Vector fields on singular varieties
Brasselet, Jean-Paul; Suwa, Tatsuo
2009-01-01
Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Singular vectors for the WN algebras
Ridout, David; Siu, Steve; Wood, Simon
2018-03-01
In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.
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).
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)
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.
Propagation property of the non-paraxial vector Lissajous singularity beams in free space
Chen, Haitao; Gao, Zenghui
2016-12-01
The analytic expressions for the free-space propagation of paraxial and non-paraxial vector Lissajous singularity beams are derived, and used to compare the propagation property of a Lissajous singularity carried by paraxial and non-paraxial vector beams in free space. It is found that the creation of a single Lissajous singularity, the creation and annihilation of pairs Lissajous singularities may take place for the both cases. However, after the annihilation of a pair of singularities, no Lissajous singularities appear in the output field for non-paraxial vector Lissajous singularity beams, which is different from the paraxial vector Lissajous singularity beams.
Families of singular and subsingular vectors of the topological N=2 superconformal algebra
International Nuclear Information System (INIS)
Gato-Rivera, B.; Rosado, J.I.
1998-01-01
We analyze several issues concerning the singular vectors of the topological N=2 superconformal algebra. First we investigate which types of singular vectors exist, regarding the relative U(1) charge and the BRST-invariance properties, finding four different types in chiral Verma modules and twenty-nine different types in complete Verma modules. Then we study the family structure of the singular vectors, every member of a family being mapped to any other member by a chain of simple transformations involving the spectral flows. The families of singular vectors in chiral Verma modules follow a unique pattern (four vectors) and contain subsingular vectors. We write down these families until level 3, identifying the subsingular vectors. The families of singular vectors in complete Verma modules follow infinitely many different patterns, grouped roughly in five main kinds. We present a particularly interesting thirty-eight-member family at levels 3, 4, 5, and 6, as well as the complete set of singular vectors at level 1 (twenty-eight different types). Finally we analyze the Doerrzapf conditions leading to two linearly independent singular vectors of the same type, at the same level in the same Verma module, and we write down four examples of those pairs of singular vectors, which belong to the same thirty-eight-member family. (orig.)
Cloud detection for MIPAS using singular vector decomposition
Directory of Open Access Journals (Sweden)
J. Hurley
2009-09-01
Full Text Available Satellite-borne high-spectral-resolution limb sounders, such as the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS onboard ENVISAT, provide information on clouds, especially optically thin clouds, which have been difficult to observe in the past. The aim of this work is to develop, implement and test a reliable cloud detection method for infrared spectra measured by MIPAS.
Current MIPAS cloud detection methods used operationally have been developed to detect cloud effective filling more than 30% of the measurement field-of-view (FOV, under geometric and optical considerations – and hence are limited to detecting fairly thick cloud, or large physical extents of thin cloud. In order to resolve thin clouds, a new detection method using Singular Vector Decomposition (SVD is formulated and tested. This new SVD detection method has been applied to a year's worth of MIPAS data, and qualitatively appears to be more sensitive to thin cloud than the current operational method.
International Nuclear Information System (INIS)
Dobrev, V. K.; Stoimenov, S.
2010-01-01
The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.
Ensemble singular vectors and their use as additive inflation in EnKF
Directory of Open Access Journals (Sweden)
Shu-Chih Yang
2015-07-01
Full Text Available Given an ensemble of forecasts, it is possible to determine the leading ensemble singular vector (ESV, that is, the linear combination of the forecasts that, given the choice of the perturbation norm and forecast interval, will maximise the growth of the perturbations. Because the ESV indicates the directions of the fastest growing forecast errors, we explore the potential of applying the leading ESVs in ensemble Kalman filter (EnKF for correcting fast-growing errors. The ESVs are derived based on a quasi-geostrophic multi-level channel model, and data assimilation experiments are carried out under framework of the local ensemble transform Kalman filter. We confirm that even during the early spin-up starting with random initial conditions, the final ESVs of the first analysis with a 12-h window are strongly related to the background errors. Since initial ensemble singular vectors (IESVs grow much faster than Lyapunov Vectors (LVs, and the final ensemble singular vectors (FESVs are close to convergence to leading LVs, perturbations based on leading IESVs grow faster than those based on FESVs, and are therefore preferable as additive inflation. The IESVs are applied in the EnKF framework for constructing flow-dependent additive perturbations to inflate the analysis ensemble. Compared with using random perturbations as additive inflation, a positive impact from using ESVs is found especially in areas with large growing errors. When an EnKF is ‘cold-started’ from random perturbations and poor initial condition, results indicate that using the ESVs as additive inflation has the advantage of correcting large errors so that the spin-up of the EnKF can be accelerated.
International Nuclear Information System (INIS)
Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher
2013-01-01
We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe–Samelson (2007 Tellus A 59 355–66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130–41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520–4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319–27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130–41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling
Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher
2013-06-01
We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe-Samelson (2007 Tellus A 59 355-66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130-41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520-4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319-27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130-41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling imitating the
Directory of Open Access Journals (Sweden)
Michael Hoff
2015-01-01
Full Text Available Instability is related to exponentially growing eigenmodes. Interestingly, when finite time intervals are considered, growth rates of certain initial perturbations can exceed the growth rates of the most unstable modes. Moreover, even when all modes are damped, such particular initial perturbations can still grow during finite time intervals. The perturbations with the largest growth rates are called singular vectors (SVs or optimal perturbations. They not only play an important role in atmospheric ensemble predictions, but also for the theory of instability and turbulence. Starting point for a classical SV-analysis is a linear dynamical system with a known system matrix. In contrast to this traditional approach, measured data are used here to estimate the linear propagator. For this estimation, a method is applied that uses the covariances of the measured time series to find the principal oscillation patterns (POPs that are the empirically estimated linear eigenmodes of the system. By using the singular value decomposition (SVD, we can estimate the modes of maximal growth of the propagator which are thus the empirically estimated SVs. These modes can be understood as a superposition of POPs that form a complete but in general non-orthogonal basis. The data used, originate from a differentially heated rotating annulus laboratory experiment. This experiment is an analogue of the earth's atmosphere and is used to study the development of baroclinic waves in a well controlled and reproducible way without the need of numerical approximations. Baroclinic waves form the background for many studies on SV growth and it is thus straight forward to apply the technique of empirical SV estimation to these laboratory data. To test the method of SV estimation, we use a quasi-geostrophic barotropic model and compare the known SVs from that model with SVs estimated from a surrogate data set that was generated with the help of the exact model propagator and some
Energy Technology Data Exchange (ETDEWEB)
Xing, Zhanqiang; Qu, Jianfeng; Chai, Yi; Tang, Qiu; Zhou, Yuming [Chongqing University, Chongqing (China)
2017-02-15
The gear vibration signal is nonlinear and non-stationary, gear fault diagnosis under variable conditions has always been unsatisfactory. To solve this problem, an intelligent fault diagnosis method based on Intrinsic time-scale decomposition (ITD)-Singular value decomposition (SVD) and Support vector machine (SVM) is proposed in this paper. The ITD method is adopted to decompose the vibration signal of gearbox into several Proper rotation components (PRCs). Subsequently, the singular value decomposition is proposed to obtain the singular value vectors of the proper rotation components and improve the robustness of feature extraction under variable conditions. Finally, the Support vector machine is applied to classify the fault type of gear. According to the experimental results, the performance of ITD-SVD exceeds those of the time-frequency analysis methods with EMD and WPT combined with SVD for feature extraction, and the classifier of SVM outperforms those for K-nearest neighbors (K-NN) and Back propagation (BP). Moreover, the proposed approach can accurately diagnose and identify different fault types of gear under variable conditions.
Singular vector decomposition of the internal variability of the Canadian Regional Climate Model
Energy Technology Data Exchange (ETDEWEB)
Diaconescu, Emilia Paula; Laprise, Rene [University of Quebec at Montreal (UQAM), Department of Earth and Atmospheric Sciences, Canadian Network for Regional Climate Modelling and Diagnostics, P.O. Box 8888, Montreal, QC (Canada); Centre ESCER (Etude et Simulation du Climat a l' Echelle Regionale), Montreal, QC (Canada); Zadra, Ayrton [University of Quebec at Montreal (UQAM), Department of Earth and Atmospheric Sciences, Canadian Network for Regional Climate Modelling and Diagnostics, P.O. Box 8888, Montreal, QC (Canada); Environment Canada, Meteorological Research Division, Montreal, QC (Canada); Centre ESCER (Etude et Simulation du Climat a l' Echelle Regionale), Montreal, QC (Canada)
2012-03-15
Previous studies have shown that Regional Climate Models (RCM) internal variability (IV) fluctuates in time depending on synoptic events. This study focuses on the physical understanding of episodes with rapid growth of IV. An ensemble of 21 simulations, differing only in their initial conditions, was run over North America using version 5 of the Canadian RCM (CRCM). The IV is quantified in terms of energy of CRCM perturbations with respect to a reference simulation. The working hypothesis is that IV is arising through rapidly growing perturbations developed in dynamically unstable regions. If indeed IV is triggered by the growth of unstable perturbations, a large proportion of the CRCM perturbations must project onto the most unstable singular vectors (SVs). A set of ten SVs was computed to identify the orthogonal set of perturbations that provide the maximum growth with respect to the dry total-energy norm during the course of the CRCM ensemble of simulations. CRCM perturbations were then projected onto the subspace of SVs. The analysis of one episode of rapid growth of IV is presented in detail. It is shown that a large part of the IV growth is explained by initially small-amplitude unstable perturbations represented by the ten leading SVs, the SV subspace accounting for over 70% of the CRCM IV growth in 36 h. The projection on the leading SV at final time is greater than the projection on the remaining SVs and there is a high similarity between the CRCM perturbations and the leading SV after 24-36 h tangent-linear model integration. The vertical structure of perturbations revealed that the baroclinic conversion is the dominant process in IV growth for this particular episode. (orig.)
Sampling strategies based on singular vectors for assimilated models in ocean forecasting systems
Fattorini, Maria; Brandini, Carlo; Ortolani, Alberto
2016-04-01
Meteorological and oceanographic models do need observations, not only as a ground truth element to verify the quality of the models, but also to keep model forecast error acceptable: through data assimilation techniques which merge measured and modelled data, natural divergence of numerical solutions from reality can be reduced / controlled and a more reliable solution - called analysis - is computed. Although this concept is valid in general, its application, especially in oceanography, raises many problems due to three main reasons: the difficulties that have ocean models in reaching an acceptable state of equilibrium, the high measurements cost and the difficulties in realizing them. The performances of the data assimilation procedures depend on the particular observation networks in use, well beyond the background quality and the used assimilation method. In this study we will present some results concerning the great impact of the dataset configuration, in particular measurements position, on the evaluation of the overall forecasting reliability of an ocean model. The aim consists in identifying operational criteria to support the design of marine observation networks at regional scale. In order to identify the observation network able to minimize the forecast error, a methodology based on Singular Vectors Decomposition of the tangent linear model is proposed. Such a method can give strong indications on the local error dynamics. In addition, for the purpose of avoiding redundancy of information contained in the data, a minimal distance among data positions has been chosen on the base of a spatial correlation analysis of the hydrodynamic fields under investigation. This methodology has been applied for the choice of data positions starting from simplified models, like an ideal double-gyre model and a quasi-geostrophic one. Model configurations and data assimilation are based on available ROMS routines, where a variational assimilation algorithm (4D-var) is
International Nuclear Information System (INIS)
Sun Bin; Zhou Yunlong; Zhao Peng; Guan Yuebo
2007-01-01
Aiming at the non-stationary characteristics of differential pressure fluctuation signals of gas-liquid two-phase flow, and the slow convergence of learning and liability of dropping into local minima for BP neural networks, flow regime identification method based on Singular Value Decomposition (SVD) and Least Square Support Vector Machine (LS-SVM) is presented. First of all, the Empirical Mode Decomposition (EMD) method is used to decompose the differential pressure fluctuation signals of gas-liquid two-phase flow into a number of stationary Intrinsic Mode Functions (IMFs) components from which the initial feature vector matrix is formed. By applying the singular vale decomposition technique to the initial feature vector matrixes, the singular values are obtained. Finally, the singular values serve as the flow regime characteristic vector to be LS-SVM classifier and flow regimes are identified by the output of the classifier. The identification result of four typical flow regimes of air-water two-phase flow in horizontal pipe has shown that this method achieves a higher identification rate. (authors)
Energy Technology Data Exchange (ETDEWEB)
Ham, Yoo-Geun [NASA/GSFC Code 610.1, Global Modeling and Assimilation Office, Greenbelt, MD (United States); Universities Space Research Association, Goddard Earth Sciences Technology and Research Studies and Investigations, Baltimore, MD (United States); Rienecker, Michele M. [NASA/GSFC Code 610.1, Global Modeling and Assimilation Office, Greenbelt, MD (United States)
2012-10-15
In this study, a new approach for extracting flow-dependent empirical singular vectors (FESVs) for seasonal prediction using ensemble perturbations obtained from an ensemble Kalman filter (EnKF) assimilation is presented. Due to the short interval between analyses, EnKF perturbations primarily contain instabilities related to fast weather variability. To isolate slower, coupled instabilities that would be more suitable for seasonal prediction, an empirical linear operator for seasonal time-scales (i.e. several months) is formulated using a causality hypothesis; then, the most unstable mode from the linear operator is extracted for seasonal time-scales. It is shown that the flow-dependent operator represents nonlinear integration results better than a conventional empirical linear operator static in time. Through 20 years of retrospective seasonal predictions, it is shown that the skill of forecasting equatorial SST anomalies using the FESV is systematically improved over that using Conventional ESV (CESV). For example, the correlation skill of the NINO3 SST index using FESV is higher, by about 0.1, than that of CESV at 8-month leads. In addition, the forecast skill improvement is significant over the locations where the correlation skill of conventional methods is relatively low, indicating that the FESV is effective where the initial uncertainty is large. (orig.)
International Nuclear Information System (INIS)
McCreery, P.N.
1981-11-01
This report presents an operational assessment of the FSV-1 spent fuel shipping cask which was developed by General Atomic specifically for the Fort St. Vrain reactor. Of primary interest is the adaptation to underwater loading and unloading of light-water-reactor (LWR) fuel in this cask which was designed for the dry-handling of high temperature gas cooled reactor (HTGR) fuel. Also presented is a concept for a system to compare the pros and cons of wet and dry handling of this and other casks
Genome-Wide Analysis of DNA Methylation During Ovule Development of Female-Sterile Rice fsv1
Directory of Open Access Journals (Sweden)
Helian Liu
2017-11-01
Full Text Available The regulation of female fertility is an important field of rice sexual reproduction research. DNA methylation is an essential epigenetic modification that dynamically regulates gene expression during development processes. However, few reports have described the methylation profiles of female-sterile rice during ovule development. In this study, ovules were continuously acquired from the beginning of megaspore mother cell meiosis until the mature female gametophyte formation period, and global DNA methylation patterns were compared in the ovules of a high-frequency female-sterile line (fsv1 and a wild-type rice line (Gui99 using whole-genome bisulfite sequencing (WGBS. Profiling of the global DNA methylation revealed hypo-methylation, and 3471 significantly differentially methylated regions (DMRs were observed in fsv1 ovules compared with Gui99. Based on functional annotation and Kyoto encyclopedia of genes and genomes (KEGG pathway analysis of differentially methylated genes (DMGs, we observed more DMGs enriched in cellular component, reproduction regulation, metabolic pathway, and other pathways. In particular, many ovule development genes and plant hormone-related genes showed significantly different methylation patterns in the two rice lines, and these differences may provide important clues for revealing the mechanism of female gametophyte abortion.
Riwinoto
2012-01-01
Sekarang ini, metode clustering telah diimplementasikan dalam riset DNA. Data dari DNA didapat melalui teknik microarray. Dengan menggunakan metode teknik SVD, dimensi data dikurangi sehingga mempermudah proses komputasi. Dalam paper ini, ditampilkan hasil clustering tanpa pengarahan terhadap gen-gen dari data bakteri ragi dengan menggunakan metode quantum clustering. Sebagai pembanding, dilakukan juga clustering menggunakan metoda Support Vector Clustering. Selain itu juga ditampilkan data h...
Directory of Open Access Journals (Sweden)
IMRAN, M.
2017-11-01
Full Text Available A novel secure and robust image watermarking technique for color images is presented in this paper. Besides robustness and imperceptibility (which are the most important requisites of any watermarking scheme, there are two other challenges a good watermarking scheme must meet: security and capacity. Therefore, in devising the presented scheme, special consideration is also given to above-mentioned requirements. In order to do so, principal component analysis is involved to enhance imperceptibility and the unique utilization of singular value decomposition is done to achieve better performance in regard to capacity and robustness. Finally, a novel method is proposed to select constituents of an image for watermark embedding, which further improves the security. As a consequence, four essential requisites of a good watermarking scheme are achieved as visible from experimental results. To measure the behavior of presented watermarking scheme, a number of experiments were conducted by utilizing several color images as host images and as watermarks. The presented technique is compared with the latest available watermarking techniques and attained better results than them.
Energy Technology Data Exchange (ETDEWEB)
Martin, William R.; Lee, John C.; baxter, Alan; Wemple, Chuck
2012-03-31
Information and measured data from the intial Fort St. Vrain (FSV) high temperature gas reactor core is used to develop a benchmark configuration to validate computational methods for analysis of a full-core, commercial HTR configuration. Large uncertainties in the geometry and composition data for the FSV fuel and core are identified, including: (1) the relative numbers of fuel particles for the four particle types, (2) the distribution of fuel kernel diameters for the four particle types, (3) the Th:U ratio in the initial FSV core, (4) and the buffer thickness for the fissile and fertile particles. Sensitivity studies were performed to assess each of these uncertainties. A number of methods were developed to assist in these studies, including: (1) the automation of MCNP5 input files for FSV using Python scripts, (2) a simple method to verify isotopic loadings in MCNP5 input files, (3) an automated procedure to conduct a coupled MCNP5-RELAP5 analysis for a full-core FSV configuration with thermal-hydraulic feedback, and (4) a methodology for sampling kernel diameters from arbitrary power law and Gaussian PDFs that preserved fuel loading and packing factor constraints. A reference FSV fuel configuration was developed based on having a single diameter kernel for each of the four particle types, preserving known uranium and thorium loadings and packing factor (58%). Three fuel models were developed, based on representing the fuel as a mixture of kernels with two diameters, four diameters, or a continuous range of diameters. The fuel particles were put into a fuel compact using either a lattice-bsed approach or a stochastic packing methodology from RPI, and simulated with MCNP5. The results of the sensitivity studies indicated that the uncertainties in the relative numbers and sizes of fissile and fertile kernels were not important nor were the distributions of kernel diameters within their diameter ranges. The uncertainty in the Th:U ratio in the intial FSV core was
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.
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...... on the most salient vectors, and this works well, but many images contain a plethora of vectors, which makes their structure quite different from the linguistic transitivity structures with which Kress and van Leeuwen have compared ‘narrative’ images. It can also be asked whether facial expression vectors...... should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined...
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...... should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined...
A Note on Inclusion Intervals of Matrix Singular Values
Cui, Shu-Yu; Tian, Gui-Xian
2012-01-01
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.
Stonesifer, R. B.; Atluri, S. N.
1982-01-01
The physical meaning of (Delta T)c and its applicability to creep crack growth are reviewed. Numerical evaluation of (Delta T)c and C(asterisk) is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.
Interaction of two singular Lissajous lines in free space.
Chen, Haitao; Gao, Zenghui; Wang, Wanqing
2017-05-20
The interaction of two singular Lissajous lines emergent from a polychromatic vector beam is studied. It is shown that singular Lissajous lines disappear with propagation; meanwhile Lissajous singularities take place. The handedness reversal, the changes in the shape of Lissajous figures, and the degree of polarization of Lissajous singularities, as well as the creation and annihilation of a single singularity, may appear by varying the control parameters. In addition, the transformation of the shape of line h=0, the creation and annihilation of pairs of Lissajous singularities not only with opposite topological charge and same handedness, but also with same degree of polarization, take place with propagation.
Singular Dimensions of theN= 2 Superconformal Algebras. I
Dörrzapf, Matthias; Gato-Rivera, Beatriz
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3).
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.
Polynomial computation of Hankel singular values
Kwakernaak, H.
1992-01-01
A revised and improved version of a polynomial algorithm is presented. It was published by N.J. Young (1990) for the computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with a rotational transfer matrix. Tentative numerical experiments
Geodesic fields with singularities
International Nuclear Information System (INIS)
Kafker, A.H.
1979-01-01
The question considered is whether or not a Riemannian metric can be found to make a given curve field on a closed surface into geodesics. Allowing singularities removes the restriction to Euler characteristic zero. The main results are the following: only two types of isolated singularities can occur in a geodesic field on a surface. No geodsic fields exist on a surface with Euler characteristic less than zero. If the Euler characteristic is zero, such a geodesic field can have only removable singularities. Only a limited number of geodesic fields exist on S 2 and RP 2 . A closed geodesic (perhaps made from several curves and singularities) always appears in such a field
Singularity and dynamics on discontinuous vector fields
Luo, Albert CJ
2006-01-01
This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional
Isotopy of Morin singularities
Saji, Kentaro
2015-01-01
We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.
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...
String theory and cosmological singularities
Indian Academy of Sciences (India)
time' can have a beginning or end. 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 ...
Juang, Jer-Nan; Kim, Hye-Young; Junkins, John L.
2003-01-01
A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value comparison is that a pairing process for individual measured and cataloged stars is not necessary, and the attitude estimation and pattern recognition process are not separated. An associated method for mission catalog design is introduced and simulation results are presented.
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.
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 Approaches to Spacetime Singularities
Directory of Open Access Journals (Sweden)
Beverly K. Berger
1998-05-01
Full Text Available This review updates a previous review article. Numerical explorationof the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
Directory of Open Access Journals (Sweden)
Akira R Kinjo
Full Text Available Position-specific scoring matrices (PSSMs are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.
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.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good Mathematics from Bad Lenses. Rajaram Nityananda. General Article Volume 19 Issue 9 September 2014 pp 787-796. Fulltext. Click here to view fulltext PDF. Permanent link:
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good ... Author Affiliations. Rajaram Nityananda1. Azim Premji University, PES Institute of Technology Campus, Pixel Park, B Block, Electronics City, Hosur Road (Beside NICE Road) Bangalore – 560100 ...
Indian Academy of Sciences (India)
IAS Admin
Standard presentations of optics concentrate on ideal systems made for imaging which bring all rays from a point ... One of the standard topics we study in school is the action of a spherical mirror. Figure 1 shows a set of ..... singularities of smooth maps, and the beauty of the mathematics needed to understand them, Arnold ...
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...
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...
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
Classification of subsurface objects using singular values derived from signal frames
Chambers, David H; Paglieroni, David W
2014-05-06
The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.
Singular potentials in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Aguilera-Navarro, V.C. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Koo, E. Ley [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica
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.
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
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.
Infinitesimal Structure of Singularities
Directory of Open Access Journals (Sweden)
Michael Heller
2017-02-01
Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.
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...
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...
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....
Image Fakery Detection Based on Singular Value Decomposition
Directory of Open Access Journals (Sweden)
T. Basaruddin
2009-11-01
Full Text Available The growing of image processing technology nowadays make it easier for user to modify and fake the images. Image fakery is a process to manipulate part or whole areas of image either in it content or context with the help of digital image processing techniques. Image fakery is barely unrecognizable because the fake image is looking so natural. Yet by using the numerical computation technique it is able to detect the evidence of fake image. This research is successfully applied the singular value decomposition method to detect image fakery. The image preprocessing algorithm prior to the detection process yields two vectors orthogonal to the singular value vector which are important to detect fake image. The result of experiment to images in several conditions successfully detects the fake images with threshold value 0.2. Singular value decomposition-based detection of image fakery can be used to investigate fake image modified from original image accurately.
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)
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)
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.
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
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. In this article, we describe some of these approaches. Keywords. String theory; cosmological singularities. PACS Nos 11.25.
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.
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
Singular traces theory and applications
Sukochev, Fedor; Zanin, Dmitriy
2012-01-01
This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Electricity consumption forecasting using singular spectrum analysis
Directory of Open Access Journals (Sweden)
Moisés Lima de Menezes
2015-01-01
Full Text Available El Análisis Espectral Singular (AES es una técnica no paramétrica que permite la descomposición de una serie de tiempo en una componente de señal y otra de ruido. De este modo, AES es una técnica útil para la extracción de la tendencia, la suavización y el filtro una serie de tiempo. En este artículo se investiga el efecto sobre el desempeño los modelos de Holt-Winters y de Box & Jenkins al ser aplicados a una serie de tiempo filtrada por AES. Tres diferentes metodologías son evaluadas con el enfoque de AES: Análisis de Componentes Principales (ACP, análisis de conglomerados y análisis gráfico de vectores singulares. Con el fin de ilustrar y comparar dichas metodologías, en este trabajo también se presentaron los principales resultados de un experimento computacional para el consumo residencial mensual de electricidad en Brasil.
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
The index of a holomorphic flow with an isolated singularity
International Nuclear Information System (INIS)
Verjovsky, A.; Gomez-Mont, X.; Seade, J.
1987-05-01
The index of a holomorphic vector field Z defined on a germ of a hypersurface V with an isolated singularity is defined. The index coincides with the Hopf index in the smooth case. Formulae for the index in terms of the ideals defining Z and V are given. Topological invariance of the index and the Chern class as well as formulae relating global invariants of the Poincare-Hopf type are proven. (author). 26 refs
Optical vortices and singularities due to interference in atomic radiation near a mirror.
Li, Xin; Shu, Jie; Arnoldus, Henk F
2009-11-15
We consider radiation emitted by an electric dipole close to a mirror. We have studied the field lines of the Poynting vector, representing the flow lines of the electromagnetic energy, and we show that numerous singularities and subwavelength optical vortices appear in this energy flow pattern. We also show that the field line pattern in the plane of the mirror contains a singular circle across which the field lines change direction.
Brane singularities and their avoidance
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros; Klaoudatou, Ifigeneia
2010-01-01
The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state P = γρ between the 'pressure' P and the 'density' ρ, our results depend crucially on the constant fluid parameter γ. (i) For γ > -1/2, the flat brane solution suffers from a collapse singularity at a finite distance that disappears in the curved case. (ii) For γ < -1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1 < γ ≤ -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.
Inverse Kinematics and Singularity Analysis for a 3-DOF Hybrid-Driven Cable-Suspended Parallel Robot
Directory of Open Access Journals (Sweden)
Bin Zi
2012-10-01
Full Text Available This paper addresses the kinematics and graphical representation of the singularity configuration of a hybrid-driven cable-suspended parallel robot (HDCPR with three translational degrees of freedom (DOFs. Applying the closed-loop vector method and geometric methodology, inverse kinematics of the HDCPR needed for singularity analysis is performed. For the sake of singularity condition calculation within the reachable workspace, the procedure utilizing analytical methodology and gradual search algorithm is presented. Simulation results demonstrate the validity of the kinematics and singularity analysis developed.
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
International Nuclear Information System (INIS)
Chen, Yu-Zhu; Li, Wen-Du; Dai, Wu-Sheng
2017-01-01
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.)
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.)
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.
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
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
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.)
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
We propose the concept of 'effective naked singularities', which will be quite helpful ... If a pressure gradient force is not sufficiently strong, a body can continue collapsing due to its self-gravity. This phenomenon is called gravitational collapse. .... approaches a self-similar solution, which is called a critical solution, and then it.
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
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Abstract. Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of ...
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
of space and time needs revision near these singularities where quantum effects of gravity become important, it is still not clear what structure could replace space ..... The dimensionful parameter μ is a Lagrange multiplier which ensures that the total number of eigenvalues is fixed. 98. Pramana – J. Phys., Vol. 69, No. 1, July ...
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
0 < w ∈ L1 loc(Rn): sup x∈Q w(Q). |Q|. ≤ Cw(x), a.e.. } and. A∞ = ⋃. 1≤p<∞. Ap. DEFINITION. (1) Let 0 <δ
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)
Singularities and Conjugate Points in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a theorem that when a non-comoving, non-spacelike geodesic in a
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)
Singularities formation, structure, and propagation
Eggers, J
2015-01-01
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Historical developments in singular perturbations
O'Malley, Robert E
2014-01-01
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
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
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstra......This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Directory of Open Access Journals (Sweden)
Borbon Martin de
2017-02-01
Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.
Fundamental solutions of singular SPDEs
Energy Technology Data Exchange (ETDEWEB)
Selesi, Dora, E-mail: dora@dmi.uns.ac.rs [Department of Mathematics and Informatics, University of Novi Sad (Serbia)
2011-07-15
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({omega}, D) Lozenge u(x, {omega}) = A(x, {omega}) are considered, where A is a singular generalized stochastic process and P({omega}, 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 Lozenge I{sup Lozenge (-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...
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.
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.
Flavour from partially resolved singularities
Energy Technology Data Exchange (ETDEWEB)
Bonelli, G. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy)]. E-mail: bonelli@sissa.it; Bonora, L. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy); Ricco, A. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy)
2006-06-15
In this Letter we study topological open string field theory on D-branes in a IIB background given by non-compact CY geometries O(n)-bar O(-2-n) on P{sup 1} with a singular point at which an extra fiber sits. We wrap N D5-branes on P{sup 1} and M effective D3-branes at singular points, which are actually D5-branes wrapped on a shrinking cycle. We calculate the holomorphic Chern-Simons partition function for the above models in a deformed complex structure and find that it reduces to multi-matrix models with flavour. These are the matrix models whose resolvents have been shown to satisfy the generalized Konishi anomaly equations with flavour. In the n=0 case, corresponding to a partial resolution of the A{sub 2} singularity, the quantum superpotential in the N=1 unitary SYM with one adjoint and M fundamentals is obtained. The n=1 case is also studied and shown to give rise to two-matrix models which for a particular set of couplings can be exactly solved. We explicitly show how to solve such a class of models by a quantum equation of motion technique.
Quantum singular-value decomposition of nonsparse low-rank matrices
Rebentrost, Patrick; Steffens, Adrian; Marvian, Iman; Lloyd, Seth
2018-01-01
We present a method to exponentiate nonsparse indefinite low-rank matrices on a quantum computer. Given access to the elements of the matrix, our method allows one to determine the singular values and their associated singular vectors in time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and nonsquare matrices via matrix embedding. Moreover, our method preserves the phase relations between the singular spaces allowing for efficient algorithms that require operating on the entire singular-value decomposition of a matrix. As an example of such an algorithm, we discuss the Procrustes problem of finding a closest isometry to a given matrix.
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.
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)
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.
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.
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.
Non-coaxial superposition of vector vortex beams.
Aadhi, A; Vaity, Pravin; Chithrabhanu, P; Reddy, Salla Gangi; Prabakar, Shashi; Singh, R P
2016-02-10
Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams. It is observed that the superposition of two vector vortex beams with same polarization singularity leads to a beam with another kind of polarization singularity in their interaction region. The results may be of importance in ultrahigh security of the polarization-encrypted data that utilizes vector vortex beams and multiple optical trapping with non-coaxial superposition of vector vortex beams. We verified our experimental results with theory.
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
DEKOMPOSISI NILAI SINGULAR PADA SISTEM PENGENALAN WAJAH
Beni Utomo
2012-01-01
Dekomposisi Nilai Singular atau Singular Value Decomposition (SVD)merupakan salah satu cara untuk menyatakan Principal Component Analysis (PCA).PCA sendiri merupakan suatu proses untuk menemukan kontributor-kontributorpenting dari suatu data berdasarkan besaran statistika deviasi standart dan variansi.SVD merupakan proses untuk mendapatkan matriks diagonal yang elementak nolnya merupakan nilai singular yang akarnya merupakan eigenvalue.SVD atas matriks kovarian C berbentuk C = U?V T dengan ma...
Box graphs and singular fibers
International Nuclear Information System (INIS)
Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schäfer-Nameki, Sakura
2014-01-01
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6 , E 7 and E 8
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.
Dissipative control for singular impulsive dynamical systems
Directory of Open Access Journals (Sweden)
Li Yang
2012-04-01
Full Text Available The aim of this work is to study the dissipative control problem for singular impulsive dynamical systems. We start by introducing the impulse to the singular systems, and give the definition of the dissipation for singular impulsive dynamical systems. Then we discuss the dissipation of singular impulsive dynamical systems, we obtain some sufficient and necessary conditions for dissipation of these systems by solving some linear matrix inequalities (LMIs. By using this method, we design a state feedback controller to make the closed-loop system dissipative. At last, we testify the feasibility of the method by a numerical example.
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.
Wavelength Dependence of the Polarization Singularities in a Two-Mode Optical Fiber
Directory of Open Access Journals (Sweden)
V. V. G. Krishna Inavalli
2012-01-01
Full Text Available We present here an experimental demonstration of the wavelength dependence of the polarization singularities due to linear combination of the vector modes excited directly in a two-mode optical fiber. The coherent superposition of the vector modes excited by linearly polarized Gaussian beam as offset skew rays propagated in a helical path inside the fiber results in the generation of phase singular beams with edge dislocation in the fiber output. The polarization character of these beams is found to change dramatically with wavelength—from left-handed elliptically polarized edge dislocation to right-handed elliptically polarized edge-dislocation through disclinations. The measured behaviour is understood as being due to intermodal dispersion of the polarization corrections to the propagating vector modes, as the wavelength of the input beam is scanned.
Newell, Homer E
2006-01-01
When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and e
Hoffmann, Banesh
1975-01-01
From his unusual beginning in ""Defining a vector"" to his final comments on ""What then is a vector?"" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar p
The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions
Huang, Jianhua Z.
2009-12-01
Two-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from oneway regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross- validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several "natural" approaches to penalized SVDs are flawed and explain why so. © 2009 American Statistical Association.
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.
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.
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)
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...
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 ...
Spectral analysis for differential operators with singularities
Directory of Open Access Journals (Sweden)
Vjacheslav Anatoljevich Yurko
2004-01-01
Full Text Available Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.
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
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...
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 delay...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
in terms of the incompleteness of non-space-like geodesics in spacetime. It is possible that such ... outside. The above discussion does not imply the absence of singularity-free solutions to Einstein's equations. ..... spherical collapse also turns out to be a stable feature as implied by the singularity theorems discussed above.
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.
Nietzsche, immortality, singularity and eternal recurrence | Olivier ...
African Journals Online (AJOL)
Moreover, once anything has existed, it is in a certain sense, for Nietzsche, necessary despite its temporal singularity. Therefore, to be able to rise to the task of affirming certain actions or experiences in one's own life, bestows on it not merely this kind of necessary singularity, but what he thought of as 'eternal recurrence' –
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...
Singularity is the Future of ICT Research
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
2014-06-01
Jun 1, 2014 ... tech systems, and how in the near future. Artificial Intelligence may impact our lives, AI, Robotics, nanotechnology, mechatronics are collaborative agents of technological singularity. The singularity is already here! Think of modern houses now remotely controlled from far distances, think of e-commerce and.
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...
Singularity: Scientific containers for mobility of compute.
Directory of Open Access Journals (Sweden)
Gregory M Kurtzer
Full Text Available Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science.
32 CFR 1602.22 - Singular and plural.
2010-07-01
....22 Singular and plural. Words importing the singular number shall include the plural number, and words importing the plural number shall include the singular, except where the context clearly indicates...
Wolstenholme, E Œ
1978-01-01
Elementary Vectors, Third Edition serves as an introductory course in vector analysis and is intended to present the theoretical and application aspects of vectors. The book covers topics that rigorously explain and provide definitions, principles, equations, and methods in vector analysis. Applications of vector methods to simple kinematical and dynamical problems; central forces and orbits; and solutions to geometrical problems are discussed as well. This edition of the text also provides an appendix, intended for students, which the author hopes to bridge the gap between theory and appl
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
Topology of singular fibers of differentiable maps
Saeki, Osamu
2004-01-01
The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.
Quantization function for attractive, singular potential tails
International Nuclear Information System (INIS)
Raab, Patrick N.
2010-01-01
The interaction between atoms and molecules with each other are deep potential wells with attractive, singular tails. Bound state energies are determined by a quantization function according to a simple quantization rule. This function is dominantly determined by the singular potential tail for near-threshold states. General expressions for the low- and high-energy contributions of the singular potential tail to the quantization function, as well as the connection to the scattering length are presented in two and three dimensions. Precise analytical expressions for the quantization function are determined for the case of potential tails proportional to -1/r 4 and -1/r 6 for three dimensions. (orig.)
DEKOMPOSISI NILAI SINGULAR PADA SISTEM PENGENALAN WAJAH
Directory of Open Access Journals (Sweden)
Beni Utomo
2012-11-01
Full Text Available Dekomposisi Nilai Singular atau Singular Value Decomposition (SVDmerupakan salah satu cara untuk menyatakan Principal Component Analysis (PCA.PCA sendiri merupakan suatu proses untuk menemukan kontributor-kontributorpenting dari suatu data berdasarkan besaran statistika deviasi standart dan variansi.SVD merupakan proses untuk mendapatkan matriks diagonal yang elementak nolnya merupakan nilai singular yang akarnya merupakan eigenvalue.SVD atas matriks kovarian C berbentuk C = U?V T dengan matriks U dan Vmemuat eigenvektor yang sudah terurut dari nilai variansi terbesar ke nilai variansiterkecilnya. Variansi terbesar memiliki arti eigenvektor menangkap ciri-ciri yangpaling banyak berubah. Sifat inilah yang dipakai untuk membentuk eigenface.
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 $m^{-1}$.
Brand, Louis
2006-01-01
The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brou
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.
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.
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.
Approximate Uniqueness Estimates for Singular Correlation Matrices.
Finkbeiner, C. T.; Tucker, L. R.
1982-01-01
The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)
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}.
Finite conformal quantum gravity and spacetime singularities
Modesto, Leonardo; Rachwał, Lesław
2017-12-01
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.
Geometric Singularities of the Stokes Problem
Directory of Open Access Journals (Sweden)
Nejmeddine Chorfi
2014-01-01
Full Text Available When the domain is a polygon of ℝ2, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.
Singularity analysis, Hadamard products, and tree recurrences
Fill, James Allen; Flajolet, Philippe; Kapur, Nevin
2005-02-01
We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relations.
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.)
Singular Continuous Floquet Operator for Periodic Quantum Systems
Bourget, O
2004-01-01
Consider the Floquet operator of a time independent quantum system, acting on a separable Hilbert space, periodically perturbed by a rank one kick: $e^{-iH_0T}e^{-i\\kappa T |\\phi\\ket\\bra\\phi|}$ where $T$, $\\kappa$ are respectively the period and the coupling constant and $H_0$ is a pure point self-adjoint operator, bounded from below. Under some hypotheses on the vector $\\phi$, cyclic for $H_0$ we prove the following: If the gaps between the eigenvalues $(\\lambda_n)$ are such that: $\\lambda_{n+1}-\\lambda_{n}\\geq C n^{-\\gamma}$ for some $\\gamma \\in ]0,1[$ and $C>0$, then the Floquet operator of the perturbed system is purely singular continuous T-a.e. If $H_0$ is the Hamiltonian of the one-dimensional rotator on $L^2({\\mathbb R}/T_0{\\mathbb Z})$ and the ratio $2\\pi T/T_0^2$ is irrational, then the Floquet operator is purely singular continuous as soon as $\\kappa T \
DEFF Research Database (Denmark)
2012-01-01
The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...
Singular Continuous Floquet Operator for Systems with Increasing Gaps
Bourget, O
2002-01-01
Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: $e^{-iH_0T}e^{-i\\kappa T |\\phi \\ket \\bra \\phi|}$ where $T$ and $\\kappa$ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator $H_0$ is pure point, simple, bounded from below and the gaps between the eigenvalues $(\\lambda_n)$ grow like: $\\lambda_{n+1} - \\lambda_{n} \\sim C n^d$ with $d \\geq 2$. Under some hypotheses on the arithmetical nature of the eigenvalues and on the vector $\\phi$, cyclic for $H_0$, we prove the Floquet operator of the perturbed system has purely singular continuous spectrum.
Guilfoyle, R.A.; Smith, L.M.
1994-12-27
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site. 2 figures.
Guilfoyle, Richard A.; Smith, Lloyd M.
1994-01-01
A vector comprising a filamentous phage sequence containing a first copy of filamentous phage gene X and other sequences necessary for the phage to propagate is disclosed. The vector also contains a second copy of filamentous phage gene X downstream from a promoter capable of promoting transcription in a bacterial host. In a preferred form of the present invention, the filamentous phage is M13 and the vector additionally includes a restriction endonuclease site located in such a manner as to substantially inactivate the second gene X when a DNA sequence is inserted into the restriction site.
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.
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.
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.)
Modeling material failure with a vectorized routine
Cramer, S. M.; Goodman, J. R.
1984-01-01
The computational aspects of modelling material failure in structural wood members are presented with particular reference to vector processing aspects. Wood members are considered to be highly orthotropic, inhomogeneous, and discontinuous due to the complex microstructure of wood material and the presence of natural growth characteristics such as knots, cracks and cross grain in wood members. The simulation of strength behavior of wood members is accomplished through the use of a special purpose finite element/fracture mechanics routine, program STARW (Strength Analysis Routine for Wood). Program STARW employs quadratic finite elements combined with singular crack tip elements in a finite element mesh. Vector processing techniques are employed in mesh generation, stiffness matrix formation, simultaneous equation solution, and material failure calculations. The paper addresses these techniques along with the time and effort requirements needed to convert existing finite element code to a vectorized version. Comparisons in execution time between vectorized and nonvectorized routines are provided.
Are Bred Vectors The Same As Lyapunov Vectors?
Kalnay, E.; Corazza, M.; Cai, M.
Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the
Ran, Changyan; Cheng, Xianghong
2016-09-02
This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method.
Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space
DEFF Research Database (Denmark)
Brander, David
2011-01-01
We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space L-3. We show how to solve the singular Bjorling problem for such surfaces, which is stated as follows: given a real analytic null-curve f(0)(x), and a real analytic null vector...... field v(x) parallel to the tangent field of f(0), find a conformally parameterized (generalized) CMC H surface in L-3 which contains this curve as a singular set and such that the partial derivatives f(x) and f(y) are given by df(0)/dx and v along the curve. Within the class of generalized surfaces...... considered, the solution is unique and we give a formula for the generalized Weierstrass data for this surface. This gives a framework for studying the singularities of non-maximal CMC surfaces in L-3. We use this to find the Bjorling data - and holomorphic potentials - which characterize cuspidal edge...
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
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating ...
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
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
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 ...
Singular Nonlinear H∞ Optimal Control Problem
Schaft, A.J. van der
1996-01-01
The theory of nonlinear H∞ optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
Ray tracing in anisotropic media with singularities
Czech Academy of Sciences Publication Activity Database
Vavryčuk, Václav
2001-01-01
Roč. 145, č. 1 (2001), s. 265-276 ISSN 0956-540X R&D Projects: GA ČR GA205/00/1350 Institutional research plan: CEZ:AV0Z3012916 Keywords : anisotropic media * ray tracing * singularities Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.366, year: 2001
Inverting dedevelopment: geometric singularity theory in embryology
Bookstein, Fred L.; Smith, Bradley R.
2000-10-01
The diffeomorphism model so useful in the biomathematics of normal morphological variability and disease is inappropriate for applications in embryogenesis, where whole coordinate patches are created out of single points. For this application we need a suitable algebra for the creation of something from nothing in a carefully organized geometry: a formalism for parameterizing discrete nondifferentiabilities of invertible functions on Rk, k $GTR 1. One easy way to begin is via the inverse of the development map - call it the dedevelopment map, the deformation backwards in time. Extrapolated, this map will inevitably have singularities at which its derivative is zero. When the dedevelopment map is inverted to face forward in time, the singularities become appropriately isolated infinities of derivative. We have recently introduced growth visualizations via extrapolations to the isolated singularities at which only one directional derivative is zero. Maps inverse to these create new coordinate patches directionally rather than radically. The most generic singularity that suits this purpose is the crease f(x,y) equals (x,x2y+y3), which has already been applied in morphometrics for the description of focal morphogenetic phenomena. We apply it to embryogenesis in the form of its analytic inverse, and demonstrate its power using a priceless new data set of mouse embryos imaged in 3D by micro-MR with voxels smaller than 100micrometers 3.
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
the framework of a general spacetime without any symmetry conditions, in terms of the overall behaviour of .... We now outline the basic idea and the chain of logic behind the proof of a typical singularity theorem ..... a detailed investigation of the dynamics of gravitational collapse within the frame- work of Einstein's theory.
'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
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
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 $D(\\alpha)$.
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.
Wave Vector Dependent Susceptibility at T>Tc in a Dipolar Ising Ferromagnet
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Holmes, L. M:; Guggenheim, H. J.
1974-01-01
The wave-vector-dependent susceptibility of LiTbF4 has been investigated by means of neutron scattering. The observations show a singularity of the susceptibility near wave vector Q=0 which is characteristic of the dipolar Coulomb interaction and good agreement with theory is obtained...
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
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
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
... )) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a `big' subset of the true initial data set ...
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.
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. Keywords. Positive solution; singular BVPs; sufficient and necessary conditions; p-Laplacian equations. 1. Introduction. In this paper, we are concerned with higher order singular p-Laplacian boundary value problems. ⎧. ⎨. ⎩.
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.
The principal part of plane vector fields with fixed Newton diagram
International Nuclear Information System (INIS)
Berezovskaya, F.
1991-09-01
Considering the main part of a plane vector field in a neighbourhood of a singular point 0(0,0) it is well known that if the singularity real parts of eigenvalues are non-zero, the linear part of the vector field provides the topological normal form and tangents of all the o-curves. The problem is to find the main part of a plane vector field which would provide the topological orbital normal form in a neighbourhood of singular point and asymptotics of all characteristics trajectories. In this work the solution to the problem for the generic ease of so-called nondegenerate vector fields, using Newton diagram is given. 13 refs, 5 figs
Energy Technology Data Exchange (ETDEWEB)
Emery, L.
1999-04-13
Magnet errors and off-center orbits through sextuples perturb the dispersion and beta functions in a storage ring (SR), which affects machine performance. In a large ring such as the Advanced Photon Source (APS), the magnet errors are difficult to determine with beam-based methods. Also the non-zero orbit through sextuples result from user requests for steering at light source points. For expediency, a singular value decomposition (SVD) matrix method analogous to orbit correction was adopted to make global corrections to these functions using strengths of several quadrupoles as correcting elements. The direct response matrix is calculated from the model of the perfect lattice. The inverse is calculated by SVD with a selected number of singular vectors. Resulting improvement in the lattice functions and machine performance will be presented.
An introduction to vectors, vector operators and vector analysis
Joag, Pramod S
2016-01-01
Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.
Singular electrostatic energy of nanoparticle clusters
Qin, Jian; Krapf, Nathan W.; Witten, Thomas A.
2016-02-01
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation h has a singular logarithmic dependence on h . We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact c (h ) , together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of pseudodifferential boundary problems. In particular, the boundary term in a Krein resolvent formula...... 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...
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
Method of rotations for bilinear singular integrals
Czech Academy of Sciences Publication Activity Database
Diestel, G.; Grafakos, L.; Honzík, Petr; Zengyan, S.; Terwilleger, E.
2011-01-01
Roč. 3, - (2011), s. 99-107 ISSN 1938-9787. [Analysis, Mathematical Physics and Applications. Ixtapa, 01.03.2010-05.03.2010] R&D Projects: GA AV ČR KJB100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : bilinear singular integrals * bilinear Hilbert transform * Fourier multipliers Subject RIV: BA - General Mathematics http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.cma/1298670006&page=record
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)
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
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...
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.
Singular inflation from generalized equation of state fluids
Energy Technology Data Exchange (ETDEWEB)
Nojiri, S., E-mail: nojiri@gravity.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, S.D., E-mail: odintsov@ieec.uab.es [Institut de Ciencies de lEspai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Cerdanyola del Valles, Barcelona (Spain); ICREA, Passeig Lluîs Companys, 23, 08010 Barcelona (Spain); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation); Oikonomou, V.K., E-mail: v.k.oikonomou1979@gmail.com [Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation)
2015-07-30
We study models with a generalized inhomogeneous equation of state fluids, in the context of singular inflation, focusing to so-called Type IV singular evolution. In the simplest case, this cosmological fluid is described by an equation of state with constant w, and therefore a direct modification of this constant w fluid is achieved by using a generalized form of an equation of state. We investigate from which models with generalized phenomenological equation of state, a Type IV singular inflation can be generated and what the phenomenological implications of this singularity would be. We support our results with illustrative examples and we also study the impact of the Type IV singularities on the slow-roll parameters and on the observational inflationary indices, showing the consistency with Planck mission results. The unification of singular inflation with singular dark energy era for specific generalized fluids is also proposed.
Principal-vector-directed fringe-tracking technique.
Zhang, Zhihui; Guo, Hongwei
2014-11-01
Fringe tracking is one of the most straightforward techniques for analyzing a single fringe pattern. This work presents a principal-vector-directed fringe-tracking technique. It uses Gaussian derivatives for estimating fringe gradients and uses hysteresis thresholding for segmenting singular points, thus improving the principal component analysis method. Using it allows us to estimate the principal vectors of fringes from a pattern with high noise. The fringe-tracking procedure is directed by these principal vectors, so that erroneous results induced by noise and other error-inducing factors are avoided. At the same time, the singular point regions of the fringe pattern are identified automatically. Using them allows us to determine paths through which the "seed" point for each fringe skeleton is easy to find, thus alleviating the computational burden in processing the fringe pattern. The results of a numerical simulation and experiment demonstrate this method to be valid.
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Global representations of the Heat and Schrodinger equation with singular potential
Directory of Open Access Journals (Sweden)
Jose A. Franco
2013-07-01
Full Text Available The n-dimensional Schrodinger equation with a singular potential $V_lambda(x=lambda |x|^{-2}$ is studied. Its solution space is studied as a global representation of $widetilde{SL(2,mathbb{R}}imes O(n$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for $lambda$ so that this space is non-empty. The direct sum of solution spaces over such admissible values of $lambda$ is studied as a representation of the (2n+1-dimensional Heisenberg group.
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.
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”...
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)....
Clifford wavelets, singular integrals, and Hardy spaces
Mitrea, Marius
1994-01-01
The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.
Phase singularities and energy fluxes of a noncanonical vortex dipole Airy beam in the far field
Cheng, Ke; You, Yunqi; Zhong, Xianqiong
2015-10-01
Based on the vector angular spectrum representation and stationary phase method, analytical far-field vectorial expressions of a noncanonical vortex dipole Airy beam, namely, a pair of noncanonical vortices with opposite charges embedded in an Airy beam are derived and used to investigate the phase singularities and energy flux distributions of the corresponding beam in the far-field regime, where the noncanonical characteristic of vortex is stressed. It is shown that the noncanonical strength, off-axis distance, and aperture coefficient affect the position and number of phase singularities, and the motion, creation, and annihilation of phase singularities are found by adjusting these parameters. For a low aperture coefficient, the energy flux distributions exhibit different numbers and orientations of lobes by varying the noncanonical strength. With increasing aperture coefficient, the symmetries of lobes are broken, and the energy flux distributions gradually become ellipses and the directions of their major axes vary with different noncanonical strengths. Finally, the energy flux distributions of an Airy beam carrying a single noncanonical vortex are discussed and compared.
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)
Pursell-Shanks type theorems for fewnomial singularities
International Nuclear Information System (INIS)
Khimshiashvili, G.
2006-04-01
We discuss certain situations in which the analytic isomorphism class of an isolated hypersurface singularity is determined by the Lie algebra of derivations of its moduli algebra. Our main attention is given to singularities defined by polynomials with the number of monomials equal to the number of variables. In this context, we indicate several classes of singularities which are classified by the associated Lie algebras. In particular, it is shown that this takes place for isolated singularities defined by binomials in two variables with the Milnor number not less than 7, which implies that simple singularities with Milnor number not less than 7 can be classified by the associated Lie algebras. Similar results are obtained for several other classes of isolated hypersurfaces singularities. A number of related results and open problems are also presented. (author)
Identify Foot of Continental Slope by singular spectrum and fractal singularity analysis
Li, Q.; Dehler, S.
2012-04-01
Identifying the Foot of Continental Slope (FOCS) plays a critical role in the determination of exclusive economic zone (EEZ) for coastal nations. The FOCS is defined by the Law of the Sea as the point of maximum change of the slope and it is mathematically equivalent to the point which has the maximum curvature value in its vicinity. However, curvature is the second derivative and the calculation of second derivative is a high pass and noise-prone filtering procedure. Therefore, identification of FOCS with curvature analysis methods is often uncertain and erroneous because observed bathymetry profiles or interpolated raster maps commonly include high frequency noises and artifacts, observation errors, and local sharp changes. Effective low-pass filtering methods and robust FOCS indicator algorithms are highly desirable. In this approach, nonlinear singular spectral filtering and singularity FOCS-indicator methods and software tools are developed to address this requirement. The normally used Fourier domain filtering methods decompose signals into Fourier space, composed of a fixed base that depends only on the acquisition interval of the signal; the signal is required to be stationary or at least weak stationary. In contrast to that requirement, the developed singular spectral filtering method constructs orthogonal basis functions dynamically according to different signals, and it does not require the signal to be stationary or weak stationary. Furthermore, singular spectrum analysis (SSA) can assist in designing suitable filters to carefully remove high-frequency local or noise components while reserving useful global and local components according to energy distribution. Geoscientific signals, including morphological ocean bathymetry data, often demonstrate fractal or multifractal properties. With proper definition of scales in the vicinity of a certain point and related measures, it is found that 1-dimensional bathymetry profiles and 2-dimensional raster maps
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.
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.
Metric dimensional reduction at singularities with implications to Quantum Gravity
Stoica, Ovidiu Cristinel
2014-08-01
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.
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
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.)
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.
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
Singular Instantons and Painlevé VI
Muñiz Manasliski, Richard
2016-06-01
We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU_2 on S^4, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (P_VI}) and we will give an explicit expression of the map between instantons and solutions to P_{VI}. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S^4. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.
Generalized decomposition methods for singular oscillators
International Nuclear Information System (INIS)
Ramos, J.I.
2009-01-01
Generalized decomposition methods based on a Volterra integral equation, the introduction of an ordering parameter and a power series expansion of the solution in terms of the ordering parameter are developed and used to determine the solution and the frequency of oscillation of a singular, nonlinear oscillator with an odd nonlinearity. It is shown that these techniques provide solutions which are free from secularities if the unknown frequency of oscillation is also expanded in power series of the ordering parameter, require that the nonlinearities be analytic functions of their arguments, and, at leading-order, provide the same frequency of oscillation as two-level iterative techniques, the homotopy perturbation method if the constants that appear in the governing equation are expanded in power series of the ordering parameter, and modified artificial parameter - Linstedt-Poincare procedures.
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.
Spectral singularities and zero energy bound states
Energy Technology Data Exchange (ETDEWEB)
Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2011-08-15
Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled. (authors)
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
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.
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
to choose the velocity function and rest of the initial data so that the end state of collapse is either a black hole (BH) or a naked singularity (NS). This result is significant for two reasons: (1) It produces a substantially 'big' initial data set which under gravitational collapse results into a naked singularity. (2) Type I matter fields.
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.
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...
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Singular Differential Equations and g-Drazin Invertible Operators
Directory of Open Access Journals (Sweden)
Alrazi Abdeljabbar
2016-01-01
Full Text Available We extend results of Favini, Nashed, and Zhao on singular differential equations using the g-Drazin inverse and the order of a quasinilpotent operator in the sense of Miekka and Nevanlinna. Two classes of singularly perturbed differential equations are studied using the continuity properties of the g-Drazin inverse obtained by Koliha and Rakočević.
Singular Differential Equations and g-Drazin Invertible Operators
Abdeljabbar, Alrazi; Tran, Trung Dinh
2016-01-01
We extend results of Favini, Nashed, and Zhao on singular differential equations using the g-Drazin inverse and the order of a quasinilpotent operator in the sense of Miekka and Nevanlinna. Two classes of singularly perturbed differential equations are studied using the continuity properties of the g-Drazin inverse obtained by Koliha and Rakočević.
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
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
The Metaphysics and Epistemology of Singular Terms | Borg ...
African Journals Online (AJOL)
Can we draw apart questions of what it is to be a singular term (a metaphysical issue) from questions about how we tell when some expression is a singular term (an epistemological matter)? Prima facie, it might seem we can't: language, as a man-made edifice, might seem to prohibit such a distinction, and, indeed, some ...
Dynamics of Learning in MLP: Natural Gradient and Singularity Revisited.
Amari, Shun-Ichi; Ozeki, Tomoko; Karakida, Ryo; Yoshida, Yuki; Okada, Masato
2018-01-01
The dynamics of supervised learning play a main role in deep learning, which takes place in the parameter space of a multilayer perceptron (MLP). We review the history of supervised stochastic gradient learning, focusing on its singular structure and natural gradient. The parameter space includes singular regions in which parameters are not identifiable. One of our results is a full exploration of the dynamical behaviors of stochastic gradient learning in an elementary singular network. The bad news is its pathological nature, in which part of the singular region becomes an attractor and another part a repulser at the same time, forming a Milnor attractor. A learning trajectory is attracted by the attractor region, staying in it for a long time, before it escapes the singular region through the repulser region. This is typical of plateau phenomena in learning. We demonstrate the strange topology of a singular region by introducing blow-down coordinates, which are useful for analyzing the natural gradient dynamics. We confirm that the natural gradient dynamics are free of critical slowdown. The second main result is the good news: the interactions of elementary singular networks eliminate the attractor part and the Milnor-type attractors disappear. This explains why large-scale networks do not suffer from serious critical slowdowns due to singularities. We finally show that the unit-wise natural gradient is effective for learning in spite of its low computational cost.
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.
Singularity is the future of ICT research | Osuagwu | West African ...
African Journals Online (AJOL)
Proponents of the singularity call the event an "intelligence explosion" which is a key factor of the Singularity where super-intelligence design successive generations of increasingly powerful minds. The originator of the term – Vernor Vinge - and popularized by Ray Kurzwei has proposed that Artificial Intelligence, human ...
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
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.
The structure of singularities in nonlocal transport equations
Energy Technology Data Exchange (ETDEWEB)
Hoz, F de la [Departamento de Matematica Aplicada, Universidad del PaIs Vasco-Euskal Herriko Unibertsitatea, Escuela Universitaria de IngenierIa Tecnica Industrial, Plaza de la Casilla 3, 48012 Bilbao (Spain); Fontelos, M A [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones CientIficas, C/Serrano 123, 28006 Madrid (Spain)
2008-05-09
We describe the structure of solutions developing singularities in the form of cusps in finite time in nonlocal transport equations of the family: {theta}{sub t}-{delta}({theta}H({theta})){sub x}-(1-{delta})H({theta}){theta}{sub x}=0, 0<={delta}<=1, where H represents the Hilbert transform. Equations of this type appear in various contexts: evolution of vortex sheets, models for quasi-geostrophic equation and evolution equations for order parameters. Equation (1) was studied, and the existence of singularities developing in finite time was proved. The structure of such singularities was, nevertheless, not described. In this paper, we will describe the geometry of the solution in the neighborhood of the singularity once it develops and the (self-similar) way in which it is approached as t {yields} t{sub 0}, where t{sub 0} is the singular time.
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 ...
Detection of Singularities in Fingerprint Images Using Linear Phase Portraits
Ram, Surinder; Bischof, Horst; Birchbauer, Josef
abstract The performance of fingerprint recognition depends heavily on the reliable extraction of singularities. Common algorithms are based on a Poinc’are Index estimation. These algorithms are only robust when certain heuristics and rules are applied. In this chapter we present a model-based approach for the detection of singular points. The presented method exploits the geometric nature of linear differential equation systems. Our method is robust against noise in the input image and is able to detect singularities even if they are partly occluded. The algorithm proceeds by fitting linear phase portraits at each location of a sliding window and then analyses its parameters. Using a well-established mathematical background, our algorithm is able to decide if a singular point is existent. Furthermore, the parameters can be used to classify the type of the singular point into whorls, deltas and loops.
Iris identification system based on Fourier coefficients and singular value decomposition
Somnugpong, Sawet; Phimoltares, Suphakant; Maneeroj, Saranya
2011-12-01
Nowadays, both personal identification and classification are very important. In order to identify the person for some security applications, physical or behavior-based characteristics of individuals with high uniqueness might be analyzed. Biometric becomes the mostly used in personal identification purpose. There are many types of biometric information currently used. In this work, iris, one kind of personal characteristics is considered because of its uniqueness and collectable. Recently, the problem of various iris recognition systems is the limitation of space to store the data in a variety of environments. This work proposes the iris recognition system with small-size of feature vector causing a reduction in space complexity term. For this experiment, each iris is presented in terms of frequency domain, and based on neural network classification model. First, Fast Fourier Transform (FFT) is used to compute the Discrete Fourier Coefficients of iris data in frequency domain. Once the iris data was transformed into frequency-domain matrix, Singular Value Decomposition (SVD) is used to reduce a size of the complex matrix to single vector. All of these vectors would be input for neural networks for the classification step. With this approach, the merit of our technique is that size of feature vector is smaller than that of other techniques with the acceptable level of accuracy when compared with other existing techniques.
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.
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.
C-point and V-point singularity lattice formation and index sign conversion methods
Kumar Pal, Sushanta; Ruchi; Senthilkumaran, P.
2017-06-01
The generic singularities in an ellipse field are C-points namely stars, lemons and monstars in a polarization distribution with C-point indices (-1/2), (+1/2) and (+1/2) respectively. Similar to C-point singularities, there are V-point singularities that occur in a vector field and are characterized by Poincare-Hopf index of integer values. In this paper we show that the superposition of three homogenously polarized beams in different linear states leads to the formation of polarization singularity lattice. Three point sources at the focal plane of the lens are used to create three interfering plane waves. A radial/azimuthal polarization converter (S-wave plate) placed near the focal plane modulates the polarization states of the three beams. The interference pattern is found to host C-points and V-points in a hexagonal lattice. The C-points occur at intensity maxima and V-points occur at intensity minima. Modulating the state of polarization (SOP) of three plane waves from radial to azimuthal does not essentially change the nature of polarization singularity lattice as the Poincare-Hopf index for both radial and azimuthal polarization distributions is (+1). Hence a transformation from a star to a lemon is not trivial, as such a transformation requires not a single SOP change, but a change in whole spatial SOP distribution. Further there is no change in the lattice structure and the C- and V-points appear at locations where they were present earlier. Hence to convert an interlacing star and V-point lattice into an interlacing lemon and V-point lattice, the interferometer requires modification. We show for the first time a method to change the polarity of C-point and V-point indices. This means that lemons can be converted into stars and stars can be converted into lemons. Similarly the positive V-point can be converted to negative V-point and vice versa. The intensity distribution in all these lattices is invariant as the SOPs of the three beams are changed in an
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.
Terminal singularities, Milnor numbers, and matter in F-theory
Arras, Philipp; Grassi, Antonella; Weigand, Timo
2018-01-01
We initiate a systematic investigation of F-theory on elliptic fibrations with singularities which cannot be resolved without breaking the Calabi-Yau condition, corresponding to Q-factorial terminal singularities. It is the purpose of this paper to elucidate the physical origin of such non-crepant singularities in codimension two and to systematically analyze F-theory compactifications containing such singularities. The singularities reflect the presence of localized matter states from wrapped M2-branes which are not charged under any massless gauge potential. We identify a class of Q-factorial terminal singularities on elliptically fibered Calabi-Yau threefolds for which we can compute the number of uncharged localized hypermultiplets in terms of their associated Milnor numbers. These count the local complex deformations of the singularities. The resulting six-dimensional spectra are shown to be anomaly-free. We exemplify this in a variety of cases, including models with non-perturbative gauge groups with both charged and uncharged localized matter. The underlying mathematics will be discussed further in a forthcoming publication.
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.
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.)
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 Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
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
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...
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 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...
Raster images vectorization system
Genytė, Jurgita
2006-01-01
The problem of raster images vectorization was analyzed and researched in this work. Existing vectorization systems are quite expensive, the results are inaccurate, and the manual vectorization of a large number of drafts is impossible. That‘s why our goal was to design and develop a new raster images vectorization system using our suggested automatic vectorization algorithm and the way to record results in a new universal vectorial file format. The work consists of these main parts: analysis...
International Nuclear Information System (INIS)
Pavicic, Mladen; Merlet, Jean-Pierre; McKay, Brendan; Megill, Norman D
2005-01-01
We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in an n-dimensional Hilbert space, H n , n≥3, to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R n , on algorithms that single out those diagrams on which algebraic (0)-(1) states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all four-dimensional KS vector systems containing up to 24 vectors were generated and described, all three-dimensional vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found
Descriptive vector, relative error matrix, and interaction analysis of multivariable plants
Monshizadeh-Naini, Nima; Fatehi, Alireza; Kahki-Sedigh, Ali
In this paper, we introduce a vector which is able to describe the Niederlinski Index (NI), Relative Gain array (RGA), and the characteristic equation of the relative error matrix. The spectral radius and the structured singular value of the relative error matrix are investigated. The cases where
Gato-Rivera, B.
1993-01-01
We use the Kontsevich-Miwa transform to relate the different pictures describing matter coupled to topological gravity in two dimensions: topological theories, Virasoro constraints on integrable hierarchies, and a DDK-type formalism. With the help of the Kontsevich-Miwa transform, we solve the Virasoro constraints on the KP hierarchy in terms of minimal models dressed with a (free) Liouville-like scalar. The dressing prescription originates in a topological (twisted N=2) theory. The Virasoro constraints are thus related to essentially the N=2 null state decoupling equations. The N=2 generators are constructed out of matter, the `Liouville' scalar, and $c=-2$ ghosts. By a `dual' construction involving the reparametrization $c=-26$ ghosts, the DDK dressing prescription is reproduced from the N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary $d\\leq1$ or $d\\geq25$ matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which intr...
Singular perturbation for nonlinear boundary-value problems
Directory of Open Access Journals (Sweden)
Rina Ling
1979-01-01
studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular-perturbation type and approximations are constructed by the method of matched asymptotic expansions.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
Energy Technology Data Exchange (ETDEWEB)
de Leon, M. [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); de Diego, D.M. [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, 28040 Madrid (Spain)
1997-06-01
We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}
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...
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.
A singularity-free WEC-respecting time machine
Krasnikov, S. V.
1997-01-01
A time machine (TM) is constructed whose creating in contrast to all TMs known so far requires neither singularities, nor violation of the weak energy condition (WEC). The spacetime exterior to the TM closely resembles the Friedmann universe.
Pulses in singularly perturbed reaction-diffusion systems
Veerman, Frederik Willem Johan
2013-01-01
In this thesis, the existence and stability of pulse solutions in two-component, singularly perturbed reaction-diffusion systems is analysed using dynamical systems techniques. New phenomena in very general types of systems emerge when geometrical techniques are applied.
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...
Object detection with a multistatic array using singular value decomposition
Hallquist, Aaron T.; Chambers, David H.
2014-07-01
A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across a surface and that travels down the surface. The detection system converts the return signals from a time domain to a frequency domain, resulting in frequency return signals. The detection system then performs a singular value decomposition for each frequency to identify singular values for each frequency. The detection system then detects the presence of a subsurface object based on a comparison of the identified singular values to expected singular values when no subsurface object is present.
Statistical analysis of effective singular values in matrix rank determination
Konstantinides, Konstantinos; Yao, Kung
1988-01-01
A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.
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...... use a Poincaré compactiﬁcation to study the system near inﬁnity. At inﬁnity, the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identiﬁcation of a new attracting manifold, that organises...... singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We...
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...
Directory of Open Access Journals (Sweden)
Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
Biswas, Sounak; Damle, Kedar
2018-02-01
A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.
Two-Sided Gravitational Mirror: Sealing off Curvature Singularities
Davidson, Aharon; Yellin, Ben
2011-01-01
A gravitational mirror is a non-singular finite redshift surface which bounces all incident null geodesics. While a white mirror (outward bouncing) resembles 't Hooft's brick wall, a black mirror (inward bouncing) offers a novel mechanism for sealing off curvature singularities. The geometry underlying a two-sided mirror is characterized by a single signature change, to be contrasted with the signature flip which governs the black hole geometry. To demonstrate the phenomenon analytically, we ...
Wave-breaking and generic singularities of nonlinear hyperbolic equations
International Nuclear Information System (INIS)
Pomeau, Yves; Le Berre, Martine; Guyenne, Philippe; Grilli, Stephan
2008-01-01
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behaviour of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science. (open problem)
Uniqueness of singular solution of semilinear elliptic equation
Indian Academy of Sciences (India)
Nonhomogeneous semilinear elliptic equation; positive solutions; asymptotic behavior; singular ... a removable singular point of a solution of equation (1.1), the existence of the derivatives of the solution depends on the 'blow up' ..... On the other hand, for 0 <ε
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
Resonance scattering and singularities of the scattering function
Energy Technology Data Exchange (ETDEWEB)
Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation)
2010-05-15
Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel. (authors)
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.
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.
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
Lv, Yan; Roberts, A. J.
2012-06-01
An averaging method is applied to derive effective approximation to a singularly perturbed nonlinear stochastic damped wave equation. Small parameter ν > 0 characterizes the singular perturbation, and να, 0 ⩽ α ⩽ 1/2, parametrizes the strength of the noise. Some scaling transformations and the martingale representation theorem yield the effective approximation, a stochastic nonlinear heat equation, for small ν in the sense of distribution.
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.)
Fields generated by sums and products of singular moduli
Faye, Bernadette; Riffaut, Antonin
2017-01-01
We show that the field $\\mathbb{Q}(x,y)$, generated by two singular moduli~$x$ and~$y$, is generated by their sum ${x+y}$, unless~$x$ and~$y$ are conjugate over~$\\mathbb{Q}$, in which case ${x+y}$ generates a subfield of degree at most~$2$. We obtain a similar result for the product of two singular moduli.
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
On the singular values decoupling in the Singular Spectrum Analysis of volcanic tremor at Stromboli
Directory of Open Access Journals (Sweden)
R. Carniel
2006-01-01
Full Text Available The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion was not forecasted, although the island was by then effectively monitored by a dense deployment of instruments. After having tackled in a previous paper the problem of highlighting the timescale of preparation of this event, we investigate here the possibility of highlighting precursors in the volcanic tremor continuously recorded by a short period summit seismic station. We show that a promising candidate is found by examining the degree of coupling between successive singular values that result from the Singular Spectrum Analysis of the raw seismic data. We suggest therefore that possible anomalies in the time evolution of this parameter could be indicators of volcano instability to be taken into account e.g. in a bayesian eruptive scenario evaluator. Obviously, further (and possibly forward testing on other cases is needed to confirm the usefulness of this parameter.
Symmetry breaking and singularity structure in Bose-Einstein condensates
Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.
2012-08-01
We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.
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.
Double parton scattering singularity in one-loop integrals
Gaunt, Jonathan R.; Stirling, W. James
2011-06-01
We present a detailed study of the double parton scattering (DPS) singularity, which is a specific type of Landau singularity that can occur in certain one-loop graphs in theories with massless particles. A simple formula for the DPS singular part of a four-point diagram with arbitrary internal/external particles is derived in terms of the transverse momentum integral of a product of light cone wavefunctions with tree-level matrix elements. This is used to reproduce and explain some results for DPS singularities in box integrals that have been obtained using traditional loop integration techniques. The formula can be straightforwardly generalised to calculate the DPS singularity in loops with an arbitrary number of external particles. We use the generalised version to explain why the specific MHV and NMHV six-photon amplitudes often studied by the NLO multileg community are not divergent at the DPS singular point, and point out that whilst all NMHV amplitudes are always finite, certain MHV amplitudes do contain a DPS divergence. It is shown that our framework for calculating DPS divergences in loop diagrams is entirely consistent with the `two-parton GPD' framework of Diehl and Schafer for calculating proton-proton DPS cross sections, but is inconsistent with the `double PDF' framework of Snigirev.
Chen, Kan; Pang, Cheng-Qun; Liu, Xiang; Matsuki, Takayuki
2015-04-01
Inspired by the abundant experimental observation of axial-vector states, we study whether the observed axial-vector states can be categorized into the conventional axial-vector meson family. In this paper we carry out an analysis based on the mass spectra and two-body Okubo-Zweig-Iizuka-allowed decays. Besides testing the possible axial-vector meson assignments, we also predict abundant information for their decays and the properties of some missing axial-vector mesons, which are valuable for further experimental exploration of the observed and predicted axial-vector mesons.
Broer, Henk W.; Kaper, Tasso J.; Krupa, Martin
2013-01-01
The cusp singularity-a point at which two curves of fold points meet-is a prototypical example in Takens' classification of singularities in constrained equations, which also includes folds, folded saddles, folded nodes, among others. In this article, we study cusp singularities in singularly
Energy Technology Data Exchange (ETDEWEB)
Cao, Yi; Zhou, Hui; Li, Baokun [Jiangnan University, Province (China); Shen, Long [Shanghai University, Shanghai (China)
2011-02-15
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.
U.S. Department of Health & Human Services — VectorBase is a Bioinformatics Resource Center for invertebrate vectors. It is one of four Bioinformatics Resource Centers funded by NIAID to provide web-based...
Application of Bred Vectors To Data Assimilation
Corazza, M.; Kalnay, E.; Patil, Dj
We introduced a statistic, the BV-dimension, to measure the effective local finite-time dimensionality of the atmosphere. We show that this dimension is often quite low, and suggest that this finding has important implications for data assimilation and the accuracy of weather forecasting (Patil et al, 2001). The original database for this study was the forecasts of the NCEP global ensemble forecasting system. The initial differences between the control forecast and the per- turbed forecasts are called bred vectors. The control and perturbed initial conditions valid at time t=n(t are evolved using the forecast model until time t=(n+1) (t. The differences between the perturbed and the control forecasts are scaled down to their initial amplitude, and constitute the bred vectors valid at (n+1) (t. Their growth rate is typically about 1.5/day. The bred vectors are similar by construction to leading Lya- punov vectors except that they have small but finite amplitude, and they are valid at finite times. The original NCEP ensemble data set has 5 independent bred vectors. We define a local bred vector at each grid point by choosing the 5 by 5 grid points centered at the grid point (a region of about 1100km by 1100km), and using the north-south and east- west velocity components at 500mb pressure level to form a 50 dimensional column vector. Since we have k=5 global bred vectors, we also have k local bred vectors at each grid point. We estimate the effective dimensionality of the subspace spanned by the local bred vectors by performing a singular value decomposition (EOF analysis). The k local bred vector columns form a 50xk matrix M. The singular values s(i) of M measure the extent to which the k column unit vectors making up the matrix M point in the direction of v(i). We define the bred vector dimension as BVDIM={Sum[s(i)]}^2/{Sum[s(i)]^2} For example, if 4 out of the 5 vectors lie along v, and one lies along v, the BV- dimension would be BVDIM[sqrt(4), 1, 0
A numerical method for singular boundary value problem of ordinary differential equation
International Nuclear Information System (INIS)
He Qibing
1992-12-01
A numerical method, regularizing method, is suggested to treat the singular boundary problem of ordinary differential equation that is raised from controlled nuclear fusion science and other fields owing to their singular physical mechanism. This kind of singular boundary problem has been successfully solved by special treatment near the singular points and using difference method. This method overcomes difficulties in numerical calculation due to the singularity. The convergence results and numerical test are also given
DEFF Research Database (Denmark)
Becciolini, Diego; Franzosi, Diogo Buarque; Foadi, Roshan
2015-01-01
We analyze the Large Hadron Collider (LHC) phenomenology of heavy vector resonances with a $SU(2)_L\\times SU(2)_R$ spectral global symmetry. This symmetry partially protects the electroweak S-parameter from large contributions of the vector resonances. The resulting custodial vector model spectrum...
International Nuclear Information System (INIS)
Corbera, Montserrat; Llibre, Jaume; Perez-Chavela, Ernesto
2006-01-01
In this paper we consider vector fields in R 3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e + and e - ) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e - ) and one of dimension 1 (the open diameter of the sphere having endpoints e + and e - ). In particular, we analyse the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar? map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R 3 , and the second one is the charged rhomboidal four-body problem
Self-consistent descriptions of vector mesons in hot matter reexamined
International Nuclear Information System (INIS)
Riek, Felix; Knoll, Joern
2010-01-01
Technical concepts are presented that improve the self-consistent treatment of vector mesons in a hot and dense medium. First applications concern an interacting gas of pions and ρ mesons. As an extension of earlier studies, we thereby include random-phase-approximation-type vertex corrections and further use dispersion relations to calculate the real part of the vector-meson self-energy. An improved projection method preserves the four transversality of the vector-meson polarization tensor throughout the self-consistent calculations, thereby keeping the scheme void of kinematical singularities.
On the initial singularity problem in rainbow cosmology
Energy Technology Data Exchange (ETDEWEB)
Santos, Grasiele [Dipartimento di Fisica, Università ' ' La Sapienza' ' , P.le A. Moro 2, Roma, 00185 (Italy); Gubitosi, Giulia [Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ United Kingdom (United Kingdom); Amelino-Camelia, Giovanni, E-mail: grasiele.dossantos@icranet.org, E-mail: g.gubitosi@imperial.ac.uk, E-mail: giovanni.amelino-camelia@roma1.infn.it [Dipartimento di Fisica, Università ' ' La Sapienza' ' and Sez. Roma1 INFN, P.le A. Moro 2, Roma, 00185 (Italy)
2015-08-01
It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ('rainbow') spacetime metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbow metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.
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)
Rotations with Rodrigues' vector
International Nuclear Information System (INIS)
Pina, E
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears to be a fundamental matrix that is used to express the components of the angular velocity, the rotation matrix and the angular momentum vector. The Hamiltonian formalism of rotational dynamics in terms of this vector uses the same matrix. The quantization of the rotational dynamics is performed with simple rules if one uses Rodrigues' vector and similar formal expressions for the quantum operators that mimic the Hamiltonian classical dynamics.
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
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.
Polarization singularity anarchy in three dimensional ellipse fields
Freund, Isaac
2004-11-01
Lines of circular polarization, C lines, and lines of linear polarization, L lines, are studied in a computer simulated random three-dimensional ellipse field. Although we verify existing predictions for the location of particular points on these lines at which the sign of the topological index of the line inverts, we show that from the point of view of foliations of the field such points are better described as points of pair production. We find a new set of true sign inversion points, and show that when all possible foliations are considered this set includes all points on the line. We also find three new families of polarization singularities whose members include all polarization ellipses. The recently described polarization singularity democracy in two-dimensional fields evidently explodes into polarization singularity anarchy in three-dimensional fields.
hp-finite element methods for singular perturbations
Melenk, Jens M
2002-01-01
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Singular cosmological evolution using canonical and ghost scalar fields
Energy Technology Data Exchange (ETDEWEB)
Nojiri, Shin' ichi [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, S.D. [Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Torre C5-Par-2a pl, E-08193 Bellaterra, Barcelona (Spain); Oikonomou, V.K. [Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); Saridakis, Emmanuel N., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com, E-mail: Emmanuel_Saridakis@baylor.edu [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece)
2015-09-01
We demonstrate that finite time singularities of Type IV can be consistently incorporated in the Universe's cosmological evolution, either appearing in the inflationary era, or in the late-time regime. While using only one scalar field instabilities can in principle occur at the time of the phantom-divide crossing, when two fields are involved we are able to avoid such instabilities. Additionally, the two-field scalar-tensor theories prove to be able to offer a plethora of possible viable cosmological scenarios, at which various types of cosmological singularities can be realized. Amongst others, it is possible to describe inflation with the appearance of a Type IV singularity, and phantom late-time acceleration which ends in a Big Rip. Finally, for completeness, we also present the Type IV realization in the context of suitably reconstructed F(R) gravity.
PT -symmetric spectral singularity and negative-frequency resonance
Pendharker, Sarang; Guo, Yu; Khosravi, Farhad; Jacob, Zubin
2017-03-01
Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.
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.
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
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.
Singularity problem of control moment gyro cluster with vibration isolators
Directory of Open Access Journals (Sweden)
Cui Yinghui
2016-02-01
Full Text Available As powerful torque amplification actuators, control moment gyros (CMGs are often used in the attitude control of many state-of-the-art high resolution satellites. However, the disturbance generated by the CMGs can not only reduce the attitude stability of a satellite but also deteriorate the performance of optic payloads. Currently, CMG vibration isolators are widely used to target this problem. The isolators can affect the singularity of the CMG system as they are placed between the CMGs and the satellite bus and provide additional freedoms to the CMG system due to their flexibility. The formulation of the output torque of a CMG is studied first considering the dynamic imbalance of its spin rotor and then the deformation angle as a result of the isolator’s flexibility is calculated. With the additional freedoms, the influence of isolator on the singularity problem is studied and a new steering logic to escape from the singular states is proposed.
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.
Singularity analysis of potential fields to enhance weak anomalies
Chen, G.; Cheng, Q.; Liu, T.
2013-12-01
Geoanomalies generally are nonlinear, non-stationary and weak, especially in the land cover areas, however, the traditional methods of geoanomaly identification are usually based on linear theory. In past two decades, many power-law function models have been developed based on fractal concept in mineral exploration and mineral resource assessment, such that the density-area (C-A) model and spectrum-area model (S-A) suggested by Qiuming Cheng have played important roles in extracting geophysical and geochemical anomalies. Several power-law relationships are evident in geophysical potential fields, such as field value-distance, power spectrum-wave number as well as density-area models. The singularity index based on density-area model involves the first derivative transformation of the measure. Hence, we introduce the singularity analysis to develop a novel high-pass filter for extracting gravity and magnetic anomalies with the advantage of scale invariance. Furthermore, we suggest that the statistics of singularity indices can provide a new edge detection scheme for the gravity or magnetic source bodies. Meanwhile, theoretical magnetic anomalies are established to verify these assertions. In the case study from Nanling mineral district in south China and Qikou Depression in east China, compared with traditional geophysical filtering methods including multiscale wavelet analysis and total horizontal gradient methods, the singularity method enhances and extracts the weak anomalies caused by buried magmatic rocks more effectively, and provides more distinct boundary information of rocks. Moreover, the singularity mapping results have good correspondence relationship with both the outcropping rocks and known mineral deposits to support future mineral resource exploration. The singularity method based on fractal analysis has potential to be a new useful theory and technique for processing gravity and magnetic anomaly data.
Directory of Open Access Journals (Sweden)
Seoghyun Lee
2016-01-01
Full Text Available Controlled gene expression is an indispensable technique in biomedical research. Here, we report a convenient, straightforward, and reliable way to induce expression of a gene of interest with negligible background expression compared to the most widely used tetracycline (Tet-regulated system. Exploiting a Drosophila ecdysone receptor (EcR-based gene regulatory system, we generated nonviral and adenoviral singular vectors designated as pEUI(+ and pENTR-EUI, respectively, which contain all the required elements to guarantee regulated transgene expression (GAL4-miniVP16-EcR, termed GvEcR hereafter, and 10 tandem repeats of an upstream activation sequence promoter followed by a multiple cloning site. Through the transient and stable transfection of mammalian cell lines with reporter genes, we validated that tebufenozide, an ecdysone agonist, reversibly induced gene expression, in a dose- and time-dependent manner, with negligible background expression. In addition, we created an adenovirus derived from the pENTR-EUI vector that readily infected not only cultured cells but also rodent tissues and was sensitive to tebufenozide treatment for regulated transgene expression. These results suggest that EcR-based singular gene regulatory switches would be convenient tools for the induction of gene expression in cells and tissues in a tightly controlled fashion.
Seung-Nelson representation for singular thin sheets
Witten, Thomas; Wang, Jin
2011-03-01
We extend the popular Seung-Nelson model to better study thin elastic sheets with singular or multi-scale structures, which are common phenomena in thin sheets. Because it requires a uniform distribution of lattice points over the simulated sheets, the original model is ill-equipped to study these singular structures. Our extended model retains the essence of the original one, but it allows lattice points to be concentrated as needed in regions of large curvatures. We will compare the two methods by applying them to study the energy of the core region of a developable cone. Supported by NSF award DMR 0820054.
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.
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.
Dimorphism by Singularity Theory in a Model for River Ecology.
Golubitsky, Martin; Hao, Wenrui; Lam, King-Yeung; Lou, Yuan
2017-05-01
Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics.
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. .
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
Fatigue crack shape prediction based on the stress singularity exponent
Czech Academy of Sciences Publication Activity Database
Hutař, Pavel; Ševčík, Martin; Náhlík, Luboš; Knésl, Zdeněk
488-489, č. 1 (2012), s. 178-181 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics - FDM 2011 /10./. Dubrovník, 19.09.2011-21.09.2011] R&D Projects: GA ČR GA101/09/0867 Grant - others:GA AV ČR(CZ) M100420901 Institutional research plan: CEZ:AV0Z2041904 Keywords : stress singularity exponent * crack front curvature * vertex singularity * free surface effect Subject RIV: JL - Materials Fatigue, Friction Mechanics
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.
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.
Controllability of linear vector fields on Lie groups
International Nuclear Information System (INIS)
Ayala, V.; Tirao, J.
1994-11-01
In this paper, we shall deal with a linear control system Σ defined on a Lie group G with Lie algebra g. The dynamic of Σ is determined by the drift vector field which is an element in the normalizer of g in the Lie algebra of all smooth vector field on G and by the control vectors which are elements in g considered as left-invariant vector fields. We characterize the normalizer of g identifying vector fields on G with C ∞ -functions defined on G into g. For this class of control systems we study algebraic conditions for the controllability problem. Indeed, we prove that if the drift vector field has a singularity then the Lie algebra rank condition is necessary for the controllability property, but in general this condition does not determine this property. On the other hand, we show that the rank (ad-rank) condition is sufficient for the controllability of Σ. In particular, we extend the fundamental Kalman's theorem when G is an Abelian connected Lie group. Our work is related with a paper of L. Markus and we also improve his results. (author). 7 refs
Supergravity inspired vector curvaton
International Nuclear Information System (INIS)
Dimopoulos, Konstantinos
2007-01-01
It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied
Indian Academy of Sciences (India)
The vectors aI, a2 are lin- early independent and each of them has norm 1. How- ever, they are not orthogonal to each other. The Gram-. Schmidt process applied to them gives the vectors ql == (1,0), q2 = (0,1). The distance between the pair {all a2} and the pair {q I' q2} is (t) ~. Can we find another pair of orthonormal vectors ...
Design of 2D Time-Varying Vector Fields
Chen, Guoning
2012-10-01
Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects. © 1995-2012 IEEE.
Vectors and their applications
Pettofrezzo, Anthony J
2005-01-01
Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters.Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concept
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...
Transitions of the Multi-Scale Singularity Trees
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Kreiborg, Sven
2005-01-01
Multi-Scale Singularity Trees(MSSTs) [10] are multi-scale image descriptors aimed at representing the deep structures of images. Changes in images are directly translated to changes in the deep structures; therefore transitions in MSSTs. Because MSSTs can be used to represent the deep structure o...
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 Keywords : 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
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
big' ... data in spherically symmetric gravitational collapse for Type I matter fields. ... data. In §2, we briefly summarize the analysis given in [3] and state the conditions on the initial data under which the collapse will lead to a naked singularity.
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2015-11-27
Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 4. Solitary wave solution to a singularly perturbed generalized ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: ...
Singular nonlinear H-infinity optimal control problem
Maas, W.C.A.; Maas, W.C.A.; van der Schaft, Arjan
1996-01-01
The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
Probing singularities in quantum cosmology with curvature scalars
International Nuclear Information System (INIS)
Oliveira-Neto, G.; Correa Silva, E.V.; Lemos, N.A.; Monerat, G.A.
2009-01-01
We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the de Broglie-Bohm interpretation of quantum mechanics. We compute the 'local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time.
Image Denoising Using Singular Value Difference in the Wavelet Domain
Directory of Open Access Journals (Sweden)
Min Wang
2018-01-01
Full Text Available Singular value (SV difference is the difference in the singular values between a noisy image and the original image; it varies regularly with noise intensity. This paper proposes an image denoising method using the singular value difference in the wavelet domain. First, the SV difference model is generated for different noise variances in the three directions of the wavelet transform and the noise variance of a new image is used to make the calculation by the diagonal part. Next, the single-level discrete 2-D wavelet transform is used to decompose each noisy image into its low-frequency and high-frequency parts. Then, singular value decomposition (SVD is used to obtain the SVs of the three high-frequency parts. Finally, the three denoised high-frequency parts are reconstructed by SVD from the SV difference, and the final denoised image is obtained using the inverse wavelet transform. Experiments show the effectiveness of this method compared with relevant existing methods.
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.
Nuclear power plant sensor fault detection using singular value ...
Indian Academy of Sciences (India)
In this paper, a method is proposed to detect and identify any degradation of sensor performance. The validation process consists of two steps: (i) residual generation and (ii) fault detection by residual evaluation.Singular value decomposition (SVD) and Euclidean distance (ED) methods are used to generate the residual ...
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 2. Positive Solutions for Higher Order Singular -Laplacian Boundary Value Problems. Guoliang Shi Junhong Zhang ... Guoliang Shi1 Junhong Zhang1. Department of Mathematics, Tianjin University, Tianjin 300072, People's Republic of China ...
A generalized Dirichlet distribution accounting for singularities of the variables
DEFF Research Database (Denmark)
Lewy, Peter
1996-01-01
A multivariate generalized Dirichlet distribution has been formulated for the case where the stochastic variables are allowed to have singularities at 0 and 1. Small sample properties of the estimates of moments of the variables based on maximum likelihood estimates of the parameters have been co...
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
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/
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
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.
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...
Print to Paint: Breaking Away from Singular Images
Alexander, Kristi
2010-01-01
Each fall, the author presents a printmaking unit, starting with simple techniques such as rubbings, stamping and stenciling. In this article, the author describes a linoleum printmaking lesson wherein students are challenged to break away from singular images of peace signs and initials, and create illustrative plates that could communicate a…
Universality of mass singularities beyond leading logarithm approximation
International Nuclear Information System (INIS)
Kripfganz, J.
1978-08-01
Lepton pair production is studied in low order QCD perturbation theory. Mass singularities are analyzed. Also non-leading logarithms are found to factorize. This allows the consistent computation of correction terms to the Drell-Yan formula. The same factorization properties remain true in case of polarized initial state hadrons and final state leptons. Working in Coulomb gauge greatly simplifies the calculations. (author)
Laplacian growth, elliptic growth, and singularities of the Schwarz potential
Lundberg, Erik
2011-04-01
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or 'Hele-Shaw') problem in the plane. The guiding principle in this connection is the fact that 'non-physical' singularities in the 'oil domain' of the Schwarz function are stationary, and the 'physical' singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by Khavinson and Shapiro (1989 Technical Report TRITA-MAT-1989-36 Royal Institute of Technology, Stockholm). An extension is also given for the so-called elliptic growth problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how {C}^n-techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing 'globalizing families'.
Laplacian growth, elliptic growth, and singularities of the Schwarz potential
International Nuclear Information System (INIS)
Lundberg, Erik
2011-01-01
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or 'Hele-Shaw') problem in the plane. The guiding principle in this connection is the fact that 'non-physical' singularities in the 'oil domain' of the Schwarz function are stationary, and the 'physical' singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by Khavinson and Shapiro (1989 Technical Report TRITA-MAT-1989-36 Royal Institute of Technology, Stockholm). An extension is also given for the so-called elliptic growth problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how C n -techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing 'globalizing families'.
Properties of singular integral operators S α , β
Indian Academy of Sciences (India)
18
45E10, 47B35, 47B20, 30D55. Key words and phrases. Singular integral operator, Toeplitz operator, Hardy space. The first author is supported by the NBHM Postdoctoral Fellowship, Govt. of India. The second author is supported by the Feinberg Postdoctoral Fellowship of the Weizmann Institute of Science. 1. Manuscript. 1.
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)
Slowly growing solutions of singular linear functional differential systems
Czech Academy of Sciences Publication Activity Database
Pylypenko, V.; Rontó, András
2012-01-01
Roč. 285, 5-6 (2012), s. 727-743 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : functional differential equation * singular Cauchy problem * slowly growing solution Subject RIV: BA - General Mathematics Impact factor: 0.576, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/ mana .201000014/abstract
Solutions for a class of iterated singular equations
Indian Academy of Sciences (India)
Euler) equation as special cases. In [1] and [2], Altın studied radial type solutions of a class of singular partial differential equations of even order and obtained Lord Kelvin principle for this class of equations. In [5], all radial type solutions of eq.
Fourth order compact finite difference method for solving singularly ...
African Journals Online (AJOL)
A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Existence of solutions to singular fractional differential systems with impulses
Directory of Open Access Journals (Sweden)
Xingyuan Liu
2012-11-01
Full Text Available By constructing a weighted Banach space and a completely continuous operator, we establish the existence of solutions for singular fractional differential systems with impulses. Our results are proved using the Leray-Schauder nonlinear alternative, and are illustrated with examples.
Entanglement entropy of singular surfaces under relevant deformations in holography
Ghasemi, Mostafa; Parvizi, Shahrokh
2018-02-01
In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.
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.)
Positive solutions of singular boundary value problem of negative ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Thus we complete the proof of. Theorem 2.2. Acknowledgement. This work is supported in part by the NSF(Youth) of Shandong Province and NNSF of. China. References. [1] Fink A M, Gatica J A, Hernandez G E and Waltman P, Approximation of solutions of singular second order boundary value problems, SIAM J. Math.
New singularities in nonrelativistic coupled channel scattering. II. Fourth order
International Nuclear Information System (INIS)
Khuri, N.N.; Tsun Wu, T.
1997-01-01
We consider a two-channel nonrelativistic potential scattering problem, and study perturbation theory in fourth order for the forward amplitude. The main result is that the new singularity demonstrated in second order in the preceding paper I also occurs at the same point in fourth order. Its strength is again that of a pole. copyright 1997 The American Physical Society
Singularity free non-rotating cosmological solutions for perfect fluids ...
Indian Academy of Sciences (India)
Again an analysis leads to the Senovilla solution with. = ½. ¿ i.e.. Ф = ½. ¿p. 6. Conclusion. Our motivation was to examine whether non-singular non-rotating perfect fluid (with Ф = ) cosmologies exist besides those already discovered and presented in the literature. We have not been able to give an unequivocal answer but ...
Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...
African Journals Online (AJOL)
A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...
Application of singular eigenfunctions method of neutron transport theory
International Nuclear Information System (INIS)
Simovicj, R.
1974-11-01
A possibility of applying analitical method of neutron transport theory was investigated in research of processes governed by linearized Boltzmann equation, especially in semiconducting media. Analitical singular eigenfunctions method was developed and improved. It was applied in solving the electron transport equation for nonpolar semiconductors in case of constant high electrical field. Energy and angular distribution of high energy electrons was obtained
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 ...
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 diffusionless limits of double-diffusive instabilities in magnetohydrodynamics.
Kirillov, Oleg N
2017-09-01
We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, Pm =1. At a fixed Pm ≠1, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity-time-symmetric.
Priapism after a Singular Dose of Chlorpromazine | Suleekwe ...
African Journals Online (AJOL)
A case of priapism in a young Nigerian man following a singular dose of chlorpromazine is presented. Complete detumescence was achieved with needle aspiration and adrenaline infiltration. Potency was retained. A review of relevant literature is done. Key words: Priapism, Chlorpromazine, Needle aspiration.
Nuclear power plant sensor fault detection using singular value
Indian Academy of Sciences (India)
The validation process consists of two steps: (i) residual generation and (ii) fault detection by residual evaluation.Singular value decomposition (SVD) and Euclidean distance (ED) methods are used to generate the residual and evaluate the fault on the residual space, respectively. This paper claims that SVD-based fault ...
Topological invariants and the dynamics of an axial vector torsion field
International Nuclear Information System (INIS)
Drechsler, W.
1983-01-01
A generalized throry of gravitation is discussed which is based on a Riemann-Cartan space-time, U 4 , with an axial vector torsion field. Besides Einstein's equations determining the metric of the U 4 a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for the U 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic. (author)
Vector-Vector Scattering on the Lattice
Romero-López, Fernando; Urbach, Carsten; Rusetsky, Akaki
2018-03-01
In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
Classification of three-dimensional exceptional log canonical hypersurface singularities. II
International Nuclear Information System (INIS)
Kudryavtsev, S A
2004-01-01
We study three-dimensional exceptional canonical hypersurface singularities which do not satisfy the condition of well-formedness. The result obtained completes the classification of three-dimensional exceptional log canonical hypersurface singularities begun in [4
Classification of three-dimensional exceptional log canonical hypersurface singularities. I
International Nuclear Information System (INIS)
Kudryavtsev, S A
2002-01-01
We describe three-dimensional exceptional strictly log canonical hypersurface singularities and give a detailed classification of three-dimensional exceptional canonical hypersurface singularities under the condition of well-formedness
Classification of three-dimensional exceptional log canonical hypersurface singularities. I
Kudryavtsev, S. A.
2002-10-01
We describe three-dimensional exceptional strictly log canonical hypersurface singularities and give a detailed classification of three-dimensional exceptional canonical hypersurface singularities under the condition of well-formedness.
Classification of three-dimensional exceptional log canonical hypersurface singularities. II
Kudryavtsev, S. A.
2004-04-01
We study three-dimensional exceptional canonical hypersurface singularities which do not satisfy the condition of well-formedness. The result obtained completes the classification of three-dimensional exceptional log canonical hypersurface singularities begun in [4].
De Angelis, L.; Alpeggiani, F.; Di Falco, Andrea; Kuipers, L.
2017-01-01
Phase singularities can be created and annihilated, but always in pairs. With optical near-field measurements, we track singularities in random waves as a function of wavelength, and discover correlations between creation and annihilation events.
De Vector wetenschappelijk bekeken
Slot, D.E.; van der Weijden, F.
2009-01-01
In juni 2008 heeft de sectie Parodontologie van ACTA een systematische review gepubliceerd over het effect van de Vector®. De vraagstelling luidde: Wat is het effect van het gebruik van de Vector® op (menselijke) gebitselementen vergeleken met ultrasone apparatuur of handinstrumentarium op
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.; Nitta, Muneto; Veldhuis, T. ter; Xiong, C.
2009-01-01
Local oscillations of the brane world are manifested as massive vector fields. Their coupling to the Standard Model can be obtained using the method of nonlinear realizations of the spontaneously broken higher-dimensional space-time symmetries, and to an extent, are model independent. Phenomenological limits on these vector field parameters are obtained using LEP collider data and dark matter constraints
Advancing vector biology research
Kohl, Alain; Pondeville, Emilie; Schnettler, Esther; Crisanti, Andrea; Supparo, Clelia; Christophides, George K.; Kersey, Paul J.; Maslen, Gareth L.; Takken, Willem; Koenraadt, Constantianus J.M.; Oliva, Clelia F.; Busquets, Núria; Abad, F.X.; Failloux, Anna Bella; Levashina, Elena A.; Wilson, Anthony J.; Veronesi, Eva; Pichard, Maëlle; Arnaud Marsh, Sarah; Simard, Frédéric; Vernick, Kenneth D.
2016-01-01
Vector-borne pathogens impact public health, animal production, and animal welfare. Research on arthropod vectors such as mosquitoes, ticks, sandflies, and midges which transmit pathogens to humans and economically important animals is crucial for development of new control measures that target
Indian Academy of Sciences (India)
One consequence of the chiral restoration is the mixing of parity partners. We look for a possible signature of the mixing of vector and axial vector mesons in heavy-ion collisions. We suggest an experimental method for its observation. The dynamical evolution of the heavy-ion collision is described by a transport equation of ...
Architecture and Vector Control
DEFF Research Database (Denmark)
von Seidlein, Lorenz; Knols, Bart GJ; Kirby, Matthew
2012-01-01
The character of buildings plays a major role in disease control. It is understood that water supply and sanitation are critical for the well-being of residents. Current vector control programs aim to prevent the access of vector to the human host. This can be achieved through screened windows, c...
Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...
Light-like big bang singularities in string and matrix theories
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2011-01-01
Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.
The analysis of optimal singular controls for SEIR model of tuberculosis
Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.
2014-12-01
The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.
Revisiting the vector and axial-vector vacuum susceptibilities
International Nuclear Information System (INIS)
Chang Lei; Liu Yuxin; Sun Weimin; Zong Hongshi
2008-01-01
We re-investigate the vector and axial-vector vacuum susceptibilities by taking advantage of the vector and axial-vector Ward-Takahashi identities. We show analytically that, in the chiral limit, the vector vacuum susceptibility is zero and the axial-vector vacuum susceptibility equals three fourths of the square of the pion decay constant. Besides, our analysis reproduces the Weinberg sum rule
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed
2013-07-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.
Vafa-Witten theorem and Lee-Yang singularities
International Nuclear Information System (INIS)
Aguado, M.; Asorey, M.
2009-01-01
We prove the analyticity of the finite volume QCD partition function for complex values of the θ-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits and cusp singularities in the vacuum energy density and never or cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at θ=0 and has an important consequence: the absence of a first order phase transition at θ=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vectorlike gauge theories and follows from renormalizability, unitarity, positivity, and existence of Bogomol'nyi-Prasad-Sommerfield bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the nonlinear CP N sigma model.
Naked singularity formation in Brans-Dicke theory
Energy Technology Data Exchange (ETDEWEB)
Ziaie, Amir Hadi; Atazadeh, Khedmat [Department of Physics, Shahid Beheshti University, Evin, Tehran 19839 (Iran, Islamic Republic of); Tavakoli, Yaser, E-mail: am.ziaie@mail.sbu.ac.i, E-mail: k-atazadeh@sbu.ac.i, E-mail: tavakoli@ubi.p [Departamento de Fisica, Universidade da Beira Interior, Rua Marques d' Avila e Bolama, 6200 Covilha (Portugal)
2010-04-07
Gravitational collapse of the Brans-Dicke scalar field with non-zero potential in the presence of matter fluid obeying the barotropic equation of state, p = wrho, is studied. Utilizing the concept of the expansion parameter, it is seen that the cosmic censorship conjecture may be violated for w=-1/3 and w=-2/3 which correspond to the cosmic string and domain wall, respectively. We have shown that physically, it is the rate of collapse that governs the formation of a black hole or a naked singularity as the final fate of dynamical evolution and only for these two cases can the singularity be naked as the collapse end state. Also the weak energy condition is satisfied by the collapsing configuration.
Correlation energy for elementary bosons: Physics of the singularity
Energy Technology Data Exchange (ETDEWEB)
Shiau, Shiue-Yuan, E-mail: syshiau@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan, 701, Taiwan (China); Combescot, Monique [Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRS, 4 place Jussieu, 75005 Paris (France); Chang, Yia-Chung, E-mail: yiachang@gate.sinica.edu.tw [Research Center for Applied Sciences, Academia Sinica, Taipei, 115, Taiwan (China); Department of Physics, National Cheng Kung University, Tainan, 701, Taiwan (China)
2016-04-15
We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman “bubble” diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose–Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman “bubble” diagrams, the previous elementary boson approaches, which hide this physics, being inappropriate to do so.
Singularities at the contact point of two kissing Neumann balls
Nazarov, Sergey A.; Taskinen, Jari
2018-02-01
We investigate eigenfunctions of the Neumann Laplacian in a bounded domain Ω ⊂Rd, where a cuspidal singularity is caused by a cavity consisting of two touching balls, or discs in the planar case. We prove that the eigenfunctions with all of their derivatives are bounded in Ω ‾, if the dimension d equals 2, but in dimension d ≥ 3 their gradients have a strong singularity O (| x - O|-α), α ∈ (0 , 2 -√{ 2 } ] at the point of tangency O. Our study is based on dimension reduction and other asymptotic procedures, as well as the Kondratiev theory applied to the limit differential equation in the punctured hyperplane R d - 1 ∖ O. We also discuss other shapes producing thinning gaps between touching cavities.
Bifurcations of a class of singular biological economic models
International Nuclear Information System (INIS)
Zhang Xue; Zhang Qingling; Zhang Yue
2009-01-01
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Formation of current singularity in a topologically constrained plasma
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Huang, Yi-Min [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.; Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
2016-02-01
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Energy Technology Data Exchange (ETDEWEB)
Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-21
Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Singular symmetric functionals and Banach limits with additional invariance properties
International Nuclear Information System (INIS)
Dodds, P G; Pagter, B de; Sedaev, A A; Semenov, E M; Sukochev, F A
2003-01-01
For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy-Littlewood semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences
Wentzel-Bardeen singularity in coupled Luttinger liquids: Transport properties
International Nuclear Information System (INIS)
Martin, T.
1994-01-01
The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated elections coupled to low energy acoustic phonons in one dimension. The exponents of various response functions are calculated, and their striking sensitivity to the Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons the equivalent of a phase diagram is established. By increasing the filling factor towards half filling the WB singularity is approached. This in turn suppresses antiferromagnetic fluctuations and drives the system towards the superconducting regime, via a new intermediate (metallic) phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
Heterogeneous ice nucleation: bridging stochastic and singular freezing behavior
Niedermeier, D.; Shaw, R. A.; Hartmann, S.; Wex, H.; Clauss, T.; Voigtländer, J.; Stratmann, F.
2011-01-01
Heterogeneous ice nucleation, a primary pathway for ice formation in the atmosphere, has been described alternately as being stochastic, in direct analogy with homogeneous nucleation, or singular, with ice nuclei initiating freezing at deterministic temperatures. We present an idealized model that bridges these stochastic and singular descriptions of heterogeneous ice nucleation. This "soccer ball" model treats statistically similar particles as being covered with surface sites (patches of finite area) characterized by different nucleation barriers, but with each surface site following the stochastic nature of ice embryo formation. The model provides a phenomenological explanation for seemingly contradictory experimental results obtained in our research groups. We suggest that ice nucleation is fundamentally a stochastic process but that for realistic atmospheric particle populations this process can be masked by the heterogeneity of surface properties. Full evaluation of the model will require experiments with well characterized ice nucleating particles and the ability to vary both temperature and waiting time for freezing.
Lecture notes on mean curvature flow, barriers and singular perturbations
Bellettini, Giovanni
2013-01-01
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
S-matrix singularities and CFT correlation functions
Cardona, Carlos; Huang, Yu-tin
2017-08-01
In this note, we explore the correspondence between four-dimensional flat space S-matrix and two-dimensional CFT proposed by Pasterski et al. We demonstrate that the factorisation singularities of an n-point cubic diagram reproduces the AdS Witten diagrams if mass conservation is imposed at each vertex. Such configuration arises naturally if we consider the 4-dimensional S-matrix as a compactified massless 5-dimensional theory. This identification allows us to rewrite the massless S-matrix in the CHY formulation, where the factorisation singularities are re-interpreted as factorisation limits of a Riemann sphere. In this light, the map is recast into a form of 2 d/2 d correspondence.
Horizon quantum fuzziness for non-singular black holes
Giugno, Andrea; Giusti, Andrea; Helou, Alexis
2018-03-01
We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.
A Schwarz alternating procedure for singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)
1994-12-31
The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.
Biplot and Singular Value Decomposition Macros for Excel©
Directory of Open Access Journals (Sweden)
Ilya A. Lipkovich
2002-06-01
Full Text Available The biplot display is a graph of row and column markers obtained from data that forms a two-way table. The markers are calculated from the singular value decomposition of the data matrix. The biplot display may be used with many multivariate methods to display relationships between variables and objects. It is commonly used in ecological applications to plot relationships between species and sites. This paper describes a set of Excel macros that may be used to draw a biplot display based on results from principal components analysis, correspondence analysis, canonical discriminant analysis, metric multidimensional scaling, redundancy analysis, canonical correlation analysis or canonical correspondence analysis. The macros allow for a variety of transformations of the data prior to the singular value decomposition and scaling of the markers following the decomposition.
Topological Field Theory of the Initial Singularity of Space-Time
Bogdanoff, I
2000-01-01
Here we suggest a possible resolution of the initial space-time singularity. In this novel approach, the initial singularity of space-time corresponds to a 0 size singular gravitational instanton, characterised by a Riemannian metric configuration (++++) in dimension D = 4. Associated with the 0 scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in terms of topological field symmetries and associated invariants (in particular the first Donaldson invariant ). In this perspective, we here introduce a new topological invariant, associated with 0 scale, of the form Z = Tr (-1)s which we call "singularity invariant".
Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams
Haitao, Chen; Gao, Zenghui; Wang, Wanqing
2017-06-01
The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation .... will be used in §3 for our purpose. For convenience, we use a version of this theory due to Jones [2]. For the system. { x (t) = f (x, y, ε), y (t) = εg(x, y, ε),. (2.1) where x ∈ Rn, y ...
Fundamental groups of singular quasi-projective varieties
International Nuclear Information System (INIS)
Eyral, Christophe
2002-09-01
We express, under appropriate conditions, the fundamental group of a singular complex quasi-projective variety as a quotient of the fundamental group of a general hyperplane section, using a generic pencil. The subgroup by which the quotient is taken is described with the help of the monodromies around the exceptional hyperplanes of the pencil. This is a new generalization of the classical Zariski-van Kampen theorem on curves. (author)
Singular divergence instability thresholds of kinematically constrained circulatory systems
Energy Technology Data Exchange (ETDEWEB)
Kirillov, O.N., E-mail: o.kirillov@hzdr.de [Magnetohydrodynamics Division, Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden (Germany); Challamel, N. [University of South Brittany, LIMATB, Lorient (France); Darve, F. [Laboratoire Sols Solides Structures, UJF-INPG-CNRS, Grenoble (France); Lerbet, J. [IBISC, Universite d' Evry Val d' Essone, 40 Rue Pelvoux, CE 1455 Courcouronnes, 91020 Evry Cedex (France); Nicot, F. [Cemagref, Unite de Recherche Erosion Torrentielle Neige et Avalanches, Grenoble (France)
2014-01-10
Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraints' coefficients. Particularly, the critical buckling load of the kinematically constrained Ziegler's pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree n=2. This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability.
Singularity theory and N = 2 superconformal field theories
International Nuclear Information System (INIS)
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs
Dyslexia singular brain; Le singulier cerveau des dyslexiques
Energy Technology Data Exchange (ETDEWEB)
Habis, M.; Robichon, F. [Centre Hospitalier Universitaire de la Timone, 13 - Marseille (France); Demonet, J.F. [Centre Hospitalier Universitaire la Grave, 31 - Toulouse (France)
1996-07-01
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.). 4 refs.
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
Singular value decomposition methods for wave propagation analysis
Czech Academy of Sciences Publication Activity Database
Santolík, Ondřej; Parrot, M.; Lefeuvre, F.
2003-01-01
Roč. 38, č. 1 (2003), s. 10-1-10-13 ISSN 0048-6604 R&D Projects: GA ČR GA205/01/1064 Grant - others:Barrande(CZ) 98039/98055 Institutional research plan: CEZ:AV0Z3042911; CEZ:MSM 113200004 Keywords : wave propagation * singular value decomposition Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 0.832, year: 2003
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
(1.4). The singular or nonsingular fourth-order boundary value problems (1.4) have been exten- sively studied by many authors [1,2,6,7,10,13–15]. Shi and Chen [10,11] gave the sufficient and necessary conditions for the existence of positive solutions to superlinear problem (1.4) by the fixed point theorem in cones when 1 ...
Singularity problems of the power law for modeling creep compliance
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
The structure and singularities of quotient arc complexes
DEFF Research Database (Denmark)
Penner, Robert
2008-01-01
A well-known combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex QA(F) consisting of equivalence classes of arcs in F connecting a given finite s...... with a related quotient arc complex in the punctured case with no boundary. Namely, the essential singularities of the natural cellular compactification of Riemann's moduli space can be described....
On linear viscoelasticity within general fractional derivatives without singular kernel
Directory of Open Access Journals (Sweden)
Gao Feng
2017-01-01
Full Text Available The Riemann-Liouville and Caputo-Liouville fractional derivatives without singular kernel are proposed as mathematical tools to describe the mathematical models in line viscoelasticity in the present article. The fractional mechanical models containing the Maxwell and Kelvin-Voigt elements are graphically discussed with the Laplace transform. The results are accurate and efficient to reveal the complex behaviors of the real materials.
Singular perturbation method for evolution equations in Banach spaces
International Nuclear Information System (INIS)
Mika, J.
1976-01-01
The singular perturbation method is applied to linear evolution equations in Banach spaces containing a small parameter multiplying the time derivative. Outer and inner asymptotic solutions are formulated and the sense in which they converge to the exact solution is rigorously defined. It is then shown that the sum of the two asymptotic solutions converges uniformly to the exact solution. Possible applications to various physical situations are indicated. (Auth.)
Bifurcation for non linear ordinary differential equations with singular perturbation
Directory of Open Access Journals (Sweden)
Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
More on the initial singularity problem in gravity's rainbow cosmology
Khodadi, M.; Nozari, K.; Sepangi, H. R.
2016-12-01
Using a one-dimensional minisuperspace model with a dimensionless ratio E/E_{Pl}, we study the initial singularity problem at the quantum level for the closed rainbow cosmology with a homogeneous, isotropic classical space-time background. We derive the classical Hamiltonian within the framework of Schutz's formalism for an ideal fluid with a cosmological constant. We characterize the behavior of the system at the early stages of the universe evolution through analyzing the relevant shapes for the potential sector of the classical Hamiltonian for various matter sources, each separately modified by two rainbow functions. We show that for both rainbow universe models presented here, there is the possibility of eliminating the initial singularity by forming a potential barrier and static universe for a non-zero value of the scale factor. We investigate their quantum stability and show that for an energy-dependent space-time geometry with energies comparable with the Planck energy, the non-zero value of the scale factor may be stable. It is shown that under certain constraints the rainbow universe model filled with an exotic matter as a domain wall fluid plus a cosmological constant can result in a non-singular harmonic universe. In addition, we demonstrate that the harmonically oscillating universe with respect to the scale factor is sensitive to E/E_{Pl} and that at high energies it may become stable quantum mechanically. Through a Schrödinger-Wheeler-De Witt equation obtained from the quantization of the classical Hamiltonian, we also extract the wave packet of the universe with a focus on the early stages of the evolution. The resulting wave packet supports the existence of a bouncing non-singular universe within the context of gravity's rainbow proposal.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Relaxation periodic solutions of one singular perturbed system with delay
Kashchenko, A. A.
2017-12-01
In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.
Fatigue crack shape prediction based on vertex singularity
Czech Academy of Sciences Publication Activity Database
Hutař, Pavel; Náhlík, Luboš
2008-01-01
Roč. 2, č. 1 (2008), s. 45-52 ISSN 1802-680X R&D Projects: GA ČR GA101/08/1623; GA ČR GP106/06/P239 Institutional research plan: CEZ:AV0Z20410507 Keywords : 3D vertex singularity * crack shape * fatigue crack propagation Subject RIV: JL - Materials Fatigue, Friction Mechanics
A rapid local singularity analysis algorithm with applications
Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits
2015-04-01
The local singularity model developed by Cheng is fast gaining popularity in characterizing mineralization and detecting anomalies of geochemical, geophysical and remote sensing data. However in one of the conventional algorithms involving the moving average values with different scales is time-consuming especially while analyzing a large dataset. Summed area table (SAT), also called as integral image, is a fast algorithm used within the Viola-Jones object detection framework in computer vision area. Historically, the principle of SAT is well-known in the study of multi-dimensional probability distribution functions, namely in computing 2D (or ND) probabilities (area under the probability distribution) from the respective cumulative distribution functions. We introduce SAT and it's variation Rotated Summed Area Table in the isotropic, anisotropic or directional local singularity mapping in this study. Once computed using SAT, any one of the rectangular sum can be computed at any scale or location in constant time. The area for any rectangular region in the image can be computed by using only 4 array accesses in constant time independently of the size of the region; effectively reducing the time complexity from O(n) to O(1). New programs using Python, Julia, matlab and C++ are implemented respectively to satisfy different applications, especially to the big data analysis. Several large geochemical and remote sensing datasets are tested. A wide variety of scale changes (linear spacing or log spacing) for non-iterative or iterative approach are adopted to calculate the singularity index values and compare the results. The results indicate that the local singularity analysis with SAT is more robust and superior to traditional approach in identifying anomalies.
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
On the Initial Singularity Problem in Two Dimensional Quantum Cosmology
Gamboa, J.
1995-01-01
The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(\\alpha, \\beta)$ satisfying the algebraic relation $2\\beta - \\alpha =2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we...
Solving singular convolution equations using the inverse fast Fourier transform
Czech Academy of Sciences Publication Activity Database
Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav
2012-01-01
Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/
Canard solutions of two-dimensional singularly perturbed systems
Energy Technology Data Exchange (ETDEWEB)
Chen Xianfeng [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)]. E-mail: chenxf@sjtu.edu.cn; Yu Pei [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Applied Mathematics, University of Western Ontario London, Ont., N6A 5B7 (Canada); Han Maoan [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Zhang Weijiang [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)
2005-02-01
In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an m-22 th-order degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing results. Finally, one numerical example is given.
Biplot and Singular Value Decomposition Macros for Excel©
Lipkovich, Ilya A.; Smith, Eric P.
2002-01-01
The biplot display is a graph of row and column markers obtained from data that forms a two-way table. The markers are calculated from the singular value decomposition of the data matrix. The biplot display may be used with many multivariate methods to display relationships between variables and objects. It is commonly used in ecological applications to plot relationships between species and sites. This paper describes a set of Excel macros that may be used to draw a biplot display based ...
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Kansas Data Access and Support Center — The Kansas Tagged Vector Contour (TVC) dataset consists of digitized contours from the 7.5 minute topographic quadrangle maps. Coverage for the state is incomplete....
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
1991-01-01
Roč. 2, - (1991), s. 281-292 ISSN 0956-7925 Keywords : vector hysteresis operator * hysteresis potential * differential inequality Subject RIV: BA - General Mathematics http://www.math.cas.cz/~krejci/b15p.pdf
Singularities in and stability of Ooguri-Vafa-Verlinde cosmologies
International Nuclear Information System (INIS)
McInnes, B.
2005-04-01
Ooguri, Vafa, and Verlinde have recently proposed an approach to string cosmology which is based on the idea that cosmological string moduli should be selected by a Hartle-Hawking wave function. They are led to consider a certain Euclidean space which has two different Lorentzian interpretations, one of which is a model of an accelerating cosmology. We describe in detail how to implement this idea without resorting to a 'complex metric'. We show that the four-dimensional version of the OVV cosmology is null geodesically incomplete but has no curvature singularity; also that it is (barely) stable against the Seiberg-Witten process (nucleation of brane pairs). The introduction of matter satisfying the Null Energy Condition has the paradoxical effect of both stabilizing the spacetime and rendering it genuinely singular. We show however that it is possible to arrange for an effective violation of the NEC in such a way that the singularity is avoided and yet the spacetime remains stable. The possible implications for the early history of these cosmologies are discussed. (author)
Special frequencies and Lifshitz singularities in binary random harmonic chains
International Nuclear Information System (INIS)
Nieuwenhuizen, T.M.; Luck, J.M.; Canisius, J.; van Hemmen, J.L.; Ventevogel, W.J.
1986-01-01
The authors consider a one-dimensional chain of coupled harmonic oscillators; the mass of each atom is a random variable taking only two values (M or 1). They investigate the integrated density of states H(omega 2 ) near special frequencies: a given frequency omega/sub s/ with rational wavelength becomes special if the mass ratio M exceeds a certain critical value M/sub c/. They show that H has essential singularities of the types H/sub sg/∼ exp(-C 1 absolute value of omega 2 -omega/sub s/ 2 /sup 1/2/) or exp(-C 2 absolute value of omega 2 -omega/sub s/ 2 -1 ), according to the value of M and the sign of (omega 2 -omega/sub s/ 2 ). The Lifshitz singularity at the band edge is analyzed in the same way. In each case, the constant C 1 or C 2 is evaluated explicitly and compared with a vast amount of numerical work. All these exponential singularities are modulated by periodic amplitudes. The properties of the eigenfunctions with frequencies close to the special values are also discussed, and are illustrated by numerical data
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.
Non-singular bounce transitions in the multiverse
Energy Technology Data Exchange (ETDEWEB)
Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, 08028, Barcelona (Spain); Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2013-11-01
According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.
``All that Matter ... in One Big Bang ...'', &Other Cosmological Singularities
Elizalde, Emilio
2018-02-01
The first part of this paper contains a brief description of the beginnings of modern cosmology, which, the author will argue, was most likely born in the Year 1912. Some of the pieces of evidence presented here have emerged from recent research in the history of science, and are not usually shared with the general audiences in popular science books. In special, the issue of the correct formulation of the original Big Bang concept, according to the precise words of Fred Hoyle, is discussed. Too often, this point is very deficiently explained (when not just misleadingly) in most of the available generalist literature. Other frequent uses of the same words, Big Bang, as to name the initial singularity of the cosmos, and also whole cosmological models, are then addressed, as evolutions of its original meaning. Quantum and inflationary additions to the celebrated singularity theorems by Penrose, Geroch, Hawking and others led to subsequent results by Borde, Guth and Vilenkin. And corresponding corrections to the Einstein field equations have originated, in particular, $R^2$, $f(R)$, and scalar-tensor gravities, giving rise to a plethora of new singularities. For completeness, an updated table with a classification of the same is given.
Towards realistic string vacua from branes at singularities
Conlon, Joseph P.; Maharana, Anshuman; Quevedo, Fernando
2009-05-01
We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dPn) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singularity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also describe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.
Analysis of scintigrams by singular value decomposition (SVD) technique
Energy Technology Data Exchange (ETDEWEB)
Savolainen, S.E.; Liewendahl, B.K. (Helsinki Univ. (Finland). Dept. of Physics)
1994-05-01
The singular value decomposition (SVD) method is presented as a potential tool for analyzing gamma camera images. Mathematically image analysis is a study of matrixes as the standard scintigram is a digitized matrix presentation of the recorded photon fluence from radioactivity of the object. Each matrix element (pixel) consists of a number, which equals the detected counts of the object position. The analysis of images can be reduced to the analysis of the singular values of the matrix decomposition. In the present study the clinical usefulness of SVD was tested by analyzing two different kinds of scintigrams: brain images by single photon emission tomography (SPET), and liver and spleen planar images. It is concluded that SVD can be applied to the analysis of gamma camera images, and that it provides an objective method for interpretation of clinically relevant information contained in the images. In image filtering, SVD provides results comparable to conventional filtering. In addition, the study of singular values can be used for semiquantitation of radionuclide images as exemplified by brain SPET studies and liver-spleen planar studies. (author).
Cosmic Evolutionary Philosophy and a Dialectical Approach to Technological Singularity
Directory of Open Access Journals (Sweden)
Cadell Last
2018-04-01
Full Text Available The anticipated next stage of human organization is often described by futurists as a global technological singularity. This next stage of complex organization is hypothesized to be actualized by scientific-technic knowledge networks. However, the general consequences of this process for the meaning of human existence are unknown. Here, it is argued that cosmic evolutionary philosophy is a useful worldview for grounding an understanding of the potential nature of this futures event. In the cosmic evolutionary philosophy, reality is conceptualized locally as a universal dynamic of emergent evolving relations. This universal dynamic is structured by a singular astrophysical origin and an organizational progress from sub-atomic particles to global civilization mediated by qualitative phase transitions. From this theoretical ground, we attempt to understand the next stage of universal dynamics in terms of the motion of general ideation attempting to actualize higher unity. In this way, we approach technological singularity dialectically as an event caused by ideational transformations and mediated by an emergent intersubjective objectivity. From these speculations, a historically-engaged perspective on the nature of human consciousness is articulated where the truth of reality as an emergent unity depends on the collective action of a multiplicity of human observers.
Cosmological applications of singular hypersurfaces in general relativity
Laguna-Castillo, Pablo
Three applications to cosmology of surface layers, based on Israel's formalism of singular hypersurfaces and thin shells in general relativity, are presented. Einstein's field equations are analyzed in the presence of a bubble nucleated in vacuum phase transitions within the context of the old inflationary universe scenario. The evolution of a bubble with vanishing surface energy density is studied. It is found that such bubbles lead to a worm-hole matching. Next, the observable four-dimensional universe is considered as a singular hypersurface of discontinuity embedded in a five-dimensional Kaluza-Klein cosmology. It is possible to rewrite the projected five-dimensional Einstein equations on the surface layer in a similar way to the four-dimensional Robertson-Walker cosmology equations. Next, a model is described for an infinite-length, straight U(1) cosmic string as a cylindrical, singular shell enclosing a region of false vacuum. A set of equations is introduced which are required to develop a three-dimensional computer code whose purpose is to study the process of intercommuting cosmic strings with the inclusion of gravitational effects. The outcome is evolution and constraint equations for the gravitational, scalar and gauge field of two initially separated, perpendicular, cosmic strings.
Machine vision for timber grading singularities detection and applications
Hittawe, Mohamad Mazen; Sidibé, Désiré; Beya, Ouadi; Mériaudeau, Fabrice
2017-11-01
This article deals with machine vision techniques applied to timber grading singularities. Timber used for architectural purposes must satisfy certain mechanical requirements, and, therefore, must be mechanically graded to ensure the manufacturer that the product complies with the requirements. However, the timber material has many singularities, such as knots, cracks, and presence of juvenile wood, which influence its mechanical behavior. Thus, identifying those singularities is of great importance. We address the problem of timber defects segmentation and classification and propose a method to detect timber defects such as cracks and knots using a bag-of-words approach. Extensive experimental results show that the proposed methods are efficient and can improve grading machines performances. We also propose an automated method for the detection of transverse knots, which allows the computation of knot depth ratio (KDR) images. Finally, we propose a method for the detection of juvenile wood regions based on tree rings detection and the estimation of the tree's pith. The experimental results show that the proposed methods achieve excellent results for knots detection, with a recall of 0.94 and 0.95 on two datasets, as well as for KDR image computation and juvenile timber detection.
Directory of Open Access Journals (Sweden)
Ivaniš Predrag
2004-01-01
Full Text Available This paper presents combination of Channel Optimized Vector Quantization based on LBG algorithm and sub channel power allocation for MIMO systems with Singular Value Decomposition and limited number of active sub channels. Proposed algorithm is designed to enable maximal throughput with bit error rate bellow some tar- get level in case of backward channel capacity limitation. Presence of errors effect in backward channel is also considered.
Support vector machines applications
Guo, Guodong
2014-01-01
Support vector machines (SVM) have both a solid mathematical background and good performance in practical applications. This book focuses on the recent advances and applications of the SVM in different areas, such as image processing, medical practice, computer vision, pattern recognition, machine learning, applied statistics, business intelligence, and artificial intelligence. The aim of this book is to create a comprehensive source on support vector machine applications, especially some recent advances.
Influence of the non-singular stress on the crack extension and fatigue life
International Nuclear Information System (INIS)
Cheng, C.Z.; Recho, N.; Niu, Z.R.
2012-01-01
Highlights: ► BEM is combined by characteristic analysis to calculate the singular stress field. ► A new method is proposed to evaluate the full stress field at crack tip region. ► Effect of non-singular stress on the propagation direction of the fatigue crack is analyzed. ► The influence of non-singular stress on the fatigue crack life is evaluated. - Abstract: The complete elasticity stress field at a crack tip region can be presented by the sum of the singular stress and several non-singular stress terms according to the Williams asymptotic expansion theory. The non-singular stress has a non-negligible influence on the prediction of the crack extension direction and crack growth rate under the fatigue loading. A novel method combining the boundary element method and the singularity characteristic analysis is proposed here to evaluate the complete stress field at a crack tip region. In this new method, any non-singular stress term in the Williams series expansion can be evaluated according to the computational accuracy requirement. Then, a modified Paris law is introduced to predict the crack propagation under the mixed-mode loading for exploring the influence of the non-singular stress on the fatigue life duration. By comparing with the existed experimental results, the predicted crack fatigue life when the non-singular stress is taken into consideration is more accurate than the predicted ones only considering the singular stress.
International Nuclear Information System (INIS)
Yan, Zhenya
2011-01-01
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black–Scholes option pricing model. In this Letter, we analytically propose vector financial rogue waves of the coupled nonlinear volatility and option pricing model without an embedded w-learning. Moreover, we exhibit their dynamical behaviors for chosen different parameters. The vector financial rogue wave (rogon) solutions may be used to describe the possible physical mechanisms for the rogue wave phenomena and to further excite the possibility of relative researches and potential applications of vector rogue waves in the financial markets and other related fields. -- Highlights: ► We investigate the coupled nonlinear volatility and option pricing model. ► We analytically present vector financial rogue waves. ► The vector financial rogue waves may be used to describe the extreme events in financial markets. ► This results may excite the relative researches and potential applications of vector rogue waves.
Directory of Open Access Journals (Sweden)
George N. Galanis
2005-10-01
Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0
Li, Zizun; Wang, Wu-Sheng
2017-01-01
The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations and singular impulsive equations.
Fermionic bound states in Minkowski space. Light-cone singularities and structure
Energy Technology Data Exchange (ETDEWEB)
Paula, Wayne de; Frederico, Tobias; Pimentel, Rafael [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Jose dos Campos, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Pisa (Italy)
2017-11-15
The Bethe-Salpeter equation for two-body bound system with spin 1/2 constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one (i) to deal with end-point singularities one meets and (ii) to find stable results, up to strongly relativistic regimes, which settle in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion 0{sup +} state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector-boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in 0{sup -} state, taking both constituent-fermion and exchanged-boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom. (orig.)
Directory of Open Access Journals (Sweden)
Vahid Faghih Dinevari
2016-01-01
Full Text Available Wireless capsule endoscopy (WCE is a new noninvasive instrument which allows direct observation of the gastrointestinal tract to diagnose its relative diseases. Because of the large number of images obtained from the capsule endoscopy per patient, doctors need too much time to investigate all of them. So, it would be worthwhile to design a system for detecting diseases automatically. In this paper, a new method is presented for automatic detection of tumors in the WCE images. This method will utilize the advantages of the discrete wavelet transform (DWT and singular value decomposition (SVD algorithms to extract features from different color channels of the WCE images. Therefore, the extracted features are invariant to rotation and can describe multiresolution characteristics of the WCE images. In order to classify the WCE images, the support vector machine (SVM method is applied to a data set which includes 400 normal and 400 tumor WCE images. The experimental results show proper performance of the proposed algorithm for detection and isolation of the tumor images which, in the best way, shows 94%, 93%, and 93.5% of sensitivity, specificity, and accuracy in the RGB color space, respectively.
Faghih Dinevari, Vahid; Karimian Khosroshahi, Ghader; Zolfy Lighvan, Mina
2016-01-01
Wireless capsule endoscopy (WCE) is a new noninvasive instrument which allows direct observation of the gastrointestinal tract to diagnose its relative diseases. Because of the large number of images obtained from the capsule endoscopy per patient, doctors need too much time to investigate all of them. So, it would be worthwhile to design a system for detecting diseases automatically. In this paper, a new method is presented for automatic detection of tumors in the WCE images. This method will utilize the advantages of the discrete wavelet transform (DWT) and singular value decomposition (SVD) algorithms to extract features from different color channels of the WCE images. Therefore, the extracted features are invariant to rotation and can describe multiresolution characteristics of the WCE images. In order to classify the WCE images, the support vector machine (SVM) method is applied to a data set which includes 400 normal and 400 tumor WCE images. The experimental results show proper performance of the proposed algorithm for detection and isolation of the tumor images which, in the best way, shows 94%, 93%, and 93.5% of sensitivity, specificity, and accuracy in the RGB color space, respectively.
On the use of the singular value decomposition for text retrieval
Energy Technology Data Exchange (ETDEWEB)
Husbands, P.; Simon, H.D.; Ding, C.
2000-12-04
The use of the Singular Value Decomposition (SVD) has been proposed for text retrieval in several recent works. This technique uses the SVD to project very high dimensional document and query vectors into a low dimensional space. In this new space it is hoped that the underlying structure of the collection is revealed thus enhancing retrieval performance. Theoretical results have provided some evidence for this claim and to some extent experiments have confirmed this. However, these studies have mostly used small test collections and simplified document models. In this work we investigate the use of the SVD on large document collections. We show that, if interpreted as a mechanism for representing the terms of the collection, this technique alone is insufficient for dealing with the variability in term occurrence. Section 2 introduces the text retrieval concepts necessary for our work. A short description of our experimental architecture is presented in Section 3. Section 4 describes how term occurrence variability affects the SVD and then shows how the decomposition influences retrieval performance. A possible way of improving SVD-based techniques is presented in Section 5 and concluded in Section 6.
International Nuclear Information System (INIS)
Kulisek, Jonathan A.; Anderson, Kevin K.; Casella, Andrew M.; Gesh, Christopher J.; Warren, Glen A.
2013-01-01
This study investigates the use of a Lead Slowing-Down Spectrometer (LSDS) for the direct and independent measurement of fissile isotopes in light-water nuclear reactor fuel assemblies. The current study applies MCNPX, a Monte Carlo radiation transport code, to simulate the measurement of the assay of the used nuclear fuel assemblies in the LSDS. An empirical model has been developed based on the calibration of the LSDS to responses generated from the simulated assay of six well-characterized fuel assemblies. The effects of self-shielding are taken into account by using empirical basis vectors calculated from the singular value decomposition (SVD) of a matrix containing the self-shielding functions from the assay of assemblies in the calibration set. The performance of the empirical algorithm was tested on version 1 of the Next-Generation Safeguards Initiative (NGSI) used fuel library consisting of 64 assemblies, as well as a set of 27 diversion assemblies, both of which were developed by Los Alamos National Laboratory. The potential for direct and independent assay of the sum of the masses of Pu-239 and Pu-241 to within 2%, on average, has been demonstrated
Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.
Directory of Open Access Journals (Sweden)
Vanessa V Sochat
Full Text Available Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.
Singularities of n-fold integrals of the Ising class and the theory of elliptic curves
International Nuclear Information System (INIS)
Boukraa, S; Hassani, S; Maillard, J-M; Zenine, N
2007-01-01
We introduce some multiple integrals that are expected to have the same singularities as the singularities of the n-particle contributions χ (n) to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for n = 1, 2, 3, 4 and only modulo some primes for n = 5 and 6, thus providing a large set of (possible) new singularities of χ (n) . We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to n = 6) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a finite number of one-dimensional integrals. Among the singularities found, we underline the fact that the quadratic polynomial condition 1 + 3w + 4w 2 = 0, that occurs in the linear differential equation of χ (3) , actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves
Desingularization strategies for three-dimensional vector fields
Torres, Felipe Cano
1987-01-01
For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the pro...
Multithreading in vector processors
Energy Technology Data Exchange (ETDEWEB)
Evangelinos, Constantinos; Kim, Changhoan; Nair, Ravi
2018-01-16
In one embodiment, a system includes a processor having a vector processing mode and a multithreading mode. The processor is configured to operate on one thread per cycle in the multithreading mode. The processor includes a program counter register having a plurality of program counters, and the program counter register is vectorized. Each program counter in the program counter register represents a distinct corresponding thread of a plurality of threads. The processor is configured to execute the plurality of threads by activating the plurality of program counters in a round robin cycle.
Twisting of paramodular vectors
Johnson-Leung, Jennifer; Roberts, Brooks
2013-01-01
Let $F$ be a non-archimedean local field of characteristic zero, let $(\\pi,V)$ be an irreducible, admissible representation of $\\GSp(4,F)$ with trivial central character, and let $\\chi$ be a quadratic character of $F^\\times$ with conductor $c(\\chi)>1$. We define a twisting operator $T_\\chi$ from paramodular vectors for $\\pi$ of level $n$ to paramodular vectors for $\\chi \\otimes \\pi$ of level $\\max(n+2c(\\chi),4c(\\chi))$, and prove that this operator has properties analogous to the well-known $...
Eisenman, Richard L
2005-01-01
This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structur
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems
Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.
2018-03-01
We report on a new open-source, user-friendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy + provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.
Prevalence of superficial siderosis following singular, acute aneurysmal subarachnoid hemorrhage
Energy Technology Data Exchange (ETDEWEB)
Lummel, N.; Bochmann, K. [Ludwig-Maximilian-University, Department of Neuroradiology, Klinikum Grosshadern, Munich (Germany); Bernau, C. [Leibniz-Rechenzentrum, Munich (Germany); Thon, N. [Ludwig-Maximilian-University, Department of Neurosurgery, Klinikum Grosshadern, Munich (Germany); Linn, J. [Technical University, Department of Neuroradiology, Klinikum Dresden, Dresden (Germany)
2015-04-01
Superficial siderosis is presumably a consequence of recurrent bleeding into the subarachnoid space. The objective of this study was to assess the prevalence of superficial siderosis after singular, aneurysmal subarachnoid hemorrhage (SAH) in the long term. We retrospectively identified all patients who presented with a singular, acute, aneurysmal SAH at our institution between 2010 and 2013 and in whom a magnetic resonance imaging (MRI) including T2*-weighted imaging was available at least 4 months after the acute bleeding event. MRI scans were judged concerning the presence and distribution of superficial siderosis. Influence of clinical data, Fisher grade, localization, and cause of SAH as well as the impact of neurosurgical interventions on the occurrence of superficial siderosis was tested. Seventy-two patients with a total of 117 MRIs were included. Mean delay between SAH and the last available MRI was 47.4 months (range 4-129). SAH was Fisher grade 1 in 2 cases, 2 in 4 cases, 3 in 10 cases, and 4 in 56 cases. Superficial siderosis was detected in 39 patients (54.2 %). In all patients with more than one MRI scan, localization and distribution of superficial siderosis did not change over time. Older age (p = 0.02) and higher degree of SAH (p = 0.03) were significantly associated with the development of superficial siderosis. Superficial siderosis develops in approximately half of patients after singular, aneurysmal SAH and might be more common in patients with an older age and a greater amount of blood. However, additional factors must play a role in whether a patient is prone to develop superficial siderosis or not. (orig.)
Singular gauge fields in inclusive and differential cross sections
International Nuclear Information System (INIS)
Ore, F.R. Jr.; Sterman, G.
1981-01-01
We study differential and inclusive cross sections for the creation of massless fermions in the presence of a static external non-Abelian field A/sub c1/. We calculate to all orders in A/sub cl/ the correction to the quantum cross section which is suppressed by one power of the energy. Corrections of this type are found to be important even at high energy for sufficiently exclusive cross sections if the classical field has singularities along a line. Their contribution to inclusive cross sections, on the other hand, remains small at high energies
Conical flow near singular rays. [shock generation in ideal gas
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.
Total graph of a module with respect to singular submodule
Directory of Open Access Journals (Sweden)
Jituparna Goswami
2016-07-01
Full Text Available Let R be a commutative ring with unity and M be an R-module. We introduce the total graph of a module M with respect to singular submodule Z(M of M as an undirected graph T(Γ(M with vertex set as M and any two distinct vertices x and y are adjacent if and only if x+y∈Z(M. We investigate some properties of the total graph T(Γ(M and its induced subgraphs Z(Γ(M and Z¯(Γ(M. In some aspects, we have noticed some sort of finiteness.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Directory of Open Access Journals (Sweden)
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Motion Control of a Quadrotor Aircraft via Singular Perturbations
Directory of Open Access Journals (Sweden)
Salvador González-Vázquez
2013-10-01
Full Text Available In this paper, a new motion controller for a quadrotor aircraft is introduced. A reformulation of the control inputs of the dynamic model is discussed and then the control algorithm is given in a constructive form. The stability proof of the state space origin of the overall closed-loop system relies on the theory of singularly perturbed systems. Numerical simulations corroborate the viability of the proposed control scheme and the conclusions concerning stability. A set of simulations under practical conditions is also presented, where the system is affected by different types of disturbances and nonlinearities such as noise and actuator saturation.
Tachyon cosmology, supernovae data and the Big Brake singularity
Keresztes, Z.; Gergely, L. A.; Gorini, V.; Moschella, U.; Yu, Kamenshchik A.
2009-01-01
We compare the existing observational data on type Ia Supernovae with the evolutions of the universe predicted by a one-parameter family of tachyon models which we have introduced recently in paper \\cite{we-tach}. Among the set of the trajectories of the model which are compatible with the data there is a consistent subset for which the universe ends up in a new type of soft cosmological singularity dubbed Big Brake. This opens up yet another scenario for the future history of the universe be...
Analytical study for singular system of transistor circuits
Directory of Open Access Journals (Sweden)
Devendra Kumar
2014-06-01
Full Text Available In this paper, we propose a user friendly algorithm based on homotopy analysis transform method for solving observer design in generalized state space or singular system of transistor circuits. The homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The effectiveness of technique is described and illustrated with an example. The obtained results are in a good agreement with the existing ones in open literature and it is shown that the scheme proposed here is robust, efficient, easy to implement and computationally very attractive.
A singularly perturbed SIS model with age structure.
Banasiak, Jacek; Phongi, Eddy Kimba; Lachowicz, Mirosław
2013-06-01
We present a preliminary study of an SIS model with a basic age structure and we focus on a disease with quick turnover, such as influenza or common cold. In such a case the difference between the characteristic demographic and epidemiological times naturally introduces two time scales in the model which makes it singularly perturbed. Using the Tikhonov theorem we prove that for certain classes of initial conditions the nonlinear structured SIS model can be approximated with very good accuracy by lower dimensional linear models.
Existence and regularity of weak solutions for singular elliptic problems
Directory of Open Access Journals (Sweden)
Brahim Bougherara
2015-11-01
Full Text Available In this article we study the semilinear singular elliptic problem $$\\displaylines{ -\\Delta u = \\frac{p(x}{u^{\\alpha}}\\quad \\text{in } \\Omega \\cr u = 0\\quad \\text{on } \\partial\\Omega,\\quad u>0 \\text{ in } \\Omega, }$$ where $\\Omega$ is a regular bounded domain of $\\mathbb R^{N}$, $\\alpha\\in\\mathbb R$, $p\\in C(\\Omega$ which behaves as $d(x^{-\\beta}$ as $x\\to\\partial\\Omega$ with $d$ the distance function up to the boundary and $0\\leq \\beta 1$.
Black Holes, Geons, and Singularities in Metric-Affine Gravity
Sanchez-Puente, Antonio
2017-01-01
Uno de los problemas abiertos en la descripción de la gravedad es la existencia de singularidades. Las geometrías singulares se caracterizan por geodésicas incompletas, lo que físicamente se corresponde con observadores que desaparecen del espacio-tiempo, o que aparecen de la nada. Múltiples extensiones de la Relatividad General tratan de resolver este problema de algún modo. Por ello, en esta tesis estudio modificaciones al Lagrangiano de Relatividad General, tales como gravedad cuadráti...
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
The Singular Universe and the Reality of Time
Mangabeira Unger, Roberto; Smolin, Lee
2015-01-01
Introduction; Part I. Roberto Mangabeira Unger: 1. The science of the one universe in time; 2. The context and consequences of the argument; 3. The singular existence of the universe; 4. The inclusive reality of time; 5. The mutability of the laws of nature; 6. The selective realism of mathematics; Part II. Lee Smolin: 1. Cosmology in crisis; 2. Principles for a cosmological theory; 3. The setting: the puzzles of contemporary cosmology; 4. Hypotheses for a new cosmology; 5. Mathematics; 6. Approaches to solving the metalaw dilemma; 7. Implications of temporal naturalism for philosophy of mind; 8. An agenda for science; 9. Concluding remarks; A note concerning disagreements between our views.
Maslov indices, Poisson brackets, and singular differential forms
Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.
2014-06-01
Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.
Cosmological BCS mechanism and the big bang singularity
Alexander, Stephon; Biswas, Tirthabir
2009-07-01
We provide a novel mechanism that resolves the big bang singularity present in Friedman-Lemaitre-Robertson-Walker space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in general relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter H to zero and results in a nonsingular bounce, at least in some special cases.
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Directory of Open Access Journals (Sweden)
Jin-Xiu Hu
2014-01-01
Full Text Available A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.
Mitri, F. G.
2016-08-01
In this work, counterintuitive effects such as the generation of an axial (i.e., long the direction of wave motion) zero-energy flux density (i.e., axial Poynting singularity) and reverse (i.e., negative) propagation of nonparaxial quasi-Gaussian electromagnetic (EM) beams are examined. Generalized analytical expressions for the EM field's components of a coherent superposition of two high-order quasi-Gaussian vortex beams of opposite handedness and different amplitudes are derived based on the complex-source-point method, stemming from Maxwell's vector equations and the Lorenz gauge condition. The general solutions exhibiting unusual effects satisfy the Helmholtz and Maxwell's equations. The EM beam components are characterized by nonzero integer degree and order (n ,m ) , respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and a weighting (real) factor 0 ≤α ≤1 that describes the transition of the beam from a purely vortex (α =0 ) to a nonvortex (α =1 ) type. An attractive feature for this superposition is the description of strongly focused (or strongly divergent) wave fields. Computations of the EM power density as well as the linear and angular momentum density fluxes illustrate the analysis with particular emphasis on the polarization states of the vector potentials forming the beams and the weight of the coherent beam superposition causing the transition from the vortex to the nonvortex type. Should some conditions determined by the polarization state of the vector potentials and the beam parameters be met, an axial zero-energy flux density is predicted in addition to a negative retrograde propagation effect. Moreover, rotation reversal of the angular momentum flux density with respect to the beam handedness is anticipated, suggesting the possible generation of negative (left-handed) torques. The results are particularly useful in applications involving the design of strongly focused optical laser
Nuclear medium effects via quasielastic (p vector, p vector') and (p vector, n vector) scattering
International Nuclear Information System (INIS)
Hillhouse, G.C.; Ventel, B.I.S. van der; Wyngaardt, S.M.; De Kock, P.R.
1997-01-01
For a 40 Ca target at a fixed momentum transfer of 1.97 fm -1 , and incident energies between 135 and 300 MeV, we quantitatively investigate the sensitivity of complete sets of quasielastic (p vector, p vector') and (p vector, n vector) spin observables to medium effects, pseudoscalar versus pseudovector forms of the πNN vertex, and exchange contributions to the NN amplitudes using a relativistic PWIA. The qualitative nature of previous studies failed to give an indication of the experimental statistical uncertainty required for distinguishing between the various model predictions. New Horowitz-Love-Franey relativistic NN amplitudes have been generated in order to yield improved and more quantitative spin observable values than before. This study indicates at which energies particular spin observables need to be measured in order to test current nuclear models. A comparison to the limited available data indicates that the relativistic parametrization of the NN scattering amplitudes in terms of only the five Fermi invariants (the SVPAT form) is questionable. (author)
Indian Academy of Sciences (India)
converting these vectors to orthonormal ones demanded by the model. The process of finding the closest or- thonormal basis is called the Lowdin orthogonalisation after the Swedish chemist P 0 Lowdin who introduced it. This is related to one of the basic theorems in linear algebra as we will see. Matrix Approximation ...
Treiman, Jay S
2014-01-01
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...
DEFF Research Database (Denmark)
2000-01-01
Using a pulsed ultrasound field, the two-dimensional velocity vector can be determined with the invention. The method uses a transversally modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new...
Sesquilinear uniform vector integral
Indian Academy of Sciences (India)
absolute integral which generalizes the Lebesgue integral and is more easy to manipulate. We speak so far about scalar integrals (scalar functions integrated with respect to positive measures-speaking approximately). The idea of integrating vector functions with respect to scalar measures came naturally on the scene of ...
Centers for Disease Control (CDC) Podcasts
2011-04-18
This podcast discusses emerging vector-borne pathogens, their role as prominent contributors to emerging infectious diseases, how they're spread, and the ineffectiveness of mosquito control methods. Created: 4/18/2011 by National Center for Emerging Zoonotic and Infectious Diseases (NCEZID). Date Released: 4/27/2011.
Modified Gauss rules for approximate calculation of some strongly singular integrals
Berriochoa Esnaola, Elias Manuel Maria; Cachafeiro López, María Alicia; Illán González, Jesús Ricardo; Rebollido Lorenzo, José Manuel
2013-01-01
The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented. Ministerio de Educación | Ref. MTM2011-22713
On the behaviour of Navier–Stokes equations near a possible singular point
International Nuclear Information System (INIS)
Kang, Kyungkeun; Lee, Jihoon
2010-01-01
We show that if a singularity of suitable weak solutions to Navier–Stokes equations occurs, then either p or at least two of ∂ i v i , i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂ r v r is not bounded both below and above near a singular point, if it exists
A class of interiors for Vaidya's radiating metric: singularity-free gravitational collapse
International Nuclear Information System (INIS)
Fayos, F; Torres, R
2008-01-01
In order to study gravitational collapse we introduce a class of stellar models which neither stabilize nor bounce. In these models all the energy conditions are fulfilled, however the collapsing stars radiate away their matter avoiding the formation of singularities. We discuss the viability of such a collapse and its implications in the resolution of the singularity issue. We also examine the possibility of living in a singularity-free locally open or flat FLRW universe satisfying all the energy conditions
The exotic heat-trace asymptotics of a regular-singular operator revisited
Vertman, Boris
2013-01-01
We discuss the exotic properties of the heat-trace asymptotics for a regular-singular operator with general boundary conditions at the singular end, as observed by Falomir, Muschietti, Pisani and Seeley as well as by Kirsten, Loya and Park. We explain how their results alternatively follow from the general heat kernel construction by Mooers, a natural question that has not been addressed yet, as the latter work did not elaborate explicitly on the singular structure of the heat trace expansion...
Modal Analysis Using the Singular Value Decomposition and Rational Fraction Polynomials
2017-04-06
TECHNICAL REPORT MODAL ANALYSIS USING THE SINGULAR VALUE DECOMPOSITION AND RATIONAL FRACTION POLYNOMIALS By J. B...Modal Analysis Using the Singular Value Decomposition and Rational Fraction Polynomials By J. B. Fahnline, R. L. Campbell, S. A. Hambric, and M. R...October 2004 - April 2017 Modal Analysis Using the Singular Value Decomposition and Rational Fraction Polynomials J. B. Fahnline, R. L. Campbell, S. A
Resolving the Schwarzschild singularity in both classic and quantum gravity
Directory of Open Access Journals (Sweden)
Ding-fang Zeng
2017-04-01
Full Text Available The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr–Sommerfield like “orbital” quantisation assumption, we show that for each black hole of horizon radius rh, there are about erh2/ℓpl2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.
Cosmological solutions and finite time singularities in Finslerian geometry
Paul, Nupur; de, S. S.; Rahaman, Farook
2018-03-01
We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.
Spatialization of social process vs singular object of architecture
Directory of Open Access Journals (Sweden)
Lujak Mihailo
2010-01-01
Full Text Available The fundamental subject of this research is spatialization of social process in the period of modernism manifested through transformation and/or change in meaning of space under a variety of social processes without changing the physical structure of space. These changes in meaning represent the specificity of development in space under the influence of the said social processes, which in this case is Yugoslav modernism, resulting in the creation of a singular object of architecture specific of a certain environment. These processes have been researched in the residential complex of Block 19a in New Belgrade, designed by architects Milan Lojanica, Predrag Cagić, and Borivoje Jovanović, and constructed between 1975 and 1982. The basic objective of this paper is to establish crucial causes for this complex to be considered the landmark in the designing practice of the time in Yugoslavia through research and critical analysis of the residential complex of Block 19a, and to try and determine the importance and potential influence in further architectural development in the period following its construction. In other words, the basic objective of this paper is to establish whether residential complex Block 19a represents a singular object of architecture in Yugoslavia/Serbia.
Singular solitons of generalized Camassa-Holm models
International Nuclear Information System (INIS)
Tian Lixin; Sun Lu
2007-01-01
Two generalizations of the Camassa-Holm system associated with the singular analysis are proposed for Painleve integrability properties and the extensions of already known analytic solitons. A remarkable feature of the physical model is that it has peakon solution which has peak form. An alternative WTC test which allowed the identifying of such models directly if formulated in terms of inserting a formed ansatz into these models. For the two models have Painleve property, Painleve-Baecklund systems can be constructed through the expansion of solitons about the singularity manifold. By the implementations of Maple, plentiful new type solitonic structures and some kink waves, which are affected by the variation of energy, are explored. If the energy is infinite in finite time, there will be a collapse in soliton systems by direct numerical simulations. Particularly, there are two collapses coexisting in our regular solitons, which occurred around its central regions. Simulation shows that in the bottom of periodic waves arises the non-zero parts of compactons and anti-compactons. We also get floating solitary waves whose amplitude is infinite. In contrary to which a finite-amplitude blow-up soliton is obtained. Periodic blow-ups are found too. Special kinks which have periodic cuspons are derived
Strong-field physics with singular light beams
Zürch, M.; Kern, C.; Hansinger, P.; Dreischuh, A.; Spielmann, Ch.
2012-10-01
Light beams carrying a point singularity with a screw-type phase distribution are associated with an optical vortex. The corresponding momentum flow leads to an orbital angular momentum of the photons. The study of optical vortices has led to applications such as particle micro-manipulation, imaging, interferometry, quantum information and high-resolution microscopy and lithography. Recent analyses showed that transitions forbidden by selection rules seem to be allowed when using optical vortex beams. To exploit these intriguing new applications, it is often necessary to shorten the wavelength by nonlinear frequency conversion. However, during the conversion the optical vortices tend to break up. Here we show that optical vortices can be generated in the extreme ultraviolet (XUV) region using high-harmonic generation. The singularity impressed on the fundamental beam survives the highly nonlinear process. Vortices in the XUV region have the same phase distribution as the driving field, which is in contradiction to previous findings, where multiplication of the momentum by the harmonic order is expected. This approach opens the way for several applications based on vortex beams in the XUV region.
Nonsingular Einsteinian Cosmology: How Galactic Momentum Prevents Cosmic Singularities
Directory of Open Access Journals (Sweden)
Kenneth J. Epstein
2013-01-01
Full Text Available It is shown how Einstein's equation can account for the evolution of the universe without an initial singularity and can explain the inflation epoch as a momentum dominated era in which energy from matter and radiation drove extremely accelerated expansion of space. It is shown how an object with momentum loses energy to the expanding universe and how this energy can contribute to accelerated spatial expansion more effectively than vacuum energy, because virtual particles, the source of vacuum energy, can have negative energy, which can cancel any positive energy from the vacuum. Radiation and matter with momentum have positive but decreasing energy in the expanding universe, and the energy lost by them can contribute to accelerated spatial expansion between galactic clusters, making dark energy a classical effect that can be explained by general relativity without quantum mechanics, and, as (13 and (15 show, without an initial singularity or a big bang. This role of momentum, which was overlooked in the Standard Cosmological Model, is the basis of a simpler model which agrees with what is correct in the old model and corrects what is wrong with it.
Cosmological singularity theorems for f ( R ) gravity theories
Energy Technology Data Exchange (ETDEWEB)
Alani, Ivo [Departamento de Física and IFIBA, Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina); Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar [Instituto de Matemáticas Luis Santaló (IMAS), Facultad de Ciencias Exactas y Naturales UBA Pabellón 1, Ciudad Universitaria (1428) C.A.B.A, Buenos Aires (Argentina)
2016-05-01
In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.
Leading singularities and off-shell conformal integrals
Energy Technology Data Exchange (ETDEWEB)
Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.
2013-08-29
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.
Microscopic study reveals the singular origins of growth
Yaari, G.; Nowak, A.; Rakocy, K.; Solomon, S.
2008-04-01
Anderson [Science 177, 293 (1972)] proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with reality. In the social sciences however, the possibilities to stage experiments to validate it are limited. During the 90's a series of dramatic political and economic events have provided the opportunity to do so. We exploit the resulting empirical evidence to validate a simple agent based alternative to the classical logistic dynamics. The post-liberalization empirical data from Poland confirm the theoretical prediction that the dynamics is dominated by singular rare events which insure the resilience and adaptability of the system. We have shown that growth is led by few singular “growth centers" (Fig. 1), that initially developed at a tremendous rate (Fig. 3), followed by a diffusion process to the rest of the country and leading to a positive growth rate uniform across the counties. In addition to the interdisciplinary unifying potential of our generic formal approach, the present work reveals the strong causal ties between the “softer" social conditions and their “hard" economic consequences.
Singularities in Structural Optimization of the Ziegler Pendulum
Directory of Open Access Journals (Sweden)
O. N. Kirillov
2011-01-01
Full Text Available Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.
Cosmological singularity theorems for f ( R ) gravity theories
International Nuclear Information System (INIS)
Alani, Ivo; Santillán, Osvaldo P.
2016-01-01
In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T ij −( g ij /2) T ) k i k j ≥ 0 for any generic unit time like field k i ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruence emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.
Singular structure of polarization images of bile secret in diagnostics of human physiological state
Ushenko, A. G.; Fediv, A. I.; Marchuk, Yu. F.
2009-07-01
There have been theoretically analyzed the ways of the formation of the polarization singularities of the biological tissues images of various morphological structures. There have been also experimentally examined the coordinate distributions of a single and doubly degenerated polarization singularities of the physiologically normal and pathologically changed biological tissues. There have been determined the statistical criteria of diagnostics of the kidney tissue collagenous disease (the 3rd and the 4th statistical moments of the linear density singularity points). It was found out that the process of the pathological change of the kidney tissue morphology leads to the formation of the self-similar (fractal) distribution of the polarization singularities of its image.