Open Access Journals (Sweden)
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}.
Randomised multichannel singular spectrum analysis of the 20th century climate data
Directory of Open Access Journals (Sweden)
Teija Seitola
2015-12-01
Full Text Available In this article, we introduce a new algorithm called randomised multichannel singular spectrum analysis (RMSSA, which is a generalisation of the traditional multichannel singular spectrum analysis (MSSA into problems of arbitrarily large dimension. RMSSA consists of (1 a dimension reduction of the original data via random projections, (2 the standard MSSA step and (3 a recovery of the MSSA eigenmodes from the reduced space back to the original space. The RMSSA algorithm is presented in detail and additionally we show how to integrate it with a significance test based on a red noise null-hypothesis by Monte-Carlo simulation. Finally, RMSSA is applied to decompose the 20th century global monthly mean near-surface temperature variability into its low-frequency components. The decomposition of a reanalysis data set and two climate model simulations reveals, for instance, that the 2–6 yr variability centred in the Pacific Ocean is captured by all the data sets with some differences in statistical significance and spatial patterns.
Pure Absolutely Continuous Spectrum for Random Operators on $l^2(Z^d)$ at Low Disorder
Grinshpun, V
2006-01-01
Absence of singular continuous component, with probability one, in the spectra of random perturbations of multidimensional finite-difference Hamiltonians, is for the first time rigorously established under certain conditions ensuring either absence of point component, or absence of absolutely continuous component in the corresponding regions of spectra. The main technical tool involved is the rank-one perturbation theory of singular spectra. The respective new result (the non-mixing property) is applied to establish existence and bounds of the (non-empty) pure absolutely continuous component in the spectrum of the Anderson model with bounded random potential in dimension d=2 at low disorder (similar proof holds for d>4). The new result implies, via the trace-class perturbation analysis, Anderson model with the unbounded random potential having only pure point spectrum (complete system of localized wave-functions) with probability one in arbitrary dimension. The basic idea is to establish absence of the mixed,...
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.
Embedding Dimension Selection for Adaptive Singular Spectrum Analysis of EEG Signal.
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.
Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm
Directory of Open Access Journals (Sweden)
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.
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.
Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series
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.
Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis
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.
Singular Spectrum Analysis for Astronomical Time Series: Constructing a Parsimonious Hypothesis Test
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.
A New Continuous-Time Equality-Constrained Optimization to Avoid Singularity.
Quan, Quan; Cai, Kai-Yuan
2016-02-01
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely, that the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. In order to avoid such a singularity, a new projection matrix is proposed based on which a feasible point method to continuous-time, equality-constrained optimization is developed. First, the equality constraint is transformed into a continuous-time dynamical system with solutions that always satisfy the equality constraint. Second, a new projection matrix without singularity is proposed to realize the transformation. An update (or say a controller) is subsequently designed to decrease the objective function along the solutions of the transformed continuous-time dynamical system. The invariance principle is then applied to analyze the behavior of the solution. Furthermore, the proposed method is modified to address cases in which solutions do not satisfy the equality constraint. Finally, the proposed optimization approach is applied to three examples to demonstrate its effectiveness.
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
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.
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 $1
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.
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).
The performance of one belt and one road exchange rate: Based on improved singular spectrum analysis
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.
Daily rainfall forecasting for one year in a single run using Singular Spectrum Analysis
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.
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.
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
Through the big bang: Continuing Einstein's equations beyond a cosmological singularity
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.
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.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.
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.
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) ...
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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
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
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
International Nuclear Information System (INIS)
Berry, M.V.
2002-01-01
For illumination with white light, the spectra near a typical isolated phase singularity (nodal point of the component wavelengths) can be described by a universal function of position, up to linear distortion and a weak dependence on the spectrum of the source. The appearance of the singularity when viewed by a human observer is predicted by transforming the spectrum to trichromatic variables and chromaticity coordinates, and then rendering the colours, scaled to constant luminosity, on a computer monitor. The pattern far from the singularity is a white that depends on the source temperature, and the centre of the pattern is flanked by intensely coloured 'eyes', one orange and one blue, separated by red, and one of the eyes is surrounded by a bright white circle. Only a small range of possible colours appears near the singularity; in particular, there is no green. (author)
Signaling on the continuous spectrum of nonlinear optical fiber.
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.
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.
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).
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
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)
[Absorption spectrum of Quasi-continuous laser modulation demodulation method].
Shao, Xin; Liu, Fu-Gui; Du, Zhen-Hui; Wang, Wei
2014-05-01
A software phase-locked amplifier demodulation method is proposed in order to demodulate the second harmonic (2f) signal of quasi-continuous laser wavelength modulation spectroscopy (WMS) properly, based on the analysis of its signal characteristics. By judging the effectiveness of the measurement data, filter, phase-sensitive detection, digital filtering and other processing, the method can achieve the sensitive detection of quasi-continuous signal The method was verified by using carbon dioxide detection experiments. The WMS-2f signal obtained by the software phase-locked amplifier and the high-performance phase-locked amplifier (SR844) were compared simultaneously. The results show that the Allan variance of WMS-2f signal demodulated by the software phase-locked amplifier is one order of magnitude smaller than that demodulated by SR844, corresponding two order of magnitude lower of detection limit. And it is able to solve the unlocked problem caused by the small duty cycle of quasi-continuous modulation signal, with a small signal waveform distortion.
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....
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.
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
Gruszczynska, M.; Rosat, S.; Klos, A.; Bogusz, J.
2017-12-01
In this study, Singular Spectrum Analysis (SSA) along with its multivariate extension MSSA (Multichannel SSA) were used to estimate long-term trend and gravimetric factor at the Chandler wobble frequency from superconducting gravimeter (SG) records. We have used data from seven stations located worldwide and contributing to the International Geodynamics and Earth Tides Service (IGETS). The timespan ranged from 15 to 19 years. Before applying SSA and MSSA, we had removed local tides, atmospheric (ECMWF data), hydrological (MERRA2 products) loadings and non-tidal ocean loading (ECCO2 products) effects. In the first part of analysis, we used the SSA approach in order to estimate the long-term trends from SG observations. We use the technique based on the classical Karhunen-Loève spectral decomposition of time series into long-term trend, oscillations and noise. In the second part, we present the determination of common time-varying pole tide (annual and Chandler wobble) to estimate gravimetric factor from SG time series using the MSSA approach. The presented method takes advantage over traditional methods like Least Squares Estimation by determining common modes of variability which reflect common geophysical field. We adopted a 6-year lag-window as the optimal length to extract common seasonal signals and the Chandler components of the Earth polar motion. The signals characterized by annual and Chandler wobble account for approximately 62% of the total variance of residual SG data. Then, we estimated the amplitude factors and phase lags of Chandler wobble with respect to the IERS (International Earth Rotation and Reference Systems Service) polar motion observations. The resulting gravimetric factors at the Chandler Wobble period are finally compared with previously estimates. A robust estimate of the gravimetric Earth response to the Chandlerian component of the polar motion is required to better constrain the mantle anelasticity at this frequency and hence the
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
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)
Calculating the electron temperature in the lightning channel by continuous spectrum
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.
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...
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.
[An automatic peak detection method for LIBS spectrum based on continuous wavelet transform].
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.
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
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
Evidence for a continuous spectrum of equatorial waves in the Indian Ocean
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
DEFF Research Database (Denmark)
Høgfeldt Hansen, Leif
2016-01-01
The publication functions as a proces description of the development and construction of an urban furniture SPECTRUM in the city of Gwangju, Republic of Korea. It is used as the cataloque for the exhibition of Spectrum.......The publication functions as a proces description of the development and construction of an urban furniture SPECTRUM in the city of Gwangju, Republic of Korea. It is used as the cataloque for the exhibition of Spectrum....
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.
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.)
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
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
7 CFR 1200.50 - Words in the singular form.
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.
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 900.20 - Words in the singular form.
2010-01-01
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7 CFR 900.36 - Words in the singular form.
2010-01-01
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7 CFR 900.100 - Words in the singular form.
2010-01-01
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7 CFR 900.50 - Words in the singular form.
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...
7 CFR 61.1 - Words in singular form.
2010-01-01
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Beauchaine, Theodore P.; McNulty, Tiffany
2014-01-01
Research on child and adolescent mental health problems has burgeoned since the inaugural issue of Development and Psychopathology was published in 1989. In the quarter century since, static models of psychopathology have been abandoned in favor of transactional models, following the agenda set by editor Dante Cicchetti and other proponents of the discipline. The transactional approach, which has been applied to autism, depression, self-injury, and delinquency, (a) specifies vulnerabilities and risk factors across multiple levels of analysis spanning genes to cultures, (b) identifies multifinal and equifinal pathways to psychopathology, and (c) transcends traditional disciplinary boundaries. However, as noted by Rutter and Sroufe (2000), specific mechanisms of continuity, discontinuity, and comorbidity of psychopathology must be identified if we wish to understand etiology fully. In this article, we present a model of early-onset externalizing behavior in which comorbidities and continuities are viewed as ontogenic processes: products of complex longitudinal transactions between interdependent individual-level vulnerabilities (e.g., genetic, epigenetic, allostatic) and equally interdependent contextual risk factors (e.g., coercive parenting, deviant peer group affiliations, neighborhood criminality). Through interactions across levels of analysis, some individuals traverse along the externalizing spectrum, beginning with heritable trait impulsivity in preschool and ending in antisociality in adulthood. In describing our model, we note that (a) the approach outlined in the DSM to subtyping externalizing disorders continues to obscure developmental pathways to antisociality, (b) molecular genetics studies will likely not identify meaningful subtypes of externalizing disorder, and (c) ontogenic trait approaches to psychopathology are much more likely to advance the discipline in upcoming years. PMID:24342853
Du, Pan; Kibbe, Warren A; Lin, Simon M
2006-09-01
A major problem for current peak detection algorithms is that noise in mass spectrometry (MS) spectra gives rise to a high rate of false positives. The false positive rate is especially problematic in detecting peaks with low amplitudes. Usually, various baseline correction algorithms and smoothing methods are applied before attempting peak detection. This approach is very sensitive to the amount of smoothing and aggressiveness of the baseline correction, which contribute to making peak detection results inconsistent between runs, instrumentation and analysis methods. Most peak detection algorithms simply identify peaks based on amplitude, ignoring the additional information present in the shape of the peaks in a spectrum. In our experience, 'true' peaks have characteristic shapes, and providing a shape-matching function that provides a 'goodness of fit' coefficient should provide a more robust peak identification method. Based on these observations, a continuous wavelet transform (CWT)-based peak detection algorithm has been devised that identifies peaks with different scales and amplitudes. By transforming the spectrum into wavelet space, the pattern-matching problem is simplified and in addition provides a powerful technique for identifying and separating the signal from the spike noise and colored noise. This transformation, with the additional information provided by the 2D CWT coefficients can greatly enhance the effective signal-to-noise ratio. Furthermore, with this technique no baseline removal or peak smoothing preprocessing steps are required before peak detection, and this improves the robustness of peak detection under a variety of conditions. The algorithm was evaluated with SELDI-TOF spectra with known polypeptide positions. Comparisons with two other popular algorithms were performed. The results show the CWT-based algorithm can identify both strong and weak peaks while keeping false positive rate low. The algorithm is implemented in R and will be
Singular stochastic differential equations
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.
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.
Quantum Kramers model: Corrections to the linear response theory for continuous bath spectrum
Rips, Ilya
2017-01-01
Decay of the metastable state is analyzed within the quantum Kramers model in the weak-to-intermediate dissipation regime. The decay kinetics in this regime is determined by energy exchange between the unstable mode and the stable modes of thermal bath. In our previous paper [Phys. Rev. A 42, 4427 (1990), 10.1103/PhysRevA.42.4427], Grabert's perturbative approach to well dynamics in the case of the discrete bath [Phys. Rev. Lett. 61, 1683 (1988), 10.1103/PhysRevLett.61.1683] has been extended to account for the second order terms in the classical equations of motion (EOM) for the stable modes. Account of the secular terms reduces EOM for the stable modes to those of the forced oscillator with the time-dependent frequency (TDF oscillator). Analytic expression for the characteristic function of energy loss of the unstable mode has been derived in terms of the generating function of the transition probabilities for the quantum forced TDF oscillator. In this paper, the approach is further developed and applied to the case of the continuous frequency spectrum of the bath. The spectral density functions of the bath of stable modes are expressed in terms of the dissipative properties (the friction function) of the original bath. They simplify considerably for the one-dimensional systems, when the density of phonon states is constant. Explicit expressions for the fourth order corrections to the linear response theory result for the characteristic function of the energy loss and its cumulants are obtained for the particular case of the cubic potential with Ohmic (Markovian) dissipation. The range of validity of the perturbative approach in this case is determined (γ /ωbrate for the quantum and for the classical Kramers models. Results for the classical escape rate are in very good agreement with the numerical simulations for high barriers. The results can serve as an additional proof of the robustness and accuracy of the linear response theory.
Computation at a coordinate singularity
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
THREE-DIMENSIONAL RADIATIVE TRANSFER MODELING OF THE POLARIZATION OF THE SUN'S CONTINUOUS SPECTRUM
International Nuclear Information System (INIS)
Bueno, Javier Trujillo; Shchukina, Nataliya
2009-01-01
Polarized light provides the most reliable source of information at our disposal for diagnosing the physical properties of astrophysical plasmas, including the three-dimensional (3D) structure of the solar atmosphere. Here we formulate and solve the 3D radiative transfer problem of the linear polarization of the solar continuous radiation, which is principally produced by Rayleigh and Thomson scattering. Our approach takes into account not only the anisotropy of the solar continuum radiation but also the symmetry-breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. We show that such symmetry-breaking effects do produce observable signatures in Q/I and U/I, even at the very center of the solar disk where we observe the forward scattering case, but their detection would require obtaining very high resolution linear polarization images of the solar surface. Without spatial and/or temporal resolution U/I ∼ 0 and the only observable quantity is Q/I, whose wavelength variation at a solar disk position close to the limb has been recently determined semi-empirically. Interestingly, our 3D radiative transfer modeling of the polarization of the Sun's continuous spectrum in a well-known 3D hydrodynamical model of the solar photosphere shows remarkable agreement with the semi-empirical determination, significantly better than that obtained via the use of one-dimensional (1D) atmospheric models. Although this result confirms that the above-mentioned 3D model was indeed a suitable choice for our Hanle-effect estimation of the substantial amount of 'hidden' magnetic energy that is stored in the quiet solar photosphere, we have found however some small discrepancies whose origin may be due to uncertainties in the semi-empirical data and/or in the thermal and density structure of the 3D model. For this reason, we have paid some attention also to other (more familiar) observables, like the center-limb variation of the
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)
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...
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.
Directory of Open Access Journals (Sweden)
Woodbury-Smith Marc
2008-02-01
Full Text Available Abstract Background Autism Spectrum Conditions (ASCs are characterized by a high degree of clinical heterogeneity, but the extent to which this variation represents a severity gradient versus discrete phenotypes is unclear. This issue has complicated genetic studies seeking to investigate the genetic basis of the high hereditability observed clinically in those with an ASC. The aim of this study was to examine the possible clustering of symptoms associated with ASCs to determine whether the observed distribution of symptom type and severity supported either a severity or a symptom subgroup model to account for the phenotypic variation observed within the ASCs. Methods We investigated the responses of a group of adults with higher functioning ASCs on the fifty clinical features examined in the Autism Spectrum Quotient, a screening questionnaire used in the diagnosis of higher functioning ASCs. In contrast to previous studies we have used this instrument with no a priori assumptions about any underlying factor structure of constituent items. The responses obtained were analyzed using complete linkage hierarchical cluster analysis. For the members of each cluster identified the mean score on each Autism Spectrum Quotient question was calculated. Results Autism Spectrum Quotient responses from a total of 333 individuals between the ages of 16.6 and 78.0 years were entered into the hierarchical cluster analysis. The four cluster solution was the one that generated the largest number of clusters that did not also include very small cluster sizes, defined as a membership comprising 10 individuals or fewer. Examination of these clusters demonstrated that they varied in total Autism Spectrum Quotient but that the profiles across the symptoms comprising the Autism Spectrum Quotient did not differ independently of this severity factor. Conclusion These results are consistent with a unitary spectrum model, suggesting that the clinical heterogeneity observed
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
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.
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.
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.
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].
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
On the continuous spectrum electromagnetic radiation in electron-fullerene collision
International Nuclear Information System (INIS)
Amusia, M.Y.
1995-01-01
It is demonstrated that the electromagnetic radiation spectrum in electron-fullerene collisions is dominated by a huge maximum of multielectron nature, similar to that already predicted and observed in photoabsorption. Due to coherence, the intensity of this radiation is much stronger than the sum of the intensities of isolated atoms. Experimental detection of such radiation would be of great importance for understanding the mechanism of its formation and for investigating fullerene structures. A paper describing these results was published
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})
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, + ∞)
Singularities in FLRW spacetimes
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.
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
7 CFR 1200.1 - Words in the singular form.
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...
Effect of continuous eigenvalue spectrum on plasma transport in toroidal systems
International Nuclear Information System (INIS)
Yamagishi, Tomejiro
1993-03-01
The effect of the continuous eigenvalue of the Vlasov equation on the cross field ion thermal flux is investigated. The continuum contribution due to the toroidal drift resonance is found to play an important role in ion transport particularly near the edge, which may apply to the interpretation of the sharp increase of ion heat conductivity near the periphery observed in large tokamaks. (author)
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...
Supersymmetry in singular spaces
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
Singularities in FLRW Spacetimes
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
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.
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)
Variation method for optimization of Raman fiber amplifier pumped by continuous-spectrum radiation
International Nuclear Information System (INIS)
Ghasempour Ardekani, A.; Bahrampour, A. R.; Feizpour, A.
2007-01-01
In Raman fiber amplifiers, reduction of gain ripple versus frequency has a great importance. In this article using variational method and continuous pump, gain ripple is optimized. It is shown here that for a 40 km line the average gain is 1.3dB and the gain ripple is 0.12 dB, that is lower than the latest published data.
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
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
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.
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...
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.
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.
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.
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.
Single-Cell RNA-Sequencing Reveals a Continuous Spectrum of Differentiation in Hematopoietic Cells
Directory of Open Access Journals (Sweden)
Iain C. Macaulay
2016-02-01
Full Text Available The transcriptional programs that govern hematopoiesis have been investigated primarily by population-level analysis of hematopoietic stem and progenitor cells, which cannot reveal the continuous nature of the differentiation process. Here we applied single-cell RNA-sequencing to a population of hematopoietic cells in zebrafish as they undergo thrombocyte lineage commitment. By reconstructing their developmental chronology computationally, we were able to place each cell along a continuum from stem cell to mature cell, refining the traditional lineage tree. The progression of cells along this continuum is characterized by a highly coordinated transcriptional program, displaying simultaneous suppression of genes involved in cell proliferation and ribosomal biogenesis as the expression of lineage specific genes increases. Within this program, there is substantial heterogeneity in the expression of the key lineage regulators. Overall, the total number of genes expressed, as well as the total mRNA content of the cell, decreases as the cells undergo lineage commitment.
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...
Deformations of surface singularities
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...
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....
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.)
Energy Technology Data Exchange (ETDEWEB)
Barcellos, Luiz Felipe F.C.; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B., E-mail: luizfelipe.fcb@gmail.com, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Grupo de Estudos Nucleares; Leite, Sergio Q. Bogado, E-mail: sbogado@ibest.com.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil)
2017-07-01
In this work a Monte Carlo simulator with continuous energy is used. This simulator distinguishes itself by using the sum of three probability distributions to represent the neutron spectrum. Two distributions have known shape, but have varying population of neutrons in time, and these are the fission neutron spectrum (for high energy neutrons) and the Maxwell-Boltzmann distribution (for thermal neutrons). The third distribution has an a priori unknown and possibly variable shape with time and is determined from parametrizations of Monte Carlo simulation. It is common practice in neutron transport calculations, e.g. multi-group transport, to consider that the neutrons only lose energy with each scattering reaction and then to use a thermal group with a Maxwellian distribution. Such an approximation is valid due to the fact that for fast neutrons up-scattering occurrence is irrelevant, being only appreciable at low energies, i.e. in the thermal energy region, in which it can be regarded as a Maxwell-Boltzmann distribution for thermal equilibrium. In this work the possible neutron-matter interactions are simulated with exception of the up-scattering of neutrons. In order to preserve the thermal spectrum, neutrons are selected stochastically as being part of the thermal population and have an energy attributed to them taken from a Maxwellian distribution. It is then shown how this procedure can emulate the up-scattering effect by the increase in the neutron population kinetic energy. Since the simulator uses tags to identify the reactions it is possible not only to plot the distributions by neutron energy, but also by the type of interaction with matter and with the identification of the target nuclei involved in the process. This work contains some preliminary results obtained from a Monte Carlo simulator for neutron transport that is being developed at Federal University of Rio Grande do Sul. (author)
Directory of Open Access Journals (Sweden)
Chengxi Zhang
2017-11-01
Full Text Available Colloidal perovskite nanocrystals comprised of all inorganic cesium lead halide (CsPbX3, X = Cl, Br, I or a mixture thereof have potential as optical gain materials due to their high luminescence efficiency. In this work, cesium lead halide nanocrystals are continuously synthesized via a microreactor system consisting of poly(tetrafluoroethylene (PTFE capillaries. The synthesized nanocrystals possess excellent optical properties, including a full width at half maximum of 19–35 nm, high fluorescence quantum yield of 47.8–90.55%, and photoluminescence emission in the range of 450–700 nm. For the same precursor concentrations, the photoluminescence emission peak generally increases with increasing reaction temperature, revealing a controllable temperature effect on the photoluminescence characteristics of the synthesized nanocrystals. For quantum dots synthesized with a Br/I ratio of 1:3, a slight blue shift was observed for reaction temperatures greater than 100 °C. This PTFE-based microreactor system provides the unique capability of continuously synthesizing high-quality perovskite nanocrystals that emit over the full visible spectrum with applications ranging from displays and optoelectronic devices.
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...
Cosmological models without singularities
International Nuclear Information System (INIS)
Petry, W.
1981-01-01
A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)
Study on a kind of ϕ-Laplacian Liénard equation with attractive and repulsive singularities.
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.
Residues and duality for singularity categories of isolated Gorenstein singularities
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.
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
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
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
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.
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
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
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 $D(\\alpha)$.
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
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
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
International Nuclear Information System (INIS)
Filippov, G.F.; Lopez Trujillo, A.; Rybkin, I.Yu.
1992-01-01
Using the algebraic version of the resonating group method, the continuous spectrum of 6 Li states with zero isospin is studied. The decay channels t+ 3 He and α+α are taken into account. The astrophysical S-factor of the t( 3 He,d)α reaction is calculated. 20 refs.; 6 figs.; 2 tab. (author)
Loop quantum cosmology and singularities.
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 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
The theory of singular perturbations
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
Van Hove singularities revisited
International Nuclear Information System (INIS)
Dzyaloshinskii, I.
1987-07-01
Beginning with the work of Hirsch and Scalapino the importance of ln 2 -Van Hove singularity in T c -enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle-particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit (one bare charge) is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel (attraction) and SDW (repulsion) and CDW (attraction) in the ph-channel. It is natural that Umklapps produce an SDW + CDW mixture at either sign of the interaction. What is unusual is that both the pp-ph interplay and the Umklapps give rise to a monster-coherent SS + SDW + CDW mixture, again at either sign of the bare charge. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. 10 refs, 5 figs
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.
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
EDITORIAL: The plurality of optical singularities
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.
Singularities of robot mechanisms numerical computation and avoidance path planning
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...
National Research Council Canada - National Science Library
Ohnishi, T
2001-01-01
The motion of eyelids and eyeballs in domestic animals had been recognized well agreement with the sleep depth estimated by spectrum analyses of electroencephalogram at half closed eye and fully closed eye...
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.
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.
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
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 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
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.
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
Directory of Open Access Journals (Sweden)
José M. Beguiristain
2005-04-01
Full Text Available Antecedentes y objetivos: La Dirección Territorial de Sanidad de Gipuzkoa creó en 1996 el servicio del Plan de Salud con la finalidad de transformar los objetivos de salud priorizados por el Departamento de Sanidad en estrategias de intervención a incorporar a los contratos programa. Proceso y resultados: el procedimiento que el servicio está utilizando para cumplir este objetivo se denomina singularización y consiste en seleccionar un proceso vinculado a un problema de salud prioritario, analizarlo y reconstruirlo de forma que se conozca la actividad relacionada con él, los resultados, el coste económico y su impacto en la salud de la población. El procedimiento permite a la Dirección Territorial de Sanidad, responsable de la compra de servicios al sector público y privado, disponer de información sobre las condiciones de contratación para el proceso revisado. La evaluación anual de los Contratos programa y Conciertos controla el grado de consecución de los pactos realizados y de sus consecuencias sobre la salud de la población. El artículo que se presenta recoge la forma en la que se realiza esta singularización.Backgrounds and objectives: In 1996 the Gipuzkoa Territorial Health Agency (Basque Country, Spain created the Health Plan Service. The aim was to transform the health objectives prioritized by the Health Department into intervention strategies to be incorporated into the local contract services. Process and results: One of the procedures the service uses for this purpose, known as «singularization», involves selecting a process linked to a prioritized health problem, and analyzing and reconstructing it so that the related activity, expected results, financial costs and its impact on the population's health can be identified. After this process the service provides the Territorial Health Agency, which is responsible for service purchase for the public and private sectors, with information about contract conditions for
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.)
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.
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
Singularity Theory and its Applications
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.
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.)
Ambient cosmology and spacetime singularities
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.
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
Singular-value demodulation of phase-shifted holograms.
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.
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...
Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states
Dinani, Hossein T.; Berry, Dominic W.
2016-01-01
When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\\omega|^p$ with $p>1$, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of $1/{\\cal N}^{(p-1)/p}$ and $1/{\\cal N}^{2(p-1)/(p+1)}$, respectively, where ${\\cal N}$ is the mean photon flux. We show that this Heisenberg scaling can be a...
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.
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.
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
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)
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.
Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states
Dinani, Hossein T.; Berry, Dominic W.
2017-06-01
When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum 1 /|ω| p with p >1 , then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of 1 /N(p -1 )/p and 1 /N2 (p -1 )/(p +1 ) , respectively, where N is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of p =2 .
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.
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)
Carragher, Natacha; Krueger, Robert F; Eaton, Nicholas R; Markon, Kristian E; Keyes, Katherine M; Blanco, Carlos; Saha, Tulshi D; Hasin, Deborah S
2014-08-01
Alcohol use disorders, substance use disorders, and antisocial personality disorder share a common externalizing liability, which may also include attention-deficit hyperactivity disorder (ADHD). However, few studies have compared formal quantitative models of externalizing liability, with the aim of delineating the categorical and/or continuous nature of this liability in the community. This study compares categorical, continuous, and hybrid models of externalizing liability. Data were derived from the 2004-2005 National Epidemiologic Survey on Alcohol and Related Conditions (N = 34,653). Seven disorders were modeled: childhood ADHD and lifetime diagnoses of antisocial personality disorder (ASPD), nicotine dependence, alcohol dependence, marijuana dependence, cocaine dependence, and other substance dependence. The continuous latent trait model provided the best fit to the data. Measurement invariance analyses supported the fit of the model across genders, with females displaying a significantly lower probability of experiencing externalizing disorders. Cocaine dependence, marijuana dependence, other substance dependence, alcohol dependence, ASPD, nicotine dependence, and ADHD provided the greatest information, respectively, about the underlying externalizing continuum. Liability to externalizing disorders is continuous and dimensional in severity. The findings have important implications for the organizational structure of externalizing psychopathology in psychiatric nomenclatures.
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)
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.
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.
International Nuclear Information System (INIS)
Camargo, Dayana Q. de; Bodmann, Bardo E.J.; Vilhena, Marco T. de; Froehlich, Herberth B.
2011-01-01
In this work we developed a stochastic model to simulate neutron transport in a heterogeneous environment, considering continuous neutron spectra and the nuclear properties with its continuous dependence on energy. This model was implemented using the Monte Carlo method for the propagation of neutrons in different environments. Due to restrictions with respect to the number of neutrons that can be simulated in reasonable computational time we introduced a variable control volume together with (pseudo-) periodic boundary conditions in order to overcome this problem. This study allowed a detailed analysis of the influence of energy on the neutron population and its impact on the life cycle of neutrons. From the results, even for a simple geometrical arrangement, we can conclude that there is need to consider the energy dependence and hence defined a spectral effective multiplication factor per Monte Carlo step. (author)
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
Multidimensional singular integrals and integral equations
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
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.
Why the Singularity Cannot Happen
Modis, Theodore
2012-01-01
The concept of a Singularity as described in Ray Kurzweil's book cannot happen for a number of reasons. One reason is that all natural growth processes that follow exponential patterns eventually reveal themselves to be following S-curves thus excluding runaway situations. The remaining growth potential from Kurzweil's ''knee'', which could be approximated as the moment when an S-curve pattern begins deviating from the corresponding exponential, is a factor of only one order of magnitude grea...
Black holes, singularities and predictability
International Nuclear Information System (INIS)
Wald, R.M.
1984-01-01
The paper favours the view that singularities may play a central role in quantum gravity. The author reviews the arguments leading to the conclusion, that in the process of black hole formation and evaporation, an initial pure state evolves to a final density matrix, thus signaling a breakdown in ordinary quantum dynamical evolution. Some related issues dealing with predictability in the dynamical evolution, are also discussed. (U.K.)
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Quantum propagation across cosmological singularities
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.
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.
International Nuclear Information System (INIS)
Camargo, Dayana Queiroz de
2011-01-01
This thesis has developed a stochastic model to simulate the neutrons transport in a heterogeneous environment, considering continuous neutron spectra and the nuclear properties with its continuous dependence on energy. This model was implemented using Monte Carlo method for the propagation of neutrons in different environment. Due to restrictions with respect to the number of neutrons that can be simulated in reasonable computational processing time introduced the variable control volume along the (pseudo-) periodic boundary conditions in order to overcome this problem. The choice of class physical Monte Carlo is due to the fact that it can decompose into simpler constituents the problem of solve a transport equation. The components may be treated separately, these are the propagation and interaction while respecting the laws of energy conservation and momentum, and the relationships that determine the probability of their interaction. We are aware of the fact that the problem approached in this thesis is far from being comparable to building a nuclear reactor, but this discussion the main target was to develop the Monte Carlo model, implement the code in a computer language that allows extensions of modular way. This study allowed a detailed analysis of the influence of energy on the neutron population and its impact on the life cycle of neutrons. From the results, even for a simple geometrical arrangement, we can conclude the need to consider the energy dependence, i.e. an spectral effective multiplication factor should be introduced each energy group separately. (author)
Singularities in Free Surface Flows
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
Mathematical models with singularities a zoo of singular creatures
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.
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
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
On important precursor of singular optics (tutorial)
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)].
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
Campbell, J. Peter; Kalpathy-Cramer, Jayashree; Erdogmus, Deniz; Tian, Peng; Kedarisetti, Dharanish; Moleta, Chace; Reynolds, James D.; Hutcheson, Kelly; Shapiro, Michael J.; Repka, Michael X.; Ferrone, Philip; Drenser, Kimberly; Horowitz, Jason; Sonmez, Kemal; Swan, Ryan; Ostmo, Susan; Jonas, Karyn E.; Chan, R.V. Paul; Chiang, Michael F.
2016-01-01
vascular abnormality required for presence of plus and pre-plus disease. This has important implications for research, teaching and patient care for ROP, and suggests that a continuous ROP plus disease severity score may more accurately reflect the behavior of expert ROP clinicians, and may better standardize classification in the future. PMID:27591053
Topological resolution of gauge theory singularities
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
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 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
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
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.
Naked singularity, firewall, and Hawking radiation.
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.
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.
On local invariants of singular symplectic forms
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.
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.)
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
Coupled singular and non singular thermoelastic system and double lapalce decomposition methods
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
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
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 Semantics of Plurals: A Defense of Singularism
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…
Stable singularities in string theory
International Nuclear Information System (INIS)
Aspinwall, P.S.; Morrison, D.R.; Gross, M.
1996-01-01
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an N=2 non-linear σ-model. This target space has a singularity which may be smoothed away according to the conventional rules of geometry, but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten. (orig.). With 3 figs
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Coulomb branches with complex singularities
Argyres, Philip C.; Martone, Mario
2018-06-01
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.
Quantum transitions through cosmological singularities
International Nuclear Information System (INIS)
Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick
2017-01-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
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...
Building Reproducible Science with Singularity Containers
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 ...
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...
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.
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
Cold atoms in singular potentials
International Nuclear Information System (INIS)
Denschlag, J. P.
1998-09-01
We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
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 ...
Biclustering via Sparse Singular Value Decomposition
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.
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.
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)
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.)
Minimal solution for inconsistent singular fuzzy matrix equations
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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.
Pseudo-differential operators on manifolds with singularities
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.
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)
Initial singularity and pure geometric field theories
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.
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...
Quantum dress for a naked singularity
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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.
Cirant, Marco; Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ctor
2016-01-01
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
The singularity structure of scale-invariant rank-2 Coulomb branches
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.
The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
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...
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
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
Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
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.
Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy
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.
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.
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)
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.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
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.
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.
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}.
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.)
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.
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.
On a Monge-Amp\\`ere operator for plurisubharmonic functions with analytic singularities
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.
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.
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.)
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.)
Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories
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.
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)
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
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.
Removal of apparent singularity in grid computations
International Nuclear Information System (INIS)
Jakubovics, J.P.
1993-01-01
A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward
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.
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.
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.)
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.)
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.
Global embeddings for branes at toric singularities
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.
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.)
Singularity hypotheses a scientific and philosophical assessment
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.
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
Endpoint singularities in unintegrated parton distributions
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.
Characteristic classes, singular embeddings, and intersection homology.
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.
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
Tuning of tunneling current noise spectra singularities by localized states charging
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...
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
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
Singular Linear Differential Equations in Two Variables
Braaksma, B.L.J.; Put, M. van der
2008-01-01
The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no
'Footballs', conical singularities, and the Liouville equation
International Nuclear Information System (INIS)
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Mobile communications technology: The singular factor responsible ...
African Journals Online (AJOL)
This paper investigated the factors responsible for the growth of Internet usage on the African continent. The principal finding was that increasing growth of Internet usage is also down to one singular factor: mobile communications technology. The proliferation of mobile phone usage in Africa has resulted in the sustained ...
Diamagnetism of quantum gases with singular potentials
DEFF Research Database (Denmark)
Briet, Philippe; Cornean, Horia; Savoie, Baptiste
2010-01-01
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is analytic with respect to the chemical potential and the intensity of the external magnetic...
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
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
journal of. July 2007 physics pp. 31–47. A singularity theorem based on spatial ... In this paper I would like to present a result which confirms – at least partially – ... A detailed analysis of how the model fits in with the .... Further, the statement that the spatial average ...... Financial support under grants FIS2004-01626 and no.
Symmetries and singularities in Hamiltonian systems
International Nuclear Information System (INIS)
Miranda, Eva
2009-01-01
This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which find their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective.
Singular interactions supported by embedded curves
International Nuclear Information System (INIS)
Kaynak, Burak Tevfik; Turgut, O Teoman
2012-01-01
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed. (paper)
Resolving curvature singularities in holomorphic gravity
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
Classical resolution of singularities in dilaton cosmologies
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to
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
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.
A Systolic Architecture for Singular Value Decomposition,
1983-01-01
Presented at the 1 st International Colloquium on Vector and Parallel Computing in Scientific Applications, Paris, March 191J Contract N00014-82-K.0703...Gene Golub. Private comunication . given inputs x and n 2 , compute 2 2 2 2 /6/ G. H. Golub and F. T. Luk : "Singular Value I + X1 Decomposition
Sporadic simple groups and quotient singularities
International Nuclear Information System (INIS)
Cheltsov, I A; Shramov, C A
2013-01-01
We show that if a faithful irreducible representation of a central extension of a sporadic simple group with centre contained in the commutator subgroup gives rise to an exceptional (resp. weakly exceptional but not exceptional) quotient singularity, then that simple group is the Hall-Janko group (resp. the Suzuki group)
Singularity is the Future of ICT Research
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
2014-06-01
Jun 1, 2014 ... innovation if the black race are not to be left one hundred years ... aspects of innovation in mechatronics design philosophy which illustrate the benefits obtainable by an a priori ..... An overview of models of technological singularity ... the Singularity—representing a profound and disruptive transformation in.
São Carlos Workshop on Real and Complex Singularities
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.
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.
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.
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.
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)
7 CFR 46.1 - Words in singular form.
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...
Singularities and the geometry of spacetime
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
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.
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)
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)
Singularities in the general theory of relativity
International Nuclear Information System (INIS)
Treder, H.J.
1980-01-01
'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)
Singularity theory and equivariant symplectic maps
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...
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
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
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.
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
The technological singularity and exponential medicine
Iraj Nabipour; Majid Assadi
2016-01-01
The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested th...
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
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
Directory of Open Access Journals (Sweden)
Jesus Manuel Munoz-Pacheco
2013-01-01
Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.
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.
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.
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.
Regularization of the big bang singularity with random perturbations
Belbruno, Edward; Xue, BingKan
2018-03-01
We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.
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.
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)
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
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
is a singular Green operator. It is well-known in smooth cases that when G is of negative order −t on a bounded domain, its eigenvalues ors-numbers have the behavior (*)s j (G) ∼ cj −t/(n−1) for j → ∞, governed by the boundary dimension n − 1. In some nonsmooth cases, upper estimates (**)s j (G) ≤ Cj −t/(n−1...
Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
DEFF Research Database (Denmark)
Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
2014-01-01
We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic ...... singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA)....
The Singularity May Never Be Near
Walsh, Toby
2017-01-01
There is both much optimisim and pessimism around artificial intelligence (AI) today. The optimists are investing millions of dollars, and even in some cases billions of dollars into AI. The pessimists, on the other hand, predict that AI will end many things: jobs, warfare, and even the human race. Both the optimists and the pessimists often appeal to the idea of a technological singularity, a point in time where machine intelligence starts to run away, and a new, more in- telligent “species”...
Compacted dimensions and singular plasmonic surfaces
Pendry, J. B.; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele
2017-11-01
In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.
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)
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)
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
Observer-dependent sign inversions of polarization singularities.
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.
Transmutation of planar media singularities in a conformal cloak.
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.
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
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
7 CFR 900.80 - Words in the singular form.
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...
Quantum singularities in the FRW universe revisited
International Nuclear Information System (INIS)
Letelier, Patricio S.; Pitelli, Joao Paulo M.
2010-01-01
The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state p=(1/3)ρ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied, and it is shown that the energy conditions are violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the nonsingular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of nonnormalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.
Finite-time singularity signature of hyperinflation
Sornette, D.; Takayasu, H.; Zhou, W.-X.
2003-07-01
We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.
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.
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.
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
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)
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.)
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
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.
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.
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
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.
A vida singular de um jovem militante
Directory of Open Access Journals (Sweden)
Áurea Maria Guimarães
2012-01-01
Full Text Available Esse artigo é fruto de uma pesquisa realizada no período de 2007 a 2010, junto a jovens militantes da cidade de Campinas, com o objetivo de compreender as diferentes maneiras que conduziam esses jovens tanto a reproduzir um modelo de vida quanto a criar outras possibilidades de militância na relação com esse modelo. Entre as histórias orais de vida narradas por jovens que militavam em diferentes grupos ou instituições, escolhi a vida de Biula, representante do movimento estudantil secundarista, procurando evidenciar que a singularidade desta vida, como também e a de outros jovens, estava conectada à problematização que faziam no interior de certas práticas, histórica e culturalmente constituídas, possibilitando a criação de novas formas de subjetivação nas quais se modificava a experiência que tinham deles mesmos na relação com os seus heróis ou modelos de referência. Palavras-chave: história oral – transcriação – heróis – resistência - processos de singularização. THE SINGULAR LIFE OF A YOUNG MILITANT ABSTRACT This article is the result of a research carried out from 2007 to 2010 with young militants in the city of Campinas, aiming to understand the different ways which conducted these youngsters to both reproduce a life model and create other possibilities of militancy in the relationship with this model. Among oral stories narrated by young militants from different groups or institutions, I have chosen the life of Biula, a representative of the secondary students’ movement, trying to show that the singularity of this life and other youngsters’ lives was connected to the problematization they promoted within certain practices, historically and culturally built, thus enabling the creation of new subjectification modes in which the experience they had of themselves in the relationship with their heroes or reference models has changed. Key words: oral history - transcreation – heroes
The technological singularity and exponential medicine
Directory of Open Access Journals (Sweden)
Iraj Nabipour
2016-01-01
Full Text Available The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence provided an exponential growth rate for medicine. The "exponential medicine" is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.
Dual Vector Spaces and Physical Singularities
Rowlands, Peter
Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.
String wave function across a Kasner singularity
International Nuclear Information System (INIS)
Copeland, Edmund J.; Niz, Gustavo; Turok, Neil
2010-01-01
A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.
Branes at Singularities in Type 0 String Theory
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.
Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues
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
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
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
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.)
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 ...
K3-fibered Calabi-Yau threefolds II, singular fibers
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.
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).
Infinite derivative gravity : non-singular cosmology & blackhole solutions
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
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.
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
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
One Critical Case in Singularly Perturbed Control Problems
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.
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
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)
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.
ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS
International Nuclear Information System (INIS)
Chu Zhe; Lin, W. P.; Yang Xiaofeng
2013-01-01
Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.
Singular Null Hypersurfaces in General Relativity
International Nuclear Information System (INIS)
Dray, T
2006-01-01
Null hypersurfaces are a mathematical consequence of the Lorentzian signature of general relativity; singularities in mathematical models usually indicate where the interesting physics takes place. This book discusses what happens when you combine these ideas. Right from the preface, this is a no-nonsense book. There are two principal approaches to singular shells, one distributional and the other 'cut and paste'; both are treated in detail. A working knowledge of GR is assumed, including familiarity with null tetrads, differential forms, and 3 + 1 decompositions. Despite my own reasonably extensive, closely related knowledge, there was material unfamiliar to me already in chapter 3, although I was reunited with some old friends in later chapters. The exposition is crisp, with a minimum of transition from chapter to chapter. In fact, my main criticism is that there is no clear statement of the organization of the book, nor is there an index. Everything is here, and the story is compelling if you know what to look for, although it is less easy to follow the story if you are not already familiar with it. But this is really a book for experts, and the authors certainly qualify, having played a significant role in developing and extending the results they describe. It is also entirely appropriate that the book is dedicated to Werner Israel, who pioneered the thin-shell approach to (non-null) singular surfaces and later championed the use of similar methods for analysing null shells. After an introductory chapter on impulsive signals, the authors show how the Bianchi identities can be used to classify spacetimes with singular null hypersurfaces. This approach, due to the authors, generalizes the framework originally proposed by Penrose. While astrophysical applications are discussed only briefly, the authors point out that detailed physical characteristics of signals from isolated sources can be determined in this manner. In particular, they describe the behaviour of
Complexity, Analysis and Control of Singular Biological Systems
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 ...
Managing focal fields of vector beams with multiple polarization singularities.
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.
Workshop on Singularities in Geometry, Topology, Foliations and Dynamics
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
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.
Czech Academy of Sciences Publication Activity Database
Knésl, Zdeněk; Klusák, Jan; Náhlík, Luboš
2007-01-01
Roč. 14, č. 6 (2007), s. 399-408 ISSN 1802-1484 R&D Projects: GA ČR(CZ) GA101/05/0320; GA ČR GA101/05/0227 Institutional research plan: CEZ:AV0Z20410507 Keywords : fracture mechanics * stability criteria * singular stress concentrations * crack initiation * critical stress Subject RIV: JL - Materials Fatigue, Friction Mechanics
3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities
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.
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
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.
A spin-liquid with pinch-line singularities on the pyrochlore lattice.
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.
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.
Sensitivity analysis of automatic flight control systems using singular value concepts
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.
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
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.
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.)
Boundary singularities produced by the motion of soap films.
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.
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.
Greenslade, Thomas B., Jr.
1984-01-01
Describes several methods of executing lecture demonstrations involving the recombination of the spectrum. Groups the techniques into two general classes: bringing selected portions of the spectrum together using lenses or mirrors and blurring the colors by rapid movement or foreshortening. (JM)
Tangled nonlinear driven chain reactions of all optical singularities
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.
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)
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
On the singular perturbations for fractional differential equation.
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.
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
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)
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.
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...
Singular Value Decomposition and Ligand Binding Analysis
Directory of Open Access Journals (Sweden)
André Luiz Galo
2013-01-01
Full Text Available Singular values decomposition (SVD is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound, which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.
Singular limits in thermodynamics of viscous fluids
Feireisl, Eduard
2017-01-01
This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapt...
Singularity fitting in hydrodynamical calculations II
International Nuclear Information System (INIS)
Richtmyer, R.D.; Lazarus, R.B.
1975-09-01
This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self-similar solutions for γ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary-value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of γ; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows
Singular perturbation in the physical sciences
Neu, John C
2015-01-01
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and p...
Singular Perturbation Analysis and Gene Regulatory Networks with Delay
Shlykova, Irina; Ponosov, Arcady
2009-09-01
There are different ways of how to model gene regulatory networks. Differential equations allow for a detailed description of the network's dynamics and provide an explicit model of the gene concentration changes over time. Production and relative degradation rate functions used in such models depend on the vector of steeply sloped threshold functions which characterize the activity of genes. The most popular example of the threshold functions comes from the Boolean network approach, where the threshold functions are given by step functions. The system of differential equations becomes then piecewise linear. The dynamics of this system can be described very easily between the thresholds, but not in the switching domains. For instance this approach fails to analyze stationary points of the system and to define continuous solutions in the switching domains. These problems were studied in [2], [3], but the proposed model did not take into account a time delay in cellular systems. However, analysis of real gene expression data shows a considerable number of time-delayed interactions suggesting that time delay is essential in gene regulation. Therefore, delays may have a great effect on the dynamics of the system presenting one of the critical factors that should be considered in reconstruction of gene regulatory networks. The goal of this work is to apply the singular perturbation analysis to certain systems with delay and to obtain an analog of Tikhonov's theorem, which provides sufficient conditions for constracting the limit system in the delay case.
Autism Spectrum Disorder (ASD): Related Topics
... Facebook Tweet Share Compartir Q: Do vaccines cause autism spectrum disorder (ASD)? A: Many studies that have looked at whether there is a relationship between vaccines and autism spectrum disorder (ASD). To date, the studies continue to show ...
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.)
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.
Coulomb singularity effects in tunnelling spectroscopy of individual impurities
Arseyev, P. I.; Maslova, N. S.; Panov, V. I.; Savinov, S. V.
2002-01-01
Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristics
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)
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
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.
Phase Singularities and Termination of Spiral Wave Reentry
National Research Council Canada - National Science Library
Eason, James
2001-01-01
In order to elucidate the mechanisms by which a strong shock terminates reentrant wavefronts, we employed phase analysis techniques to study phase singularity dynamics in a finite element model of cardiac tissue...
A singular value sensitivity approach to robust eigenstructure assignment
DEFF Research Database (Denmark)
Søgaard-Andersen, Per; Trostmann, Erik; Conrad, Finn
1986-01-01
A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows...
Normal families and isolated singularities of meromorphic functions
International Nuclear Information System (INIS)
Chee, P.S.; Subramaniam, A.
1985-06-01
Based on the criterion of Zalcman for normal families, a generalization of a well-known result relating normal families and isolated essential singularities of meromorphic functions is proved, using a theorem of Lehto and Virtanen on normal functions. (author)
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
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)
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.)
Dimension counts for singular rational curves via semigroups
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.
Modified Differential Transform Method for Two Singular Boundary Values Problems
Directory of Open Access Journals (Sweden)
Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
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...
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,)
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....
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)
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.
Segmentation of singularity maps in the context of soil porosity
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
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
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.
Jitomirskaya, S.; Marx, C. A.
2012-11-01
We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.
Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
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.
Analytic solution of the BCS gap equation with a logarithmic singularity in the density of states
International Nuclear Information System (INIS)
Bhardwaj, A.; Muthu, S.K.
1999-01-01
The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically for a density of states function with a logarithmic singularity. It is an extension of our earlier work where we had assumed a constant density of states. We continue to work in the weak-coupling limit and consider both phononic and non-phononic pairings. Expressions are obtained for T c , Δ 0 (the gap at T=0), and the jump in the electronic specific heat at T=T c . We also calculate the isotope exponent and show that it is possible to reproduce the broad features of the experimental results in this framework. (orig.)
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)
Singularity detection by wavelet approach: application to electrocardiogram signal
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.
... severe defect, resulting in essentially nonfunctional peroxisomes. This phenomenon produces the range of severity of the disorders. How is the Zellweger Spectrum Diagnosed? The distinctive shape of the head and face of a child born with one of the diseases of the ...
On the Ice Nucleation Spectrum
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
A singular-value decomposition approach to X-ray spectral estimation from attenuation data
International Nuclear Information System (INIS)
Tominaga, Shoji
1986-01-01
A singular-value decomposition (SVD) approach is described for estimating the exposure-rate spectral distributions of X-rays from attenuation data measured withvarious filtrations. This estimation problem with noisy measurements is formulated as the problem of solving a system of linear equations with an ill-conditioned nature. The principle of the SVD approach is that a response matrix, representing the X-ray attenuation effect by filtrations at various energies, can be expanded into summation of inherent component matrices, and thereby the spectral distributions can be represented as a linear combination of some component curves. A criterion function is presented for choosing the components needed to form a reliable estimate. The feasibility of the proposed approach is studied in detail in a computer simulation using a hypothetical X-ray spectrum. The application results of the spectral distributions emitted from a therapeutic X-ray generator are shown. Finally some advantages of this approach are pointed out. (orig.)
Singular boundary perturbations of distributed systems
DEFF Research Database (Denmark)
Pedersen, Michael
1990-01-01
Some problems arising in real-life control applications are addressed--namely, problems concerning non-smooth control inputs on the boundary of the spatial domain. The classical variational approach is extended, and sufficient conditions are given for the solutions to continuous functions of time...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
larger, say of the order of tens of solar masses, a continual collapse is inevitable once there are no ... observed to satisfy a suitable positivity of energy requirement. The second condi ...... him, and to benefit from his penetrating insights. I like to ...
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...
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
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.
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)
Quantum no-singularity theorem from geometric flows
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.
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
Singular ways to search for the Higgs boson
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...
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 %.
Two-scale approach to oscillatory singularly perturbed transport equations
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.
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
Symposium on Singularities, Representation of Algebras, and Vector Bundles
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.
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
Singular perturbations introduction to system order reduction methods with applications
Shchepakina, Elena; Mortell, Michael P
2014-01-01
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...
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
Fermi-edge singularity and the functional renormalization group
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.
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.
Study on sampling of continuous linear system based on generalized Fourier transform
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.
Directory of Open Access Journals (Sweden)
Zhang Xuemei
2009-01-01
Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of as well as positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.
Hilbert schemes of points on some classes surface singularities
Gyenge, Ádám
2016-01-01
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...
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
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.
Surface singularities in Eddington-inspired Born-Infeld gravity.
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.
Harnack's Inequality for Degenerate and Singular Parabolic Equations
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
Kalman Filtering for Delayed Singular Systems with Multiplicative Noise
Institute of Scientific and Technical Information of China (English)
Xiao Lu; Linglong Wang; Haixia Wang; Xianghua Wang
2016-01-01
Kalman filtering problem for singular systems is dealt with, where the measurements consist of instantaneous measurements and delayed ones, and the plant includes multiplicative noise. By utilizing standard singular value decomposition, the restricted equivalent delayed system is presented, and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma. The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations, and a numerical example is presented to show the validity and efficiency of the proposed approach, where the comparison between the filter and predictor is also given.
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Einstein equation solutions with axial symmetry, conical and essential singularities
International Nuclear Information System (INIS)
Oliveira, S.R. de.
1986-01-01
New classes of exact solutions to the Einstein equations of a static axisymetric space-time associated with rings and disks are found. Also, the solutions associated to a axisymetric superposition of punctual bodies, bars, rings and disks are obtained. These solutions have a strut singularities to keep the bodies apart. When one of the bodies of the superposition is a ring, the ring interior is covered with a membrane that serve as a support for the strut that hold the other body. Furthermore, the curvature singularities for different solutions ae analised. (author) [pt
Propagation of singularities for linearised hybrid data impedance tomography
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2018-02-01
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 conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.
Tensor renormalization group with randomized singular value decomposition
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.
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
Singular charge density at the center of the pion?
International Nuclear Information System (INIS)
Miller, Gerald A.
2009-01-01
We relate the three-dimensional infinite momentum frame spatial charge density of the pion to its electromagnetic form factor F π (Q 2 ). Diverse treatments of the measured form factor data including phenomenological fits, nonrelativistic quark models, the application of perturbative quantum chromodynamics (QCD), QCD sum rules, holographic QCD, and the Nambu-Jona-Lasinio (NJL) model all lead to the result that the charge density at the center of the pion has a logarithmic divergence. Relativistic constituent quark models do not display this singularity. Future measurements planned for larger values of Q 2 may determine whether or not a singularity actually occurs.
Can noncommutativity resolve the Big-Bang singularity?
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.
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.
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
particular case of radial pressure pr(r) has been illustrated in details to get a ... In §2, we briefly summarize the analysis given in [3] and state the conditions on ...... taken for other shells to reach the singularity can be determined from the Taylor.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...
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 p dependent boundedness of singular integral operators
Czech Academy of Sciences Publication Activity Database
Honzík, Petr
2011-01-01
Roč. 267, 3-4 (2011), s. 931-937 ISSN 0025-5874 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular integral operators Subject RIV: BA - General Mathematics Impact factor: 0.749, year: 2011 http://www.springerlink.com/content/k507g30163351250/
Discrete singular convolution for the generalized variable-coefficient ...
African Journals Online (AJOL)
Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously ...
Classical Liouville action on the sphere with three hyperbolic singularities
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl
2004-08-30
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek; Jaskólski, Zbigniew
2004-08-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
International Nuclear Information System (INIS)
Hadasz, Leszek; Jaskolski, Zbigniew
2004-01-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory
Singular limit analysis of a model for earthquake faulting
DEFF Research Database (Denmark)
Bossolini, Elena; Brøns, Morten; Kristiansen, Kristian Uldall
2017-01-01
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake episodes. In particular, the limit cycles arise from...
Singularity free non-rotating cosmological solutions for perfect fluids ...
Indian Academy of Sciences (India)
Singularity free cosmological solutions of the type stated in the title known so far are of a very special class and have the following characteristics: (a) The space time is cylindrically symmetric. (b) In case the metric is diagonal, the μ's are of the form μ = a function of time multiplied by a function of the radial coordinate.
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.
Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields
DEFF Research Database (Denmark)
Angelsky, Oleg V.; Maksimyak, Alexander P.; Maksimyak, Peter P.
2009-01-01
Peculiarities of the spatial behaviour of the dislocation lines resulting from scattering of coherent radiation from random and fractal rough surfaces are studied. The technique of optical correlation is proposed for diagnostics of phase singularities in a complex speckle field by comparing...
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.
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.
A parabolic singular perturbation problem with an internal layer
Grasman, J.; Shih, S.D.
2004-01-01
A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner
Transcendental smallness in singularly perturbed equations of volterra type
International Nuclear Information System (INIS)
Bijura, Angelina M.
2003-11-01
The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...... theory....
A generalization of the virial theorem for strongly singular potentials
International Nuclear Information System (INIS)
Gesztesy, F.; Pittner, L.
1978-09-01
Using scale transformations the authors prove a generalization of the virial theorem for the eigenfunctions of non-relativistic Schroedinger Hamiltonians which are defined as the Friedrichs extension of strongly singular differential operators. The theorem also applies to situations where the ground state has divergent kinetic and potential energy and thus the usual version of the virial theorem becomes meaningless. (Auth.)
Remarks on the Schroedinger operator with singular complex potentials
International Nuclear Information System (INIS)
Brezis, Haim; Kato, Tosio
1979-01-01
To describe this method in a simple case Section 2 begin with real valued potentials. The main results in Section 2 are essentially known. In Section 3 the case of complex potentials is exposed. Schroedinger operators with complex potentials have been studied by Nelson. This results were extended. Here more general singularities are exposed
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.
Formation and morphological transformation of polarization singularities: hunting the monstar
International Nuclear Information System (INIS)
Kumar, Vijay; Philip, Geo M; Viswanathan, Nirmal K
2013-01-01
The theoretical formalism and experimental measurements to form and transform between the three morphologies of the polarization singular patterns—star, lemon and monstar—are presented here. The monstar is statistically rare in isotropic random fields but its controllable realization is achieved by tuning the field anisotropy in three-beam interference. (paper)
Singular points in moduli spaces of Yang-Mills fields
International Nuclear Information System (INIS)
Ticciati, R.
1984-01-01
This thesis investigates the metric dependence of the moduli spaces of Yang-Mills fields of an SU(2) principal bundle P with chern number -1 over a four-dimensional, simply-connected, oriented, compact smooth manifold M with positive definite intersection form. The purpose of this investigation is to suggest that the surgery class of the moduli space of irreducible connections is, for a generic metric, a Z 2 topological invariant of the smooth structure on M. There are three main parts. The first two parts are local analysis of singular points in the moduli spaces. The last part is global. The first part shows that the set of metrics for which the moduli space of irreducible connections has only non-degenerate singularities has codimension at least one in the space of all metrics. The second part shows that, for a one-parameter family of moduli spaces in a direction transverse to the set of metrics for which the moduli spaces have singularities, passing through a non-degenerate singularity of the simplest type changes the moduli space by a cobordism. The third part shows that generic one-parameter families of metrics give rise to six-dimensional manifolds, the corresponding family of moduli spaces of irreducible connections. It is shown that when M is homeomorphic to S 4 the six-dimensional manifold is a proper cobordism, thus establishing the independence of the surgery class of the moduli space on the metric on M
Robust regularized singular value decomposition with application to mortality data
Zhang, Lingsong; Shen, Haipeng; Huang, Jianhua Z.
2013-01-01
We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The Rob
Boundary triples for Schrodinger operators with singular interactions on hypersurfaces
Czech Academy of Sciences Publication Activity Database
Behrndt, J.; Langer, M.; Lotoreichik, Vladimir
2016-01-01
Roč. 7, č. 2 (2016), s. 290-302 ISSN 2220-8054 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : boundary triple * Weyl function * Schrodinger operator * singular potential * delta-interaction * hypersurface Subject RIV: BE - Theoretical Physics