THE GRAVITATIONAL SHEAR-INTRINSIC ELLIPTICITY CORRELATION FUNCTIONS OF LUMINOUS RED GALAXIES IN OBSERVATION AND IN THE ΛCDM MODEL

International Nuclear Information System (INIS)

Okumura, Teppei; Jing, Y. P.

2009-01-01

We examine whether the gravitational shear-intrinsic ellipticity (GI) correlation function of the luminous red galaxies (LRGs) can be modeled with the distribution function of a misalignment angle advocated recently by Okumura et al. For this purpose, we have accurately measured the GI correlation for the LRGs in the Data Release 6 (DR6) of the Sloan Digital Sky Survey (SDSS), which confirms the results of Hirata et al. who used the DR4 data. By comparing the GI correlation functions in the simulation and in the observation, we find that the GI correlation can be modeled in the current ΛCDM model if the misalignment follows a Gaussian distribution with a zero mean and a typical misalignment angle σ θ = 34.9 +1.9 -2.1 degrees. We also find a correlation between the axis ratios and intrinsic alignments of LRGs. This effect should be taken into account in theoretical modeling of the GI and intrinsic ellipticity-ellipticity correlations for weak lensing surveys.

Community Detection for Correlation Matrices

Directory of Open Access Journals (Sweden)

Mel MacMahon

2015-04-01

Full Text Available A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with “hard” cores and “soft” peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect “soft stocks” that alternate between communities; and discuss implications for portfolio optimization and risk management.

Community Detection for Correlation Matrices

Science.gov (United States)

MacMahon, Mel; Garlaschelli, Diego

2015-04-01

A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with "hard" cores and "soft" peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect "soft stocks" that alternate between communities; and discuss implications for portfolio optimization and risk management.

Triaxiality in elliptical galaxies

Energy Technology Data Exchange (ETDEWEB)

Benacchio, L; Galletta, G [Padua Univ. (Italy). Ist. di Astronomia

1980-12-01

The existence of a triaxial shape for elliptical galaxies has been considered in recent years to explain the new kinematical and geometrical findings, i.e. (a) the low rotation/velocity dispersion ratio found also in some flat systems, (b) the presence of twisting in the isophotes, (c) the recently found correlation between maximum twisting and maximum flattening, (d) the presence of rotation along the minor axis. A simple geometrical model of elliptical galaxies having shells with different axial ratios c/a, b/a has been produced to interpret three fundamental key-features of elliptical galaxies: (i) the distribution of the maximum flattening observed; (ii) the percentage of ellipticals showing twisting; and (iii) the correlation between maximum twisting and maximum flattening. The model has been compared with observational data for 348 elliptical systems as given by Strom and Strom. It is found that a triaxial ellipsoid with coaxial shells having axial ratios c/a and b/a mutually dependent in a linear way can satisfy the observations.

Elliptic Determinantal Processes and Elliptic Dyson Models

Science.gov (United States)

Katori, Makoto

2017-10-01

We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families {A}_{N-1}, {B}_N, {C}_N and {D}_N, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.

THE L∝σ8 CORRELATION FOR ELLIPTICAL GALAXIES WITH CORES: RELATION WITH BLACK HOLE MASS

International Nuclear Information System (INIS)

Kormendy, John; Bender, Ralf

2013-01-01

We construct the Faber-Jackson correlation between velocity dispersion σ and total galaxy luminosity L V separately for elliptical galaxies with and without cores. The coreless ellipticals show the well-known, steep relationship dlog σ/dlog L V = 0.268 or L V ∝σ 3.74 . This corresponds to dlog σ/dlog M = 0.203, where M is the stellar mass and we use M/L∝L 0.32 . In contrast, the velocity dispersions of core ellipticals increase much more slowly with L V and M: dlog σ/dlog L V = 0.120, L V ∝σ 8.33 , and dlog σ/dlog M = 0.091. Dissipationless major galaxy mergers are expected to preserve σ according to the simplest virial-theorem arguments. However, numerical simulations show that σ increases slowly in dry major mergers, with dlog σ/dlog M ≅ +0.15. In contrast, minor mergers cause σ to decrease, with dlog σ/dlog M ≅ –0.05. Thus, the observed relation argues for dry major mergers as the dominant growth mode of the most massive ellipticals. This is consistent with what we know about the formation of cores. We know no viable way to explain galaxy cores except through dissipationless mergers of approximately equal-mass galaxies followed by core scouring by binary supermassive black holes. The observed, shallow σ∝L V +0.12 relation for core ellipticals provides further evidence that they formed in dissipationless and predominantly major mergers. Also, it explains the observation that the correlation of supermassive black hole mass with velocity dispersion, M . ∝σ 4 , ''saturates'' at high M . such that M . becomes almost independent of σ.

Advanced incomplete factorization algorithms for Stiltijes matrices

Energy Technology Data Exchange (ETDEWEB)

Il`in, V.P. [Siberian Division RAS, Novosibirsk (Russian Federation)

1996-12-31

The modern numerical methods for solving the linear algebraic systems Au = f with high order sparse matrices A, which arise in grid approximations of multidimensional boundary value problems, are based mainly on accelerated iterative processes with easily invertible preconditioning matrices presented in the form of approximate (incomplete) factorization of the original matrix A. We consider some recent algorithmic approaches, theoretical foundations, experimental data and open questions for incomplete factorization of Stiltijes matrices which are {open_quotes}the best{close_quotes} ones in the sense that they have the most advanced results. Special attention is given to solving the elliptic differential equations with strongly variable coefficients, singular perturbated diffusion-convection and parabolic equations.

Flattening and radio emission among elliptical galaxies

International Nuclear Information System (INIS)

Disney, M.J.; Sparks, W.B.; Wall, J.V.

1984-01-01

In a sample of 132 bright elliptical galaxies it is shown that there is a strong correlation between radio activity and flattening in the sense that radio ellipticals are both apparently and inherently rounder than the average elliptical. Both extended and compact sources are subject to the same correlation. No galaxies with axial ratios below 0.65 are found to be radio emitters. (author)

Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification

Directory of Open Access Journals (Sweden)

Jonas Maziero

2016-01-01

Full Text Available Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell-Mann matrices and to compute the optimized and unoptimized versions of associated Bloch’s vectors and correlation matrix in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.

Estimating correlation and covariance matrices by weighting of market similarity

OpenAIRE

Michael C. M\\"unnix; Rudi Sch\\"afer; Oliver Grothe

2010-01-01

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure which compares the current correlation structure of the market to the structures at past ...

An inequality between the weighted average and the rowwise correlation coefficient for proximity matrices

NARCIS (Netherlands)

Krijnen, WP

De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this

AN INEQUALITY BETWEEN THE WEIGHTED AVERAGE AND THE ROWWISE CORRELATION-COEFFICIENT FOR PROXIMITY MATRICES

NARCIS (Netherlands)

KRIJNEN, WP

De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this

The properties of radio ellipticals

International Nuclear Information System (INIS)

Sparks, W.B.; Disney, M.J.; Rodgers, A.W.

1984-01-01

Optical and additional radio data are presented for the bright galaxies of the Disney and Wall survey (1977 Mon. Not. R. Astron. Soc. 179, 235). These data form the basis of a statistical comparison of the properties of radio elliptical galaxies to radio-quiet ellipticals. The correlations may be explained by the depth of the gravitational potential well in which the galaxy resides governing the circumstances under which an elliptical galaxy rids itself of internally produced gas. (author)

On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

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Olha P. Kupenko

2013-01-01

Full Text Available We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.

ELLIPT2D: A Flexible Finite Element Code Written Python

International Nuclear Information System (INIS)

Pletzer, A.; Mollis, J.C.

2001-01-01

The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research

Fine structure of spectral properties for random correlation matrices: an application to financial markets.

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Fine structure of spectral properties for random correlation matrices: An application to financial markets

Science.gov (United States)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Estimated correlation matrices and portfolio optimization

Science.gov (United States)

Pafka, Szilárd; Kondor, Imre

2004-11-01

Correlations of returns on various assets play a central role in financial theory and also in many practical applications. From a theoretical point of view, the main interest lies in the proper description of the structure and dynamics of correlations, whereas for the practitioner the emphasis is on the ability of the models to provide adequate inputs for the numerous portfolio and risk management procedures used in the financial industry. The theory of portfolios, initiated by Markowitz, has suffered from the “curse of dimensions” from the very outset. Over the past decades a large number of different techniques have been developed to tackle this problem and reduce the effective dimension of large bank portfolios, but the efficiency and reliability of these procedures are extremely hard to assess or compare. In this paper, we propose a model (simulation)-based approach which can be used for the systematical testing of all these dimensional reduction techniques. To illustrate the usefulness of our framework, we develop several toy models that display some of the main characteristic features of empirical correlations and generate artificial time series from them. Then, we regard these time series as empirical data and reconstruct the corresponding correlation matrices which will inevitably contain a certain amount of noise, due to the finiteness of the time series. Next, we apply several correlation matrix estimators and dimension reduction techniques introduced in the literature and/or applied in practice. As in our artificial world the only source of error is the finite length of the time series and, in addition, the “true” model, hence also the “true” correlation matrix, are precisely known, therefore in sharp contrast with empirical studies, we can precisely compare the performance of the various noise reduction techniques. One of our recurrent observations is that the recently introduced filtering technique based on random matrix theory performs

Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices.

Science.gov (United States)

Yang, Yang; DeGruttola, Victor

2012-06-22

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.

Generalized canonical correlation analysis of matrices with missing rows : A simulation study

NARCIS (Netherlands)

van de Velden, Michel; Bijmolt, Tammo H. A.

A method is presented for generalized canonical correlation analysis of two or more matrices with missing rows. The method is a combination of Carroll's (1968) method and the missing data approach of the OVERALS technique (Van der Burg, 1988). In a simulation study we assess the performance of the

Eigenstructures of MIMO Fading Channel Correlation Matrices and Optimum Linear Precoding Designs for Maximum Ergodic Capacity

Directory of Open Access Journals (Sweden)

Hamid Reza Bahrami

2007-01-01

Full Text Available The ergodic capacity of MIMO frequency-flat and -selective channels depends greatly on the eigenvalue distribution of spatial correlation matrices. Knowing the eigenstructure of correlation matrices at the transmitter is very important to enhance the capacity of the system. This fact becomes of great importance in MIMO wireless systems where because of the fast changing nature of the underlying channel, full channel knowledge is difficult to obtain at the transmitter. In this paper, we first investigate the effect of eigenvalues distribution of spatial correlation matrices on the capacity of frequency-flat and -selective channels. Next, we introduce a practical scheme known as linear precoding that can enhance the ergodic capacity of the channel by changing the eigenstructure of the channel by applying a linear transformation. We derive the structures of precoders using eigenvalue decomposition and linear algebra techniques in both cases and show their similarities from an algebraic point of view. Simulations show the ability of this technique to change the eigenstructure of the channel, and hence enhance the ergodic capacity considerably.

Products of random matrices from fixed trace and induced Ginibre ensembles

Science.gov (United States)

Akemann, Gernot; Cikovic, Milan

2018-05-01

We investigate the microcanonical version of the complex induced Ginibre ensemble, by introducing a fixed trace constraint for its second moment. Like for the canonical Ginibre ensemble, its complex eigenvalues can be interpreted as a two-dimensional Coulomb gas, which are now subject to a constraint and a modified, collective confining potential. Despite the lack of determinantal structure in this fixed trace ensemble, we compute all its density correlation functions at finite matrix size and compare to a fixed trace ensemble of normal matrices, representing a different Coulomb gas. Our main tool of investigation is the Laplace transform, that maps back the fixed trace to the induced Ginibre ensemble. Products of random matrices have been used to study the Lyapunov and stability exponents for chaotic dynamical systems, where the latter are based on the complex eigenvalues of the product matrix. Because little is known about the universality of the eigenvalue distribution of such product matrices, we then study the product of m induced Ginibre matrices with a fixed trace constraint—which are clearly non-Gaussian—and M  ‑  m such Ginibre matrices without constraint. Using an m-fold inverse Laplace transform, we obtain a concise result for the spectral density of such a mixed product matrix at finite matrix size, for arbitrary fixed m and M. Very recently local and global universality was proven by the authors and their coworker for a more general, single elliptic fixed trace ensemble in the bulk of the spectrum. Here, we argue that the spectral density of mixed products is in the same universality class as the product of M independent induced Ginibre ensembles.

Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers

CERN Document Server

Auteri, F; Quartapelle, L

2003-01-01

A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...

Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances

International Nuclear Information System (INIS)

Akemann, Gernot; Checinski, Tomasz; Kieburg, Mario

2016-01-01

We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random matrices. Typically ensembles with correlations among the matrix elements are much more difficult to solve. Using a combination of supersymmetry, superbosonisation and bi-orthogonal functions we are able to determine all spectral k -point density correlation functions of H for arbitrary matrix size N . In the half-degenerate case, when one of the covariance matrices is proportional to the identity, the recent results by Kumar for the joint eigenvalue distribution of H serve as our starting point. In this case the ensemble has a bi-orthogonal structure and we explicitly determine its kernel, providing its exact solution for finite N . The kernel follows from computing the expectation value of a single characteristic polynomial. In the general non-degenerate case the generating function for the k -point resolvent is determined from a supersymmetric evaluation of the expectation value of k ratios of characteristic polynomials. Numerical simulations illustrate our findings for the spectral density at finite N and we also give indications how to do the asymptotic large- N analysis. (paper)

Ellipticities of Elliptical Galaxies in Different Environments

Science.gov (United States)

Chen, Cheng-Yu; Hwang, Chorng-Yuan; Ko, Chung-Ming

2016-10-01

We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between -21 and -22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.

Correlations Between Central Massive Objects And Their Host Galaxies: From Bulgeless Spirals to Ellipticals

OpenAIRE

Li, Yuexing; Haiman, Zoltán; Mac Low, Mordecai-Mark

2006-01-01

Recent observations by Ferrarese et al. (2006) and Wehner et al. (2006) reveal that a majority of galaxies contain a central massive object (CMO), either a supermassive black hole (SMBH) or a compact stellar nucleus, regardless of the galaxy mass or morphological type, and that there is a tight relation between the masses of CMOs and those of the host galaxies. Several recent studies show that feedback from black holes can successfully explain the $\\msigma$ correlation in massive elliptical g...

Extreme eigenvalues of sample covariance and correlation matrices

DEFF Research Database (Denmark)

Heiny, Johannes

This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the sample size n. We generalize the growth rates of p existing in the literature. Assuming a regular variation condition with tail index ... eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high dimension...

Analytical Derivation of the Inverse Moments of One-Sided Correlated Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil

2016-02-03

This paper addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error (LMMSE) estimator or also other loss functions used to measure the accuracy of covariance matrix estimates.

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.

Science.gov (United States)

Fan, Jianqing; Rigollet, Philippe; Wang, Weichen

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.

A random matrix model for elliptic curve L-functions of finite conductor

International Nuclear Information System (INIS)

Dueñez, E; Huynh, D K; Keating, J P; Snaith, N C; Miller, S J

2012-01-01

We propose a random-matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of the critical zeros of these L-functions away from the centre of the critical strip was observed numerically by Miller (2006 Exp. Math. 15 257–79); such behaviour deviates qualitatively from the conjectural limiting distribution of the zeros (for large conductors this distribution is expected to approach the one-level density of eigenvalues of orthogonal matrices after appropriate rescaling). Our purpose here is to provide a random-matrix model for Miller’s surprising discovery. We consider the family of even quadratic twists of a given elliptic curve. The main ingredient in our model is a calculation of the eigenvalue distribution of random orthogonal matrices whose characteristic polynomials are larger than some given value at the symmetry point in the spectra. We call this sub-ensemble of SO(2N) the excised orthogonal ensemble. The sieving-off of matrices with small values of the characteristic polynomial is akin to the discretization of the central values of L-functions implied by the formulae of Waldspurger and Kohnen–Zagier. The cut-off scale appropriate to modelling elliptic curve L-functions is exponentially small relative to the matrix size N. The one-level density of the excised ensemble can be expressed in terms of that of the well-known Jacobi ensemble, enabling the former to be explicitly calculated. It exhibits an exponentially small (on the scale of the mean spacing) hard gap determined by the cut-off value, followed by soft repulsion on a much larger scale. Neither of these features is present in the one-level density of SO(2N). When N → ∞ we recover the limiting orthogonal behaviour. Our results agree qualitatively with Miller’s discrepancy. Choosing the cut-off appropriately gives a model in good quantitative agreement with the number-theoretical data. (paper)

Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix

Science.gov (United States)

Skrypnyk, Taras

2017-05-01

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3)⊗ so(3)-valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the "separating functions" B( u) and A( u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler's top, Steklov-Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and "spin" generalization of Steklov-Lyapunov model.

Covariance-Based Estimation from Multisensor Delayed Measurements with Random Parameter Matrices and Correlated Noises

Directory of Open Access Journals (Sweden)

R. Caballero-Águila

2014-01-01

Full Text Available The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms.

Event-by-Event Elliptic Flow Fluctuations from PHOBOS

Science.gov (United States)

Wosiek, B.; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Hołyński, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.

2009-04-01

Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in (Au+Au) collisions at sqrt {sNN}=200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

Science.gov (United States)

Han, Fang; Liu, Han

2017-02-01

Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign subgaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.

Visualizing complex (hydrological) systems with correlation matrices

Science.gov (United States)

Haas, J. C.

2016-12-01

When trying to understand or visualize the connections of different aspects of a complex system, this often requires deeper understanding to start with, or - in the case of geo data - complicated GIS software. To our knowledge, correlation matrices have rarely been used in hydrology (e.g. Stoll et al., 2011; van Loon and Laaha, 2015), yet they do provide an interesting option for data visualization and analysis. We present a simple, python based way - using a river catchment as an example - to visualize correlations and similarities in an easy and colorful way. We apply existing and easy to use python packages from various disciplines not necessarily linked to the Earth sciences and can thus quickly show how different aquifers work or react, and identify outliers, enabling this system to also be used for quality control of large datasets. Going beyond earlier work, we add a temporal and spatial element, enabling us to visualize how a system reacts to local phenomena such as for example a river, or changes over time, by visualizing the passing of time in an animated movie. References: van Loon, A.F., Laaha, G.: Hydrological drought severity explained by climate and catchment characteristics, Journal of Hydrology 526, 3-14, 2015, Drought processes, modeling, and mitigation Stoll, S., Hendricks Franssen, H. J., Barthel, R., Kinzelbach, W.: What can we learn from long-term groundwater data to improve climate change impact studies?, Hydrology and Earth System Sciences 15(12), 3861-3875, 2011

Measurement of the correlation between elliptic flow and higher-order flow harmonics in Pb+Pb collisions at $\\sqrt{s_{_{\\mathrm{NN}}}}$=2.76 TeV

CERN Document Server

The ATLAS collaboration

2014-01-01

Correlations between the elliptic flow coefficient, $v_2$, and higher-order flow harmonics, $v_3$, $v_4$ and $v_5$ are measured using 7 $\\mu$b$^{-1}$ of Pb+Pb collision data at $\\sqrt{s_{_{\\mathrm{NN}}}}=2.76$ TeV collected by the ATLAS experiment at the LHC. The $v_2$-$v_n$ correlations are measured as a function of centrality, and, for events within the same centrality interval, also as a function of event ellipticity. The results are compared to initial-state eccentricities calculated from initial geometry models. The $v_2$-$v_n$ correlations within a given centrality interval are very different from the $v_2$-$v_n$ correlations as a function of centrality. For events within the same centrality interval, $v_3$ is found to be anti-correlated with $v_2$ and this anti-correlation is compatible with similar anti-correlations between the corresponding eccentricities $\\epsilon_2$ and $\\epsilon_3$. On the other hand, the $v_4$ and $v_5$ are found to increase strongly with $v_2$. The trend and strength of the $v_2...

Vacuum correlation functions of superfields, properties of matrices of periods, and holomorphic structure of multiloop amplitudes in superstring theory

International Nuclear Information System (INIS)

Danilov, G.S.

1994-01-01

It is shown that matrices of periods characterizing complex (1|1) supermanifolds of genus n > 1 depend on a spinor structure. This dependence manifests itself in terms proportional to odd moduli. Properties of matrices of periods exert a strong influence on the holomorphic structure of multiloop amplitudes in superstring theory. The supersymmetric analog of the Belavin-Knizhnik theorem is obtained by taking into account the above dependence on odd moduli. Superconformal versions of the Schottky group are used to study matrices of periods. This is essentially the only parametrization in which matrices of periods can be expressed explicitly in terms of even and odd moduli. Superconformal Schottky groups suitable for describing all spinor structures, including the structures for which superfields have branch points, are constructed. A method for calculating vacuum correlation functions of superfields for the above spinor structures is proposed. 18 refs

Convergence criteria for systems of nonlinear elliptic partial differential equations

International Nuclear Information System (INIS)

Sharma, R.K.

1986-01-01

This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities

Science.gov (United States)

Bakker, Mark

2004-05-01

Two new analytic element solutions are presented for steady flow problems with elliptical boundaries. The first solution concerns groundwater flow to shallow elliptical lakes with leaky lake beds in a single-aquifer. The second solution concerns groundwater flow through elliptical cylinder inhomogeneities in a multi-aquifer system. Both the transmissivity of each aquifer and the resistance of each leaky layer may differ between the inside and the outside of an inhomogeneity. The elliptical inhomogeneity may be bounded on top by a shallow elliptical lake with a leaky lake bed. Analytic element solutions are obtained for both problems through separation of variables of the Laplace and modified-Helmholtz differential equations in elliptical coordinates. The resulting equations for the discharge potential consist of infinite sums of products of exponentials, trigonometric functions, and modified-Mathieu functions. The series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately, but up to machine accuracy provided enough terms are used. The head and flow may be computed analytically at any point in the aquifer. Examples are given of uniform flow through an elliptical lake, a well pumping near two elliptical lakes, and uniform flow through three elliptical inhomogeneities in a multi-aquifer system. Mathieu functions may be applied in a similar fashion to solve other groundwater flow problems in semi-confined aquifers and leaky aquifer systems with elliptical internal or external boundaries.

Fast computation of complete elliptic integrals and Jacobian elliptic functions

Science.gov (United States)

Fukushima, Toshio

2009-12-01

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K( m) and E( m), for the standard domain of the elliptic parameter, 0 procedure to compute simultaneously three Jacobian elliptic functions, sn( u| m), cn( u| m), and dn( u| m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic argument, u, after its domain is reduced to the standard range, 0 ≤ u procedure is 25-70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K( m) is not taken into account.

Forecasting Covariance Matrices: A Mixed Frequency Approach

DEFF Research Database (Denmark)

Halbleib, Roxana; Voev, Valeri

This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...

Planar elliptic growth

Energy Technology Data Exchange (ETDEWEB)

Mineev, Mark [Los Alamos National Laboratory

2008-01-01

The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for areapreserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.

Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices

KAUST Repository

Elkhalil, Khalil

2016-08-15

In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.

Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices

KAUST Repository

Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2016-01-01

In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.

СREATION OF CORRELATION FUNCTIONS OF LINEAR CONTINUOUS SYSTEMS BASED ON THEIR FUNDAMENTAL MATRICES

Directory of Open Access Journals (Sweden)

N. A. Vunder

2015-11-01

Full Text Available The paper presents a method of creating correlation matrices and functions of the state vectors and outputs of the linear continuous systems functioning under the conditions of stochastic stationary, in a broad sense, effects. Fundamental matrices form the basis of the method. We have shown that for the linear continuous systems with single dimensional input and single dimensional output the correlation output function of such system can be found as the free movement of this system generated by its initial state. This state is constructed from the variance matrix of the state vector and the transposed output matrix. We have elucidated that when a continuous system belongs to a class of multi-dimensional input – multi-dimensional output systems, the following options are available for solving the problem of creation of the correlation function of a linear system. The first option is to partition the system into separate channels. Then the approach developed for systems with onedimensional input and one-dimensional output is applied to each of the separate channels. The second option is used to preserve the vector nature of the stochastic external influence. It consists in partition of output vector to scalar components by separating output matrix into separate rows with subsequent formation of the correlation function according to the scheme for single dimensional input and single dimensional output type systems. The third option is based on the scalarization of matrix correlation output function by applying the singular value decomposition to it. That gives the possibility to form scalar majorant and minorant of correlation output functions. We have established that a key component of a computational procedure of creating the correlation function of continuous linear system is a variance matrix of the system state vector. In the case of functioning under an exogenous stochastic effect like "white noise" the variance matrix is calculated by

Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field

Science.gov (United States)

Skrypnyk, T.

2017-08-01

We study the problem of separation of variables for classical integrable Hamiltonian systems governed by non-skew-symmetric non-dynamical so(3)\\otimes so(3) -valued elliptic r-matrices with spectral parameters. We consider several examples of such models, and perform separation of variables for classical anisotropic one- and two-spin Gaudin-type models in an external magnetic field, and for Jaynes-Cummings-Dicke-type models without the rotating wave approximation.

Mergers in galaxy groups. I. Structure and properties of elliptical remnants

International Nuclear Information System (INIS)

Taranu, Dan S.; Dubinski, John; Yee, H. K. C.

2013-01-01

We present collisionless simulations of dry mergers in groups of 3 to 25 galaxies to test the hypothesis that elliptical galaxies form at the centers of such groups. Mock observations of the central remnants confirm their similarity to ellipticals, despite having no dissipational component. We vary the profile of the original spiral's bulge and find that ellipticals formed from spirals with exponential bulges have too low Sersic indices. Mergers of spirals with de Vaucouleurs (classical) bulges produce remnants with larger Sersic indices correlated with luminosity, as with Sloan Digital Sky Survey ellipticals. Exponential bulge mergers are better fits to faint ellipticals, whereas classical bulge mergers better match luminous ellipticals. Similarly, luminous ellipticals are better reproduced by remnants undergoing many (>5) mergers, and fainter ellipticals by those with fewer mergers. The remnants follow tight size-luminosity and velocity dispersion-luminosity (Faber-Jackson) relations (<0.12 dex scatter), demonstrating that stochastic merging can produce tight scaling relations if the merging galaxies also follow tight scaling relations. The slopes of the size-luminosity and Faber-Jackson relations are close to observations but slightly shallower in the former case. Both relations' intercepts are offset—remnants are too large but have too low dispersions at fixed luminosity. Some remnants show substantial (v/σ > 0.1) rotational support, although most are slow rotators and few are very fast rotators (v/σ > 0.5). These findings contrast with previous studies concluding that dissipation is necessary to produce ellipticals from binary mergers of spirals. Multiple, mostly minor and dry mergers can produce bright ellipticals, whereas significant dissipation could be required to produce faint, rapidly rotating ellipticals.

Ellipticity and twisting of the isophotes of some bright galaxies in Virgo

International Nuclear Information System (INIS)

Barbon, R.; Benacchio, L.; Capaccioli, M.

1980-01-01

Ellipticity and twisting of the isophotes of four lenticular and seven elliptical galaxies in the Virgo cluster are presented as a sample of a more complete photometric investigation. This work has been motivated by the increasing importance of this kind of information for the understanding of the spatial structure of E galaxies. The calibrated plate material from the Loiano 1.52 meter and Tautenburg Schmidt telescopes has been digitized with a PDS microdensitometer and analysed by means of the Interactive Numerical Mapping Package (INMP). Ellipticity and orientation profiles are presented in a graphical form together with a preliminary discussion. A correlation has been found between ellipticity and twisting in barred lenticulars which might help in the understanding of some E galaxies such as NGC 4406 and NGC 4374. Twisting has been detected in all of the seven ellipticals of the sample

Arbitrarily elliptical-cylindrical invisible cloaking

International Nuclear Information System (INIS)

Jiang Weixiang; Cui Tiejun; Yu Guanxia; Lin Xianqi; Cheng Qiang; Chin, J Y

2008-01-01

Based on the idea of coordinate transformation (Pendry, Schurig and Smith 2006 Science 312 1780), arbitrarily elliptical-cylindrical cloaks are proposed and designed. The elliptical cloak, which is composed of inhomogeneous anisotropic metamaterials in an elliptical-shell region, will deflect incoming electromagnetic (EM) waves and guide them to propagate around the inner elliptical region. Such EM waves will return to their original propagation directions without distorting the waves outside the elliptical cloak. General formulations of the inhomogeneous and anisotropic permittivity and permeability tensors are derived for arbitrarily elliptical axis ratio k, which can also be used for the circular cloak when k = 1. Hence the elliptical cloaks can make a large range of objects invisible, from round objects (when k approaches 1) to long and thin objects (when k is either very large or very small). We also show that the material parameters in elliptical cloaking are singular at only two points, instead of on the whole inner circle for circular cloaking, which are much easier to be realized in actual applications. Full-wave simulations are given to validate the arbitrarily elliptical cloaking

Elliptically polarized electromagnetic waves in a magnetized quantum electron-positron plasma with effects of exchange-correlation

Energy Technology Data Exchange (ETDEWEB)

Shahmansouri, M., E-mail: mshmansouri@gmail.com [Department of Physics, Faculty of Science, Arak University, Arak 38156-8 8349 (Iran, Islamic Republic of); Misra, A. P., E-mail: apmisra@visva-bharati.ac.in, E-mail: apmisra@gmail.com [Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)

2016-07-15

The dispersion properties of elliptically polarized electromagnetic waves in a magnetized electron-positron-pair (EP-pair) plasma are studied with the effects of particle dispersion associated with the Bohm potential, the Fermi degenerate pressure, and the exchange-correlation force. Two possible modes of the extraordinary or X wave, modified by these quantum effects, are identified and their propagation characteristics are investigated numerically. It is shown that the upper-hybrid frequency and the cutoff and resonance frequencies are no longer constants but are dispersive due to these quantum effects. It is found that the particle dispersion and the exchange-correlation force can have different dominating roles on each other depending on whether the X waves are of short or long wavelengths (in comparison with the Fermi Debye length). The present investigation should be useful for understanding the collective behaviors of EP plasma oscillations and the propagation of extraordinary waves in magnetized dense EP-pair plasmas.

Elliptic net and its cryptographic application

Science.gov (United States)

Muslim, Norliana; Said, Mohamad Rushdan Md

2017-11-01

Elliptic net is a generalization of elliptic divisibility sequence and in cryptography field, most cryptographic pairings that are based on elliptic curve such as Tate pairing can be improved by applying elliptic nets algorithm. The elliptic net is constructed by using n dimensional array of values in rational number satisfying nonlinear recurrence relations that arise from elliptic divisibility sequences. The two main properties hold in the recurrence relations are for all positive integers m>n, hm +nhm -n=hm +1hm -1hn2-hn +1hn -1hm2 and hn divides hm whenever n divides m. In this research, we discuss elliptic divisibility sequence associated with elliptic nets based on cryptographic perspective and its possible research direction.

Chemiluminescence in cryogenic matrices

Science.gov (United States)

Lotnik, S. V.; Kazakov, Valeri P.

1989-04-01

The literature data on chemiluminescence (CL) in cryogenic matrices have been classified and correlated for the first time. The role of studies on phosphorescence and CL at low temperatures in the development of cryochemistry is shown. The features of low-temperature CL in matrices of nitrogen and inert gases (fine structure of spectra, matrix effects) and the data on the mobility and reactivity of atoms and radicals at very low temperatures are examined. The trends in the development of studies on CL in cryogenic matrices, such as the search for systems involving polyatomic molecules and extending the forms of CL reactions, are followed. The reactions of active nitrogen with hydrocarbons that are accompanied by light emission and CL in the oxidation of carbenes at T >= 77 K are examined. The bibliography includes 112 references.

Lower extremity kinematics during walking and elliptical training in individuals with and without traumatic brain injury.

Science.gov (United States)

Buster, Thad; Burnfield, Judith; Taylor, Adam P; Stergiou, Nicholas

2013-12-01

Elliptical training may be an option for practicing walking-like activity for individuals with traumatic brain injuries (TBI). Understanding similarities and differences between participants with TBI and neurologically healthy individuals during elliptical trainer use and walking may help guide clinical applications incorporating elliptical trainers. Ten participants with TBI and a comparison group of 10 neurologically healthy participants underwent 2 familiarization sessions and 1 data collection session. Kinematic data were collected as participants walked on a treadmill or on an elliptical trainer. Gait-related measures, including coefficient of multiple correlations (a measure of similarity between ensemble joint movement profiles; coefficient of multiple correlations [CMCs]), critical event joint angles, variability of peak critical event joint angles (standard deviations [SDs]) of peak critical event joint angles, and maximum Lyapunov exponents (a measure of the organization of the variability [LyEs]) were compared between groups and conditions. Coefficient of multiple correlations values comparing the similarity in ensemble motion profiles between the TBI and comparison participants exceeded 0.85 for the hip, knee, and ankle joints. The only critical event joint angle that differed significantly between participants with TBI and comparison participants was the ankle during terminal stance. Variability was higher for the TBI group (6 of 11 comparisons significant) compared with comparison participants. Hip and knee joint movement patterns of both participants with TBI and comparison participants on the elliptical trainer were similar to walking (CMCs ≥ 0.87). Variability was higher during elliptical trainer usage compared with walking (5 of 11 comparisons significant). Hip LyEs were higher during treadmill walking. Ankle LyEs were greater during elliptical trainer usage. Movement patterns of participants with TBI were similar to, but more variable than

Inverse m-matrices and ultrametric matrices

CERN Document Server

Dellacherie, Claude; San Martin, Jaime

2014-01-01

The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

Origin of a bottom-heavy stellar initial mass function in elliptical galaxies

International Nuclear Information System (INIS)

Bekki, Kenji

2013-01-01

We investigate the origin of a bottom-heavy stellar initial mass function (IMF) recently observed in elliptical galaxies by using chemical evolution models with a non-universal IMF. We adopt the variable Kroupa IMF with the three slopes (α 1 , α 2 , and α 3 ) dependent on metallicities ([Fe/H]) and densities (ρ g ) of star-forming gas clouds and thereby search for the best IMF model that can reproduce (1) the observed steep IMF slope (α 2 ∼ 3, i.e., bottom-heavy) for low stellar masses (m ≤ 1 M ☉ ) and (2) the correlation of α 2 with chemical properties of elliptical galaxies in a self-consistent manner. We find that if the IMF slope α 2 depends on both [Fe/H] and ρ g , then elliptical galaxies with higher [Mg/Fe] can have steeper α 2 (∼3) in our models. We also find that the observed positive correlation of stellar mass-to-light ratios (M/L) with [Mg/Fe] in elliptical galaxies can be quantitatively reproduced in our models with α 2 ∝β[Fe/H] + γlog ρ g , where β ∼ 0.5 and γ ∼ 2. We discuss whether the IMF slopes for low-mass (α 2 ) and high-mass stars (α 3 ) need to vary independently from each other to explain a number of IMF-related observational results self-consistently. We also briefly discuss why α 2 depends differently on [Fe/H] in dwarf and giant elliptical galaxies.

Universal correlations and power-law tails in financial covariance matrices

Science.gov (United States)

Akemann, G.; Fischmann, J.; Vivo, P.

2010-07-01

We investigate whether quantities such as the global spectral density or individual eigenvalues of financial covariance matrices can be best modelled by standard random matrix theory or rather by its generalisations displaying power-law tails. In order to generate individual eigenvalue distributions a chopping procedure is devised, which produces a statistical ensemble of asset-price covariances from a single instance of financial data sets. Local results for the smallest eigenvalue and individual spacings are very stable upon reshuffling the time windows and assets. They are in good agreement with the universal Tracy-Widom distribution and Wigner surmise, respectively. This suggests a strong degree of robustness especially in the low-lying sector of the spectra, most relevant for portfolio selections. Conversely, the global spectral density of a single covariance matrix as well as the average over all unfolded nearest-neighbour spacing distributions deviate from standard Gaussian random matrix predictions. The data are in fair agreement with a recently introduced generalised random matrix model, with correlations showing a power-law decay.

Nuclear data and measurements series: Some comments on the effects of long-range correlations in covariance matrices for nuclear data

International Nuclear Information System (INIS)

Smith, D.L.

1987-03-01

Attention is called to the considerable sensitivity of many uncertainty calculations to the magnitude of the long-ranged correlations which appear in covariance matrices. If such correlations do exist, they must be included in order to properly assess the impact of the uncertainties in the data. If, however, certain assumed long-range correlations are unrealistic, then analyses involving such correlation information are almost certain to produce misleading results. The issue is discussed in general terms, and its importance is illustrated by examples based in part on recent work from this laboratory. Some practical suggestions are offered for dealing with the matter of correlations in instances where the available information is incomplete. 23 refs., 2 figs., 1 tab

Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals

Science.gov (United States)

Schwalm, William A.

2015-12-01

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

A covariance correction that accounts for correlation estimation to improve finite-sample inference with generalized estimating equations: A study on its applicability with structured correlation matrices.

Science.gov (United States)

Westgate, Philip M

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator.

Elliptic-symmetry vector optical fields.

Science.gov (United States)

Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian

2014-08-11

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

Ellipticity dependence of the near-threshold harmonics of H2 in an elliptical strong laser field.

Science.gov (United States)

Yang, Hua; Liu, Peng; Li, Ruxin; Xu, Zhizhan

2013-11-18

We study the ellipticity dependence of the near-threshold (NT) harmonics of pre-aligned H2 molecules using the time-dependent density functional theory. The anomalous maximum appearing at a non-zero ellipticity for the generated NT harmonics can be attributed to multiphoton effects of the orthogonally polarized component of the elliptical driving laser field. Our calculation also shows that the structure of the bound-state, such as molecular alignment and bond length, can be sensitively reflected on the ellipticity dependence of the near-threshold harmonics.

Elliptic Flow, Initial Eccentricity and Elliptic Flow Fluctuations in Heavy Ion Collisions at RHIC

Science.gov (United States)

Nouicer, Rachid; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holzman, B.; Iordanova, A.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wysłouch, B.

2008-12-01

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.

Critical statistics for non-Hermitian matrices

International Nuclear Information System (INIS)

Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.

2002-01-01

We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition

Elliptical concentrators.

Science.gov (United States)

Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio

2006-10-10

Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

SECOND-GENERATION STELLAR DISKS IN DENSE STAR CLUSTERS AND CLUSTER ELLIPTICITIES

International Nuclear Information System (INIS)

Mastrobuono-Battisti, Alessandra; Perets, Hagai B.

2016-01-01

Globular clusters (GCs) and nuclear star clusters (NSCs) are typically composed of several stellar populations, characterized by different chemical compositions. Different populations show different ages in NSCs, but not necessarily in GCs. The youngest populations in NSCs appear to reside in disk-like structures as observed in our Galaxy and in M31. Gas infall followed by formation of second-generation (SG) stars in GCs may similarly form disk-like structures in the clusters nuclei. Here we explore this possibility and follow the long-term evolution of stellar disks embedded in GCs, and study their effects on the evolution of the clusters. We study disks with different masses by means of detailed N-body simulations and explore their morphological and kinematic signatures on the GC structures. We find that as a SG disk relaxes, the old, first-generation stellar population flattens and becomes more radially anisotropic, making the GC structure become more elliptical. The SG stellar population is characterized by a lower velocity dispersion and a higher rotational velocity compared with the primordial older population. The strength of these kinematic signatures depends both on the relaxation time of the system and on the fractional mass of the SG disk. We therefore conclude that SG populations formed in flattened configurations will give rise to two systematic trends: (1) a positive correlation between GC ellipticity and fraction of SG population and (2) a positive correlation between GC relaxation time and ellipticity. Therefore, GC ellipticities and rotation could be related to the formation of SG stars and their initial configuration.

Intrinsic shapes of discy and boxy ellipticals

International Nuclear Information System (INIS)

Fasano, Giovanni

1991-01-01

Statistical tests for intrinsic shapes of elliptical galaxies have given so far inconclusive and sometimes contradictory results. These failures have been often charged to the fact that classical tests consider only the two axisymmetric shapes (oblate versus prolate), while ellipticals are truly triaxial bodies. On the other hand, recent analyses indicate that the class of elliptical galaxies could be a mixture of (at least) two families having different morphology and dynamical behaviour: (i) a family of fast-rotating, disc-like ellipticals (discy); (ii) a family of slow-rotating, box-shaped ellipticals (boxy). In this paper we review the tests for instrinsic shapes of elliptical galaxies using data of better quality (CCD) with respect to previous applications. (author)

The ellipticities of a sample of globular clusters in M31

International Nuclear Information System (INIS)

Lupton, R.H.

1989-01-01

Images for a sample of 18 globular clusters in M31 have been obtained. The mean ellipticity on the sky in the range 7-14 pc (2-4 arcsec) is 0.08 + or - 0.02 and 0.12 + or - 0.01 in the range 14-21 pc (4-6 arcsec), with corresponding true ellipticities of 0.12 and 0.18. The difference between the inner and outer parts is significant at a 99 percent level. The flattening of the inner parts is statistically indistinguishable from that of the Galactic globular clusters, while the outer parts are flatter than the Galactic clusters at a 99.8 percent confidence level. There is a significant anticorrelation of ellipticity with line strength; such a correlation may in retrospect also be seen in the Galactic globular cluster system. For the M31 data, this anticorrelation is stronger in the inner parts of the galaxy. 30 refs

Excursion Processes Associated with Elliptic Combinatorics

Science.gov (United States)

Baba, Hiroya; Katori, Makoto

2018-06-01

Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying q-analogues. Recently Schlosser proposed a lattice path model in the square lattice with a family of totally elliptic weight-functions including several complex parameters and discussed an elliptic extension of the binomial theorem. In the present paper, we introduce a family of discrete-time excursion processes on Z starting from the origin and returning to the origin in a given time duration 2 T associated with Schlosser's elliptic combinatorics. The processes are inhomogeneous both in space and time and hence expected to provide new models in non-equilibrium statistical mechanics. By numerical calculation we show that the maximum likelihood trajectories on the spatio-temporal plane of the elliptic excursion processes and of their reduced trigonometric versions are not straight lines in general but are nontrivially curved depending on parameters. We analyze asymptotic probability laws in the long-term limit T → ∞ for a simplified trigonometric version of excursion process. Emergence of nontrivial curves of trajectories in a large scale of space and time from the elementary elliptic weight-functions exhibits a new aspect of elliptic combinatorics.

The elliptic genus and Hidden symmetry

International Nuclear Information System (INIS)

Jaffe, A.

2001-01-01

We study the elliptic genus (a partition function) in certain interacting, twist quantum field theories. Without twists, these theories have N=2 supersymmetry. The twists provide a regularization, and also partially break the supersymmetry. In spite of the regularization, one can establish a homotopy of the elliptic genus in a coupling parameter. Our construction relies on a priori estimates and other methods from constructive quantum field theory; this mathematical underpinning allows us to justify evaluating the elliptic genus at one endpoint of the homotopy. We obtain a version of Witten's proposed formula for the elliptic genus in terms of classical theta functions. As a consequence, the elliptic genus has a hidden SL(2,Z) symmetry characteristic of conformal theory, even though the underlying theory is not conformal. (orig.)

Multicolor surface photometry of 17 ellipticals

International Nuclear Information System (INIS)

Franx, M.; Illingworth, G.; Heckman, T.

1989-01-01

Multicolor two-dimensional surface photometry was used to obtain radial profiles for surface brightness, color, ellipticity, position angle, and the residuals from the fitted ellipses described by the cos(n phi) and sin(n phi) terms (where n = 3 and 4) for 17 elliptical galaxies. It is found that at radii as large as five times the seeing FWHM, seeing can affect the ellipticity at the 10 percent level and introduce uncertainty in the position angles of several degrees, particularly for very round ellipticals. The present profiles are found to agree well with previous data, with rms differences of 0.02 in ellipticity and 2 deg in position angle. The observed color gradients are consistent with a decrease in the metallicity by a factor of about 2 per decade in radius. 61 refs

To flow or not to flow : a study of elliptic flow and nonflow in proton-proton collisions in ALICE

Science.gov (United States)

van der Kolk, N.

2012-01-01

The standard model of particle physics describes all known elementary particles and the forces between them. The strong force, which binds quarks inside hadrons and nucleons inside nuclei, is described by the theory of Quantum Chromodynamics. This theory predicts a new state of matter at extreme temperatures and densities: the Quark Gluon plasma. The ALICE experiment at the Large Hadron Collider near Geneva was build to study this QGP by looking at collisions of the most heavy stable ions: lead (Pb) ions. In such collisions one hopes to achieve sufficient energy density for the creation of a QGP. One of the signatures of QGP formation in high energy heavy ion collisions is the presence of collective behaviour in the system formed during the collision. This collectivity manifests itself in a common velocity in all produced particles: a collective flow. The most dominant contribution to collective flow is elliptic flow, which originates from the anisotropic overlap region of the two nuclei in non-central collisions and is visible in the azimuthal distribution of the produced particles. Elliptic flow is related to the equation of state of the system and its degree of thermalisation. The analysis of elliptic flow is complicated by the presence of correlations between particles from other sources, summarised in the term nonflow. Several analysis methods have become available over the years and have been implemented for elliptic flow analysis within the ALICE computing framework. These methods have different sensitivities to these nonflow correlations. Because the centre of mass energy at the LHC is so high, predictions have been made of collective behaviour even in proton-proton collisions. These predictions are very divers and give values between 0 and 0.2 for elliptic flow using different models. To constrain these predictions proton-proton data, recorded with the ALICE experiment at the LHC in the 2010 7 TeV proton-proton run, was studied. In proton-proton collisions

Young and Old X-ray Binary and IXO Populations in Spiral and Elliptical Galaxies

Science.gov (United States)

Colbert, E.; Heckman, T.; Ptak, A.; Strickland, D.; Weaver, K.

2003-03-01

We have analyzed Chandra ACIS observations of 32 nearby spiral and elliptical galaxies and present the results of 1441 X-ray point sources, which are presumed to be mostly X-ray binaries (XRBs) and Intermediate-luminosity X-ray Objects (IXOs, a.k.a. ULXs). The X-ray luminosity functions (XLFs) of the point sources show that the slope of the elliptical galaxy XLFs are significantly steeper than the spiral galaxy XLFs, indicating grossly different types of point sources, or different stages in their evolution. Since the spiral galaxy XLF is so shallow, the most luminous points sources (usually the IXOs) dominate the total X-ray point source luminosity LXP. We show that the galaxy total B-band and K-band light (proxies for the stellar mass) are well correlated with LXP for both spirals and ellipticals, but the FIR and UV emission is only correlated for the spirals. We deconvolve LXP into two components, one that is proportional to the galaxy stellar mass (pop II), and another that is proportional to the galaxy SFR (pop I). We also note that IXOs (and nearly all of the other point sources) in both spirals and ellipticals have X-ray colors that are most consistent with power-law slopes of Gamma ˜ 1.5--3.0, which is inconsistent with high-mass XRBS (HMXBs). Thus, HMXBs are not important contributors to LXP. We have also found that IXOs in spiral galaxies may have a slightly harder X-ray spectrum than those in elliptical galaxies. The implications of these findings will be discussed.

Elliptical shape of the coma cluster

International Nuclear Information System (INIS)

Schipper, L.; King, I.R.

1978-01-01

The elliptical shape of the Coma cluster is examined quantitatively. The degree of ellipticity is high and depends to some extent on the radial distance of the sample from the Coma center as well as on the brightness of the sample. The elliptical shape does not appear to be caused by rotation; other possible causes are briefly discussed

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)

Pressure algorithm for elliptic flow calculations with the PDF method

Science.gov (United States)

Anand, M. S.; Pope, S. B.; Mongia, H. C.

1991-01-01

An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.

Overdetermined elliptic problems in topological disks

Science.gov (United States)

Mira, Pablo

2018-06-01

We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

Science.gov (United States)

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

2018-06-01

We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure mathematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals, and we develop a formalism that enables us to compute these Feynman integrals in terms of our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group

International Nuclear Information System (INIS)

Muender, W; Weichselbaum, A; Holzner, A; Delft, Jan von; Henley, C L

2010-01-01

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix (CDM). For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all the correlations between the two clusters. We show how to extract from the CDM a survey of the relative strengths of the system's correlations in different symmetry sectors and the nature of their decay with distance (power law or exponential), as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To achieve this goal, we introduce a new method of analysing the CDM, termed the dominant operator basis (DOB) method, which identifies in an unbiased fashion a small set of operators for each cluster that serve as a basis for the dominant correlations of the system. We illustrate this method by analysing the CDM for a spinless extended Hubbard model that features a competition between charge density correlations and pairing correlations, and show that the DOB method successfully identifies their relative strengths and dominant correlators. To calculate the ground state of this model, we use the density matrix renormalization group, formulated in terms of a variational matrix product state (MPS) approach within which subsequent determination of the CDM is very straightforward. In an extended appendix, we give a detailed tutorial introduction to our variational MPS approach for ground state calculations for one-dimensional quantum chain models. We present in detail how MPSs overcome the problem of large Hilbert space dimensions in these models and describe all the techniques needed for handling them in practice.

Directed and elliptic flow of charged pions and protons in Pb+Pb collisions at 40 and 158 AGeV

CERN Document Server

Alt, C; Baatar, B; Barna, D; Bartke, J; Behler, M; Betev, L; Bialkowska, H; Billmeier, A; Blume, C; Boimska, B; Borghini, N; Botje, M; Bracinik, J; Bramm, R; Brun, R; Buncic, P; Cerny, V; Chvala, O; Cooper, G E; Cramer, J G; Csató, P; Dinh, P M; Dinkelaker, P; Eckardt, V; Filip, P; Fodor, Z; Foka, P; Freund, P; Friese, V; Gál, J; Gazdzicki, M; Georgopoulos, G; Gladysz-Dziadus, E; Hegyi, S; Höhne, C; Jacobs, P; Kadija, K; Karev, A; Kniege, S; Kolesnikov, V I; Kollegger, T; Korus, R; Kowalski, M; Kraus, I; Kreps, M; Van Leeuwen, M; Lévai, Peter; Malakhov, A I; Markert, C; Mayes, B W; Melkumov, G L; Meurer, C; Mischke, A; Mitrovski, M; Molnár, J; Mrówczynski, S; Odyniec, Grazyna Janina; Ollitrault, J Y; Pálla, G; Panagiotou, A D; Perl, K; Petridis, A; Pikna, M; Pinsky, L; Poskanzer, A M; Pühlhofer, F; Reid, J G; Renfordt, R; Retyk, W; Ritter, H G; Roland, C; Roland, G; Rybczynski, M; Rybicki, A; Sandoval, A; Sann, H; Schmitz, N; Seyboth, P; Siklér, F; Sitár, B; Skrzypczak, E; Snellings, R J; Stefanek, G; Stock, R; Ströbele, H; Susa, T; Szentpétery, I; Sziklai, J; Trainor, T A; Varga, D; Vassiliou, M; Veres, G I; Vesztergombi, G; Voloshin, S A; Vranic, D; Wetzler, A; Wlodarczyk, Z; Yoo, I K; Zaranek, J; Zimányi, J

2003-01-01

Directed and elliptic flow measurements for charged pions and protons are reported as a function of transverse momentum, rapidity, and centrality for 40 and 158 AGeV Pb + Pb collisions as recorded by the NA49 detector. Both the standard method of correlating particles with an event plane, and the cumulant method of studying multiparticle correlations are used. In the standard method the directed flow is corrected for conservation of momentum. In the cumulant method elliptic flow is reconstructed from genuine 4, 6, and 8-particle correlations, showing the first unequivocal evidence for collective motion in A+A collisions at SPS energies.

Diffeomorphisms of elliptic 3-manifolds

CERN Document Server

Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam

2012-01-01

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

Elliptic genera from multi-centers

Energy Technology Data Exchange (ETDEWEB)

Gaddam, Nava [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, 3508 TD Utrecht (Netherlands)

2016-05-13

I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera — explicitly verifying this in the cases of the quintic in ℙ{sup 4}, the sextic in Wℙ{sub (2,1,1,1,1)}, the octic in Wℙ{sub (4,1,1,1,1)} and the dectic in Wℙ{sub (5,2,1,1,1)}. With an input of the corresponding ‘single-center’ indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in N=2 supergravity.

Elliptic genus of singular algebraic varieties and quotients

Science.gov (United States)

Libgober, Anatoly

2018-02-01

This paper discusses the basic properties of various versions of the two-variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the theories regarding the elliptic genera of phases on N  =  2 introduced in Witten (1993 Nucl. Phys. B 403 159-222).

Elliptic curves for applications (Tutorial)

NARCIS (Netherlands)

Lange, T.; Bernstein, D.J.; Chatterjee, S.

2011-01-01

More than 25 years ago, elliptic curves over finite fields were suggested as a group in which the Discrete Logarithm Problem (DLP) can be hard. Since then many researchers have scrutinized the security of the DLP on elliptic curves with the result that for suitably chosen curves only exponential

Partial differential operators of elliptic type

CERN Document Server

Shimakura, Norio

1992-01-01

This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

Developing a composite based elliptic spring for automotive applications

International Nuclear Information System (INIS)

Talib, Abdul Rahim Abu; Ali, Aidy; Goudah, G.; Lah, Nur Azida Che; Golestaneh, A.F.

2010-01-01

An automotive suspension system is designed to provide both safety and comfort for the vehicle occupants. In this study, finite element models were developed to optimize the material and geometry of the composite elliptical spring based on the spring rate, log life and shear stress parameters. The influence of the ellipticity ratio on the performance of woven roving-wrapped composite elliptical springs was investigated both experimentally and numerically. The study demonstrated that composite elliptical springs can be used for light and heavy trucks with substantial weight reduction. The results showed that the ellipticity ratio significantly influenced the design parameters. Composite elliptic springs with ellipticity ratios of a/b = 2 had the optimum spring parameters.

Exact exchange-correlation potential and approximate exchange potential in terms of density matrices

International Nuclear Information System (INIS)

Holas, A.; March, N.H.

1995-01-01

An exact expression in terms of density matrices (DM) is derived for δF[n]/δn(r), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential v xc (r) is obtained which is analogous in character to that for δF[n]/δn(r), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact v xc (r) to that for an approximate exchange-only potential v x (r). This leads naturally to the Harbola-Sahni exchange-only potential

Coercive properties of elliptic-parabolic operator

International Nuclear Information System (INIS)

Duong Min Duc.

1987-06-01

Using a generalized Poincare inequality, we study the coercive properties of a class of elliptic-parabolic partial differential equations, which contains many degenerate elliptic equations considered by the other authors. (author). 16 refs

A class of strongly degenerate elliptic operators

International Nuclear Information System (INIS)

Duong Minh Duc.

1988-04-01

Using a weighted Poincare inequality, we study (ω 1 ,...,ω n )-elliptic operators. This method is applicable to solve singular elliptic equations with conditions in W 1,2 on the boundary. We also get a result about the regularity of solutions of singular elliptic equations. An application to (ω 1 ,...ω n )-parabolic equations is given. (author). 33 refs

Two phase formation of massive elliptical galaxies: study through cross-correlation including spatial effect

Science.gov (United States)

Modak, Soumita; Chattopadhyay, Tanuka; Chattopadhyay, Asis Kumar

2017-11-01

Area of study is the formation mechanism of the present-day population of elliptical galaxies, in the context of hierarchical cosmological models accompanied by accretion and minor mergers. The present work investigates the formation and evolution of several components of the nearby massive early-type galaxies (ETGs) through cross-correlation function (CCF), using the spatial parameters right ascension (RA) and declination (DEC), and the intrinsic parameters mass (M_{*}) and size. According to the astrophysical terminology, here these variables, namely mass, size, RA and DEC are termed as parameters, whereas the unknown constants involved in the kernel function are called hyperparameters. Throughout this paper, the parameter size is used to represent the effective radius (Re). Following Huang et al. (2013a), each nearby ETG is divided into three parts on the basis of its Re value. We study the CCF between each of these three components of nearby massive ETGs and the ETGs in the high redshift range, 0.5conflict raised in a previous work (De et al. 2014) suggesting other possibilities for the formation of the outermost part. A probable cause of this improvement is the inclusion of the spatial effects in addition to the other parameters in the study.

Averaging operations on matrices

Indian Academy of Sciences (India)

2014-07-03

Jul 3, 2014 ... Role of Positive Definite Matrices. • Diffusion Tensor Imaging: 3 × 3 pd matrices model water flow at each voxel of brain scan. • Elasticity: 6 × 6 pd matrices model stress tensors. • Machine Learning: n × n pd matrices occur as kernel matrices. Tanvi Jain. Averaging operations on matrices ...

Elliptical excisions: variations and the eccentric parallelogram.

Science.gov (United States)

Goldberg, Leonard H; Alam, Murad

2004-02-01

The elliptical (fusiform) excision is a basic tool of cutaneous surgery. To assess the design, functionality, ease of construction, and aesthetic outcomes of the ellipse. A systematic review of elliptical designs and their site-specific benefits and limitations. In particular, we consider the (1). context of prevailing relaxed skin tension lines and tissue laxity; and (2). removal of the smallest possible amount of tissue around the lesion and in the "dog-ears." Attention is focused on intuitive methods that can be reproducibly planned and executed. Elliptical variations are easily designed and can be adapted to many situations. The eccentric parallelogram excision is offered as a new technique that minimizes notching and focal tension in the center of an elliptical closure. Conclusion The elliptical (fusiform) excision is an efficient, elegant, and versatile technique that will remain a mainstay of the cutaneous surgical armamentarium.

Elliptic flow of charged particles in Pb-Pb collisions at $\\sqrt{s_{NN}}$ = 2.76 TeV

CERN Document Server

Aamodt, K; Abrahantes Quintana, A; Adamova, D; Adare, A M; Aggarwal, M M; Aglieri Rinella, G; Agocs, A G; Aguilar Salazar, S; Ahammed, Z; Ahmad Masoodi, A; Ahmad, N; Ahn, S U; Akindinov, A; Aleksandrov, D; Alessandro, B; Alfaro Molina, R; Alici, A; Alkin, A; Almaraz Avina, E; Alt, T; Altini, V; Altinpinar, S; Altsybeev, I; Andrei, C; Andronic, A; Anguelov, V; Anson, C; Anticic, T; Antinori, F; Antonioli, P; Aphecetche, L; Appelshauser, H; Arbor, N; Arcelli, S; Arend, A; Armesto, N; Arnaldi, R; Aronsson, T; Arsene, I C; Asryan, A; Augustinus, A; Averbeck, R; Awes, T C; Aysto, J; Azmi, M D; Bach, M; Badala, A; Baek, Y W; Bagnasco, S; Bailhache, R; Bala, R; Baldini-Ferroli, R; Baldisseri, A; Baldit, A; Baltasar Dos Santos Pedrosa, F; Ban, J; Barbera, R; Barile, F; Barnafoldi, G G; Barnby, L S; Barret, V; Bartke, J; Basile, M; Bastid, N; Bathen, B; Batigne, G; Batyunya, B; Baumann, C; Bearden, I G; Beck, H; Belikov, I; Bellini, F; Bellwied, R; Belmont-Moreno, E.; Beole, S; Berceanu, I; Bercuci, A; Berdermann, E; Berdnikov, Y; Bergmann, C; Betev, L; Bhasin, A; Bhati, A K; Bianchi, L; Bianchi, N; Bianchin, C; Bielcik, J; Bielcikova, J; Bilandzic, A; Biolcati, E; Blanc, A; Blanco, F; Blanco, F; Blau, D; Blume, C; Boccioli, M; Bock, N; Bogdanov, A; Boggild, H; Bogolyubsky, M; Boldizsar, L; Bombara, M; Bombonati, C; Book, J; Borel, H; Borissov, A; Bortolin, C; Bose, S; Bossu, F; Botje, M; Bottger, S; Boyer, B; Braun-Munzinger, P.; Bravina, L; Bregant, M; Breitner, T; Broz, M; Brun, R; Bruna, E; Bruno, G E; Budnikov, D; Buesching, H; Bugaiev, K; Busch, O; Buthelezi, Z; Caffarri, D; Cai, X; Caines, H; Calvo Villar, E; Camerini, P; Canoa Roman, V; Cara Romeo, G; Carena, F; Carena, W; Carminati, F; Casanova Diaz, A; Caselle, M; Castillo Castellanos, J; Catanescu, V; Cavicchioli, C; Cepila, J; Cerello, P; Chang, B; Chapeland, S; Charvet, J L; Chattopadhyay, S; Chattopadhyay, S; Cherney, M; Cheshkov, C; Cheynis, B; Chiavassa, E; Chibante Barroso, V; Chinellato, D D; Chochula, P; Chojnacki, M; Christakoglou, P; Christensen, C H; Christiansen, P; Chujo, T; Cicalo, C; Cifarelli, L; Cindolo, F; Cleymans, J; Coccetti, F; Coffin, J P; Coli, S; Conesa Balbastre, G; Conesa del Valle, Z; Constantin, P; Contin, G; Contreras, J G; Cormier, T M; Corrales Morales, Y; Cortes Maldonado, I; Cortese, P; Cosentino, M R; Costa, F; Cotallo, M E; Crescio, E; Crochet, P; Cuautle, E; Cunqueiro, L; D'Erasmo, G; Dainese, A; Dalsgaard, H H; Danu, A; Das, D; Das, I; Das, K; Dash, A; Dash, S; De, S; De Azevedo Moregula, A; de Barros, G O V; De Caro, A; de Cataldo, G; de Cuveland, J; De Falco, A; De Gruttola, D; De Marco, N; De Pasquale, S; De Remigis, R; de Rooij, R; Debski, P R; Del Castillo Sanchez, E; Delagrange, H; Delgado Mercado, Y; Dellacasa, G; Deloff, A; Demanov, V; Denes, E; Deppman, A; Di Bari, D; Di Giglio, C; Di Liberto, S; Di Mauro, A; Di Nezza, P; Dietel, T; Divia, R; Djuvsland, O; Dobrin, A; Dobrowolski, T; Dominguez, I; Donigus, B; Dordic, O; Driga, O; Dubey, A K; Dubuisson, J; Ducroux, L; Dupieux, P; Dutta Majumdar, A K; Dutta Majumdar, M R; Elia, D; Emschermann, D; Engel, H; Erdal, H A; Espagnon, B; Estienne, M; Esumi, S; Evans, D; Evrard, S; Eyyubova, G; Fabjan, C W; Fabris, D; Faivre, J; Falchieri, D; Fantoni, A; Fasel, M; Fearick, R; Fedunov, A; Fehlker, D; Fekete, V; Felea, D; Feofilov, G; Fernandez Tellez, A; Ferretti, A; Ferretti, R; Figiel, J; Figueredo, M A S; Filchagin, S; Fini, R; Finogeev, D; Fionda, F M; Fiore, E M; Floris, M; Foertsch, S; Foka, P; Fokin, S; Fragiacomo, E; Fragkiadakis, M; Frankenfeld, U; Fuchs, U; Furano, F; Furget, C; Fusco Girard, M; Gaardhoje, J J; Gadrat, S; Gagliardi, M; Gago, A; Gallio, M; Gangadharan, D R; Ganoti, P; Ganti, M S; Garabatos, C; Garcia-Solis, E; Garishvili, I; Gemme, R; Gerhard, J; Germain, M; Geuna, C; Gheata, A; Gheata, M; Ghidini, B; Ghosh, P; Gianotti, P; Girard, M R; Giraudo, G; Giubellino, P; Gladysz-Dziadus, E; Glassel, P; Gomez, R; Ferreiro, E G; Gonzalez Santos, H; González-Trueba, L H; González-Zamora, P; Gorbunov, S; Gotovac, S; Grabski, V; Grajcarek, R; Grelli, A; Grigoras, A; Grigoras, C; Grigoriev, V; Grigoryan, A; Grigoryan, S; Grinyov, B; Grion, N; Gros, P; Grosse-Oetringhaus, J F; Grossiord, J Y; Grosso, R; Guber, F; Guernane, R; Guerra Gutierrez, C; Guerzoni, B; Gulbrandsen, K; Gunji, T; Gupta, A; Gupta, R; Haaland, O; Hadjidakis, C; Haiduc, M; Hamagaki, H; Hamar, G; Harris, J W; Hartig, M; Hasch, D; Hasegan, D; Hatzifotiadou, D; Hayrapetyan, A; Heide, M; Heinz, M; Helstrup, H; Herghelegiu, A; Hernandez, C; Herrera Corral, G; Herrmann, N; Hetland, K F; Hicks, B; Hille, P T; Hippolyte, B; Horaguchi, T; Hori, Y; Hristov, P; Hrivnacova, I; Huang, M; Huber, S; Humanic, T J; Hwang, D S; Ichou, R; Ilkaev, R; Ilkiv, I; Inaba, M; Incani, E; Innocenti, G M; Innocenti, P G; Ippolitov, M; Irfan, M; Ivan, C; Ivanov, A; Ivanov, M; Ivanov, V; Jacholkowski, A; Jacobs, P M; Jancurova, L; Jangal, S; Janik, R; Jena, S; Jirden, L; Jones, G T; Jones, P G; Jovanovic, P; Jung, H; Jung, W; Jusko, A; Kalcher, S; Kalinak, P; Kalisky, M; Kalliokoski, T; Kalweit, A; Kamermans, R; Kanaki, K; Kang, E; Kang, J H; Kaplin, V; Karavichev, O; Karavicheva, T; Karpechev, E; Kazantsev, A; Kebschull, U; Keidel, R; Khan, M M; Khan, S A; Khanzadeev, A; Kharlov, Y; Kileng, B; Kim, D J; Kim, D S; Kim, D W; Kim, H N; Kim, J H; Kim, J S; Kim, M; Kim, M; Kim, S; Kim, S H; Kirsch, S; Kisel, I; Kiselev, S; Kisiel, A; Klay, J L; Klein, J; Klein-Bosing, C; Kliemant, M; Klovning, A; Kluge, A; Knichel, M L; Koch, K; Kohler, M; Kolevatov, R; Kolojvari, A; Kondratiev, V; Kondratyeva, N; Konevskih, A; Kornas, E; Kottachchi Kankanamge Don, C; Kour, R; Kowalski, M; Kox, S; Koyithatta Meethaleveedu, G; Kozlov, K; Kral, J; Kralik, I; Kramer, F; Kraus, I; Krawutschke, T; Kretz, M; Krivda, M; Krizek, F; Krumbhorn, D; Krus, M; Kryshen, E; Krzewicki, M; Kucheriaev, Y; Kuhn, C; Kuijer, P G; Kurashvili, P; Kurepin, A; Kurepin, A B; Kuryakin, A; Kushpil, S; Kushpil, V; Kweon, M J; Kwon, Y; La Rocca, P; Ladron de Guevara, P; Lafage, V; Lara, C; Lardeux, A; Larsen, D T; Lazzeroni, C; Le Bornec, Y; Lea, R; Lee, K S; Lee, S C; Lefevre, F; Lehnert, J; Leistam, L; Lenhardt, M; Lenti, V; Leon Monzon, I; Leon Vargas, H; Levai, P; Li, X; Lien, J; Lietava, R; Lindal, S; Lindenstruth, V; Lippmann, C; Lisa, M A; Liu, L; Loenne, P I; Loggins, V R; Loginov, V; Lohn, S; Loizides, C; Loo, K K; Lopez, X; Lopez Noriega, M; Lopez Torres, E; Lovhoiden, G; Lu, X G; Luettig, P; Lunardon, M; Luparello, G; Luquin, L; Luzzi, C; Ma, K; Ma, R; Madagodahettige-Don, D M; Maevskaya, A; Mager, M; Mahapatra, D P; Maire, A; Mal'Kevich, D; Malaev, M; Maldonado Cervantes, I; Malinina, L; Malzacher, P; Mamonov, A; Manceau, L; Mangotra, L; Manko, V; Manso, F; Manzari, V; Mao, Y; Mares, J; Margagliotti, G V; Margotti, A; Marin, A; Markert, C; Martashvili, I; Martinengo, P; Martinez, M I; Martinez Davalos, A; Martinez Garcia, G; Martynov, Y; Masciocchi, S; Masera, M; Masoni, A; Massacrier, L; Mastromarco, M; Mastroserio, A; Matthews, Z L; Matyja, A; Mayani, D; Mayer, C; Mazza, G; Mazzoni, M A; Meddi, F; Menchaca-Rocha, A; Mendez Lorenzo, P; Menis, I; Mercado Perez, J; Meres, M; Mereu, P; Miake, Y; Midori, J; Milano, L; Milosevic, J; Mischke, A; Miskowiec, D; Mitu, C; Mlynarz, J; Mohanty, A K; Mohanty, B; Molnar, L; Montano Zetina, L; Monteno, M; Montes, E; Morando, M; Moreira De Godoy, D A; Moretto, S; Morsch, A; Muccifora, V; Mudnic, E; Muhuri, S; Muller, H; Munhoz, M G; Munoz, J; Musa, L; Musso, A; Nandi, B K; Nania, R; Nappi, E; Nattrass, C; Navach, F; Navin, S; Nayak, T K; Nazarenko, S; Nazarov, G; Nedosekin, A; Nendaz, F; Newby, J; Nicassio, M; Nielsen, B S; Niida, T; Nikolaev, S; Nikolic, V; Nikulin, S; Nikulin, V; Nilsen, B S; Nilsson, M S; Noferini, F; Nooren, G; Novitzky, N; Nyanin, A; Nyatha, A; Nygaard, C; Nystrand, J; Obayashi, H; Ochirov, A; Oeschler, H; Oh, S K; Oleniacz, J; Oppedisano, C; Ortiz Velasquez, A; Ortona, G; Oskarsson, A; Ostrowski, P; Otterlund, I; Otwinowski, J; Oyama, K; Ozawa, K; Pachmayer, Y; Pachr, M; Padilla, F; Pagano, P; Jayarathna, S P; Paic, G; Painke, F; Pajares, C; Pal, S; Pal, S K; Palaha, A; Palmeri, A; Pappalardo, G S; Park, W J; Patalakha, D I; Paticchio, V; Pavlinov, A; Pawlak, T; Peitzmann, T; Peresunko, D; Perez Lara, C E; Perini, D; Perrino, D; Peryt, W; Pesci, A; Peskov, V; Pestov, Y; Peters, A J; Petracek, V; Petran, M; Petris, M; Petrov, P; Petrovici, M; Petta, C; Piano, S; Piccotti, A; Pikna, M; Pillot, P; Pinazza, O; Pinsky, L; Pitz, N; Piuz, F; Piyarathna, D B; Platt, R; Ploskon, M; Pluta, J; Pocheptsov, T; Pochybova, S; Podesta-Lerma, P L M; Poghosyan, M G; Polak, K; Polichtchouk, B; Pop, A; Porteboeuf, S; Pospisil, V; Potukuchi, B; Prasad, S K; Preghenella, R; Prino, F; Pruneau, C A; Pshenichnov, I; Puddu, G; Pulvirenti, A; Punin, V; Putis, M; Putschke, J; Quercigh, E; Qvigstad, H; Rachevski, A; Rademakers, A; Rademakers, O; Radomski, S; Raiha, T S; Rak, J; Rakotozafindrabe, A; Ramello, L; Ramirez Reyes, A; Rammler, M; Raniwala, R; Raniwala, S; Rasanen, S S; Read, K F; Real, J; Redlich, K; Renfordt, R; Reolon, A R; Reshetin, A; Rettig, F; Revol, J P; Reygers, K; Ricaud, H; Riccati, L; Ricci, R A; Richter, M; Riedler, P; Riegler, W; Riggi, F; Rodriguez Cahuantzi, M; Rohr, D; Rohrich, D; Romita, R; Ronchetti, F; Rosinsky, P; Rosnet, P; Rossegger, S; Rossi, A; Roukoutakis, F; Rousseau, S; Roy, C; Roy, P; Rubio Montero, A J; Rui, R; Rivetti, A; Rusanov, I; Ryabinkin, E; Rybicki, A; Sadovsky, S; Safarik, K; Sahoo, R; Sahu, P K; Saini, J; Saiz, P; Sakai, S; Sakata, D; Salgado, C A; Samanta, T; Sambyal, S; Samsonov, V; Sanchez Castro, X; Sandor, L; Sandoval, A; Sano, M; Sano, S; Santo, R; Santoro, R; Sarkamo, J; Saturnini, P; Scapparone, E; Scarlassara, F; Scharenberg, R P; Schiaua, C; Schicker, R; Schmidt, C; Schmidt, H R; Schreiner, S; Schuchmann, S; Schukraft, J; Schutz, Y; Schwarz, K; Schweda, K; Scioli, G; Scomparin, E; Scott, P A; Scott, R; Segato, G; Selyuzhenkov, I; Senyukov, S; Seo, J; Serci, S; Serradilla, E; Sevcenco, A; Sgura, I; Shabratova, G; Shahoyan, R; Sharma, N; Sharma, S; Shigaki, K; Shimomura, M; Shtejer, K; Sibiriak, Y; Siciliano, M; Sicking, E; Siemiarczuk, T; Silenzi, A; Silvermyr, D; Simonetti, G; Singaraju, R; Singh, R; Singhal, V; Sinha, B C; Sinha, T; Sitar, B; Sitta, M; Skaali, T B; Skjerdal, K; Smakal, R; Smirnov, N; Snellings, R; Sogaard, C; Soloviev, A; Soltz, R; Son, H; Song, J; Song, M; Soos, C; Soramel, F; Spyropoulou-Stassinaki, M; Srivastava, B K; Stachel, J; Stan, I; Stefanek, G; Stefanini, G; Steinbeck, T; Steinpreis, M; Stenlund, E; Steyn, G; Stocco, D; Stock, R; Stokkevag, C H; Stolpovskiy, M; Strmen, P; Suaide, A A P; Subieta Vasquez, M A; Sugitate, T; Suire, C; Sukhorukov, M; Sumbera, M; Susa, T; Swoboda, D; Symons, T J M; Szanto de Toledo, A; Szarka, I; Szostak, A; Tagridis, C; Takahashi, J; Takaki, J D Tapia; Tauro, A; Tavlet, M; Tejeda Munoz, G; Telesca, A; Terrevoli, C; Thader, J; Thomas, D; Thomas, J H; Tieulent, R; Timmins, A R; Tlusty, D; Toia, A; Torii, H; Toscano, L; Tosello, F; Traczyk, T; Truesdale, D; Trzaska, W H; Tsuji, T; Tumkin, A; Turrisi, R; Turvey, A J; Tveter, T S; Ulery, J; Ullaland, K; Uras, A; Urban, J; Urciuoli, G M; Usai, G L; Vacchi, A; Vajzer, M; Vala, M; Valencia Palomo, L; Vallero, S; van der Kolk, N; van Leeuwen, M; Vande Vyvre, P; Vannucci, L; Vargas, A; Varma, R; Vasileiou, M; Vasiliev, A; Vechernin, V; Veldhoen, M; Venaruzzo, M; Vercellin, E; Vergara, S; Vernekohl, D C; Vernet, R; Verweij, M; Vickovic, L; Viesti, G; Vikhlyantsev, O; Vilakazi, Z; Villalobos Baillie, O; Vinogradov, A; Vinogradov, L; Vinogradov, Y; Virgili, T; Viyogi, Y P; Vodopyanov, A; Voloshin, K; Voloshin, S; Volpe, G; von Haller, B; Vranic, D; Ovrebekk, G; Vrlakova, J; Vulpescu, B; Vyushin, A; Wagner, B; Wagner, V; Wan, R; Wang, D; Wang, Y; Wang, Y; Watanabe, K; Wessels, J P; Westerhoff, U; Wiechula, J; Wikne, J; Wilde, M; Wilk, A; Wilk, G; Williams, M C S; Windelband, B; Xaplanteris Karampatsos, L; Yang, H; Yang, S; Yasnopolskiy, S; Yi, J; Yin, Z; Yokoyama, H; Yoo, I K; Yu, W; Yuan, X; Yushmanov, I; Zabrodin, E; Zach, C; Zampolli, C; Zaporozhets, S; Zarochentsev, A; Zavada, P; Zaviyalov, N; Zbroszczyk, H; Zelnicek, P; Zenin, A; Zgura, I; Zhalov, M; Zhang, X; Zhou, D; Zichichi, A; Zinovjev, G; Zoccarato, Y; Zynovyev, M

2010-01-01

We report the first measurement of charged particle elliptic flow in Pb-Pb collisions at 2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|eta|<0.8) and transverse momentum range 0.2< p_t< 5.0 GeV/c. The elliptic flow signal v_2, measured using the 4-particle correlation method, averaged over transverse momentum and pseudorapidity is 0.087 +/- 0.002 (stat) +/- 0.004 (syst) in the 40-50% centrality class. The differential elliptic flow v_2(p_t) reaches a maximum of 0.2 near p_t = 3 GeV/c. Compared to RHIC Au-Au collisions at 200 GeV, the elliptic flow increases by about 30%. Some hydrodynamic model predictions which include viscous corrections are in agreement with the observed increase.

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Doppler Velocity Signatures of Idealized Elliptical Vortices

Directory of Open Access Journals (Sweden)

Wen-Chau Lee

2006-01-01

Full Text Available Doppler radar observations have revealed a class of atmospheric vortices (tropical cyclones, tornadoes, dust devils that possess elliptical radar reflectivity signatures. One famous example is Typhoon Herb (1996 that maintained its elliptical reflectivity structure over a 40-hour period. Theoretical work and dual-Doppler analyses of observed tropical cyclones have suggested two physical mechanisms that can explain the formation of two types of elliptical vortices observed in nature, namely, the combination of a circular vortex with either a wavenumber two vortex Rossby wave or a deformation field. The characteristics of these two types of elliptical vortices and their corresponding Doppler velocity signatures have not been previously examined.

Elliptic hypergeometric functions associated with root systems

OpenAIRE

Rosengren, Hjalmar; Warnaar, S. Ole

2017-01-01

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integeral and series on root systems. The third and final part gives an introduction to Rains' elliptic Macdonald-Koornwinder theory (in part also developed by Coskun and Gustafson).

Anisotropic elliptic optical fibers

Science.gov (United States)

Kang, Soon Ahm

1991-05-01

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Newton`s iteration for inversion of Cauchy-like and other structured matrices

Energy Technology Data Exchange (ETDEWEB)

Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)

1996-12-31

We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

VanderLaan Circulant Type Matrices

Directory of Open Access Journals (Sweden)

Hongyan Pan

2015-01-01

Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.

Scaling of Elliptic Flow, Recombination and Sequential Freeze-Out of Hadrons in Heavy-Ion Collisions

Energy Technology Data Exchange (ETDEWEB)

Fries, R.; He, M., and Rapp, R.

2010-09-21

The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, p{sub T} {le} 2 GeV. Utilizing empirical parametrizations of a thermalized fireball with collective-flow fields, the resonance recombination model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a controlled extraction of quark distributions of the bulk matter at hadronization from spectra of multistrange hadrons which are believed to decouple close to the critical temperature. The resulting elliptic flow from empirical fits at the BNL Relativistic Heavy Ion Collider exhibits transverse kinetic-energy and valence-quark scaling. Utilizing the well-established concept of sequential freeze-out, the scaling at low momenta extends to bulk hadrons ({pi}, K, p) at thermal freeze-out, albeit with different source parameters compared to chemical freeze-out. Elliptic-flow scaling is thus compatible with both equilibrium hydrodynamics and quark recombination.

Systematics of elliptic flow in heavy-ion collisions

Indian Academy of Sciences (India)

We analyze elliptic flow from SIS to RHIC energies systematically in a realistic dynamical cascade model. We compare our results with the recent data from STAR and PHOBOS collaborations on elliptic flow of charged particles at midrapidity in Au + Au collisions at RHIC. In the analysis of elliptic flow at RHIC energy, we find ...

Two-dimensional steady unsaturated flow through embedded elliptical layers

Science.gov (United States)

Bakker, Mark; Nieber, John L.

2004-12-01

New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.

Drinfeld currents of dynamical elliptic algebra

International Nuclear Information System (INIS)

Hou Boyu; Fan Heng; Yang Wenli; Cao Junpeng

2000-01-01

From the generalized Yang-Baxter relations RLL=LLR*, where R and R* are the dynamical R-matrix of A n-1 (1) type face model with the elliptic module shifted by the center of the algebra, using the Ding-Frenkel correspondence, the authors obtain the Drinfeld currents of dynamical elliptic algebra

Heterodyne detector for measuring the characteristic of elliptically polarized microwaves

DEFF Research Database (Denmark)

Leipold, Frank; Nielsen, Stefan Kragh; Michelsen, Susanne

2008-01-01

In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light (ellipticity, angle of ellipticity, and direction of rotation) for microwave radiation at a frequency of 110 GHz. The device consists of two perpendicu......In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light (ellipticity, angle of ellipticity, and direction of rotation) for microwave radiation at a frequency of 110 GHz. The device consists of two...... be calculated. Results from measured and calculated wave characteristics of an elliptically polarized 110 GHz microwave beam for plasma heating launched into the TEXTOR-tokamak experiment are presented. Measurement and calculation are in good agreement. ©2008 American Institute of Physics...

Theoretical and experimental researches of methanol clusters in low - temperature matrices

International Nuclear Information System (INIS)

Chernolevs'ka, Je.A.; Doroshenko, Yi.Yu.; Pogorelov, V.Je.; Vas'kyivs'kij, Je.V.; Shablyinskas, V.; Balyavyichus, V.; Yasajev, O.

2015-01-01

Molecular vibrational spectra of methanol in argon and nitrogen matrices have been studied. Since methanol belongs to a class of substances with hydrogen bonds, there is a possibility of forming molecular associations and clusters with various numbers of molecules. IR spectra of methanol in Ar and N 2 matrices experimentally obtained in the temperature range from 10 to 50 K are compared with the results of computer simulation using the ab initio Car-Parrinello molecular dynamics (CPMD) method. The results obtained for small clusters in model calculations demonstrate a good correlation with experimental data for various matrices at the corresponding temperatures

Convex bodies with many elliptic sections

OpenAIRE

Arelio, Isaac; Montejano, Luis

2014-01-01

{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the $C^2$-differentiable boundary of a convex body also essentially characterize an ellipsoid.

Performances study of UWB monopole antennas using half-elliptic radiator conformed on elliptical surface

Energy Technology Data Exchange (ETDEWEB)

Djidel, S.; Bouamar, M.; Khedrouche, D., E-mail: dkhedrouche@yahoo.com [LASS (Laboratoired’Analyse des Signaux et Systèmes), Department of Electronics, University of M’sila BP.166, Route Ichebilia, M’sila, 28000 Algeria (Algeria)

2016-04-21

This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.

On the Wigner law in dilute random matrices

Science.gov (United States)

Khorunzhy, A.; Rodgers, G. J.

1998-12-01

We consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables. We show that random dilution can change the limiting eigenvalue distribution of such matrices. We prove that under general and natural conditions the normalised eigenvalue counting function coincides with the semicircle (Wigner) distribution in the limit N → ∞. This can be explained by the observation that dilution (or more generally, random modulation) eliminates the weak dependence (or correlations) between random matrix entries. It also supports our earlier conjecture that the Wigner distribution is stable to random dilution and modulation.

Transient thermal stress analysis of a near-edge elliptical defect in a semi-infinite plate subjected to a moving heat source

International Nuclear Information System (INIS)

Mingjong Wang; Weichung Wang

1994-01-01

In this paper, the maximum transient thermal stresses on the boundary of a near-edge elliptical defect in a semi-infinite thin plate were determined by the digital photoelastic technique, when the plate edge experiences a moving heat source. The relationships between the maximum transient thermal stresses and the size and inclination of the elliptical defect, the minimum distance from the elliptical defect to the plate edge as well as the speed of the moving heat source were also studied. Finally, by using a statistical analysis package, the variations of the maximum transient thermal stresses were then correlated with the time, the minimum distance between the edge and the elliptical defect, temperature difference, and speed of the moving heat source. (author)

Ellipticity of near-threshold harmonics from stretched molecules.

Science.gov (United States)

Li, Weiyan; Dong, Fulong; Yu, Shujuan; Wang, Shang; Yang, Shiping; Chen, Yanjun

2015-11-30

We study the ellipticity of near-threshold harmonics (NTH) from aligned molecules with large internuclear distances numerically and analytically. The calculated harmonic spectra show a broad plateau for NTH which is several orders of magnitude higher than that for high-order harmonics. In particular, the NTH plateau shows high ellipticity at small and intermediate orientation angles. Our analyses reveal that the main contributions to the NTH plateau come from the transition of the electron from continuum states to these two lowest bound states of the system, which are strongly coupled together by the laser field. Besides continuum states, higher excited states also play a role in the NTH plateau, resulting in a large phase difference between parallel and perpendicular harmonics and accordingly high ellipticity of the NTH plateau. The NTH plateau with high intensity and large ellipticity provides a promising manner for generating strong elliptically-polarized extreme-ultraviolet (EUV) pulses.

In-cylinder tumble flows and performance of a motorcycle engine with circular and elliptic intake ports

Science.gov (United States)

Huang, R. F.; Lin, K. H.; Yeh, C.-N.; Lan, J.

2009-01-01

The temporal and spatial evolution processes of the flows in the cylinder of a four-valve, four-stroke, single cylinder, reciprocating motorcycle engine installed with the elliptic and circular intake ports were experimentally studied by using the particle image velocimetry (PIV). The engine was modified to fit the requirements of PIV measurement. The velocity fields measured by the PIV were analyzed and quantitatively presented as the tumble ratio and turbulence intensity. In the symmetry plane, both the circular and elliptic intake ports could initiate a vortex around the central region during the intake stroke. During the compression stroke, the central vortex created in the cylinder of the engine with the circular intake port disappeared, while that in the engine cylinder with the elliptic intake port further developed into the tumble motion. In the offset plane, weak vortical structures were initiated by the bluff-body effect of the intake valves during the intake stroke. The vortical structures induced by the elliptic intake port were more coherent than those generated by the circular intake port; besides, this feature extends to the compression stroke. The cycle-averaged tumble ratio and the turbulence intensity of the engine with the elliptic intake port were dramatically larger than those of the engine with the circular intake port. The measured engine performance was improved a lot by installing the elliptic intake port. The correlation between the flow features and the enhancement of the engine performance were argued and discussed.

A simultaneous CONCOR algorithm for the analysis of two partitioned matrices

NARCIS (Netherlands)

Lafosse, R; Ten Berge, J.M.F.

2006-01-01

A standard approach to derive underlying components from two or more data matrices, holding data from the same individuals or objects, is the (generalized) canonical correlation analysis. This technique finds components (canonical variates) with maximal sums of correlations between them. The

Elliptic genus derivation of 4d holomorphic blocks

Science.gov (United States)

Poggi, Matteo

2018-03-01

We study elliptic vortices on ℂ × T 2 by considering the 2d quiver gauge theory describing their moduli spaces. The elliptic genus of these moduli spaces is the elliptic version of vortex partition function of the 4d theory. We focus on two examples: the first is a N = 1, U( N ) gauge theory with fundamental and anti-fundamental matter; the second is a N = 2, U( N ) gauge theory with matter in the fundamental representation. The results are instances of 4d "holomorphic blocks" into which partition functions on more complicated surfaces factorize. They can also be interpreted as free-field representations of elliptic Virasoro algebrae.

Quasilinear infiltration from an elliptical cavity

Science.gov (United States)

Kuhlman, Kristopher L.; Warrick, Arthur W.

2008-08-01

We develop analytic solutions to the linearized steady-state Richards equation for head and total flowrate due to an elliptic cylinder cavity with a specified pressure head boundary condition. They are generalizations of the circular cylinder cavity solutions of Philip [Philip JR. Steady infiltration from circular cylindrical cavities. Soil Sci Soc Am J 1984;48:270-8]. The circular and strip sources are limiting cases of the elliptical cylinder solution, derived for both horizontally- and vertically-aligned ellipses. We give approximate rational polynomial expressions for total flowrate from an elliptical cylinder over a range of sizes and shapes. The exact elliptical solution is in terms of Mathieu functions, which themselves are generalizations of and computed from trigonometric and Bessel functions. The required Mathieu functions are computed from a matrix eigenvector problem, a modern approach that is straightforward to implement using available linear algebra libraries. Although less efficient and potentially less accurate than the iterative continued fraction approach, the matrix approach is simpler to understand and implement and is valid over a wider parameter range.

International Workshop on Elliptic and Parabolic Equations

CERN Document Server

Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

2015-01-01

This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

Advanced topics in the arithmetic of elliptic curves

CERN Document Server

Silverman, Joseph H

1994-01-01

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...

On the Behavior of Eisenstein Series Through Elliptic Degeneration

Science.gov (United States)

Garbin, D.; Pippich, A.-M. V.

2009-12-01

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

On mod 2 and higher elliptic genera

International Nuclear Information System (INIS)

Liu Kefeng

1992-01-01

In the first part of this paper, we construct mod 2 elliptic genera on manifolds of dimensions 8k+1, 8k+2 by mod 2 index formulas of Dirac operators. They are given by mod 2 modular forms or mod 2 automorphic functions. We also obtain an integral formula for the mod 2 index of the Dirac operator. As a by-product we find topological obstructions to group actions. In the second part, we construct higher elliptic genera and prove some of their rigidity properties under group actions. In the third part we write down characteristic series for all Witten genera by Jacobi theta-functions. The modular property and transformation formulas of elliptic genera then follow easily. We shall also prove that Krichever's genera, which come from integrable systems, can be written as indices of twisted Dirac operators for SU-manifolds. Some general discussions about elliptic genera are given. (orig.)

Constructing elliptic curves from Galois representations

OpenAIRE

Snowden, Andrew; Tsimerman, Jacob

2017-01-01

Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse $\\ell$-adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforward properties: cyclotomic determinant, finite ramification, rational traces of Frobenius, and somewhere not potentially good reduction. We prove that any lisse sheaf of rank two possessing these properties comes from an elliptic curve.

Note on twisted elliptic genus of K3 surface

International Nuclear Information System (INIS)

Eguchi, Tohru; Hikami, Kazuhiro

2011-01-01

We discuss the possibility of Mathieu group M 24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M 24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M 24 . In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

Rational points on elliptic curves

CERN Document Server

Silverman, Joseph H

2015-01-01

The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and ...

Rayleigh wave ellipticity across the Iberian Peninsula and Morocco

Science.gov (United States)

Gómez García, Clara; Villaseñor, Antonio

2015-04-01

Spectral amplitude ratios between horizontal and vertical components (H/V ratios) from seismic records are useful to evaluate site effects, predict ground motion and invert for S velocity in the top several hundred meters. These spectral ratios can be obtained from both ambient noise and earthquakes. H/V ratios from ambient noise depend on the content and predominant wave types: body waves, Rayleigh waves, a mixture of different waves, etc. The H/V ratio computed in this way is assumed to measure Rayleigh wave ellipticity since ambient vibrations are dominated by Rayleigh waves. H/V ratios from earthquakes are able to determine the local crustal structure at the vicinity of the recording station. These ratios obtained from earthquakes are based on surface wave ellipticity measurements. Although long period (>20 seconds) Rayleigh H/V ratio is not currently used because of large scatter has been reported and uncertainly about whether these measurements are compatible with traditional phase and group velocity measurements, we will investigate whether it is possible to obtain stable estimates after collecting statistics for many earthquakes. We will use teleseismic events from shallow earthquakes (depth ≤ 40 km) between 2007 January 1 and 2012 December 31 with M ≥ 6 and we will compute H/V ratios for more than 400 stations from several seismic networks across the Iberian Peninsula and Morocco for periods between 20 and 100 seconds. Also H/V ratios from cross-correlations of ambient noise in different components for each station pair will be computed. Shorter period H/V ratio measurements based on ambient noise cross-correlations are strongly sensitive to near-surface structure, rather than longer period earthquake Rayleigh waves. The combination of ellipticity measurements based on earthquakes and ambient noise will allow us to perform a joint inversion with Rayleigh wave phase velocity. Upper crustal structure is better constrained by the joint inversion compared

Kinematically Decoupled Cores in Dwarf (Elliptical) Galaxies

NARCIS (Netherlands)

Toloba, E.; Peletier, R. F.; Guhathakurta, P.; van de Ven, G.; Boissier, S.; Boselli, A.; Brok, M. d.; Falcón-Barroso, J.; Hensler, G.; Janz, J.; Laurikainen, E.; Lisker, T.; Paudel, S.; Ryś, A.; Salo, H.

An overview is given of what we know about the frequency of kinematically decoupled cores in dwarf elliptical galaxies. New observations show that kinematically decoupled cores happen just as often in dwarf elliptical as in ordinary early-type galaxies. This has important consequences for the

Elliptic hypergeometric functions and the representation theory

International Nuclear Information System (INIS)

Spiridonov, V.P.

2011-01-01

Full text: (author)Elliptic hypergeometric functions were discovered around ten years ago. They represent the top level known generalization of the Euler beta integral and Euler-Gauss 2 F 1 hypergeometric function. In general form they are defined by contour integrals involving elliptic gamma functions. We outline the structure of the simplest examples of such functions and discuss their relations to the representation theory of the classical Lie groups and their various deformations. In one of the constructions elliptic hypergeometric integrals describe purely group-theoretical objects having the physical meaning of superconformal indices of four-dimensional supersymmetric gauge field theories

Picone-type inequalities for nonlinear elliptic equations and their applications

Directory of Open Access Journals (Sweden)

Takaŝi Kusano

2001-01-01

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

ACORNS, Covariance and Correlation Matrix Diagonalization

International Nuclear Information System (INIS)

Szondi, E.J.

1990-01-01

1 - Description of program or function: The program allows the user to verify the different types of covariance/correlation matrices used in the activation neutron spectrometry. 2 - Method of solution: The program performs the diagonalization of the input covariance/relative covariance/correlation matrices. The Eigen values are then analyzed to determine the rank of the matrices. If the Eigen vectors of the pertinent correlation matrix have also been calculated, the program can perform a complete factor analysis (generation of the factor matrix and its rotation in Kaiser's 'varimax' sense to select the origin of the correlations). 3 - Restrictions on the complexity of the problem: Matrix size is limited to 60 on PDP and to 100 on IBM PC/AT

Elliptic and parabolic equations for measures

Energy Technology Data Exchange (ETDEWEB)

Bogachev, Vladimir I [M. V. Lomonosov Moscow State University, Moscow (Russian Federation); Krylov, Nikolai V [University of Minnesota, Minneapolis, MN (United States); Roeckner, Michael [Universitat Bielefeld, Bielefeld (Germany)

2009-12-31

This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L{sup p}-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.

Iterated elliptic and hypergeometric integrals for Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Ablinger, J.; Radu, C.S.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Van Hoeij, M.; Imamoglu, E. [Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics; Raab, C.G. [Linz Univ. (Austria). Inst. for Algebra

2017-05-15

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as {sub 2}F{sub 1} Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ{sub i} functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η{sup κ}(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

Iterated elliptic and hypergeometric integrals for Feynman diagrams

International Nuclear Information System (INIS)

Ablinger, J.; Radu, C.S.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Van Hoeij, M.; Imamoglu, E.; Raab, C.G.

2017-05-01

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as _2F_1 Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ_i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η"κ(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

Infinite matrices and sequence spaces

CERN Document Server

Cooke, Richard G

2014-01-01

This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi

The two-loop sunrise integral and elliptic polylogarithms

Energy Technology Data Exchange (ETDEWEB)

Adams, Luise; Weinzierl, Stefan [Institut fuer Physik, Johannes Gutenberg-Universitaet Mainz (Germany); Bogner, Christian [Institut fuer Physik, Humboldt-Universitaet zu Berlin (Germany)

2016-07-01

In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation ε of the two-dimensional equal mass solution. Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral. Around four space-time dimensions the sunrise integral can be expressed with the ε{sup 0}- and ε{sup 1}-solution around two dimensions, mass derivatives thereof and simpler terms. Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the ε{sup 0}- and ε{sup 1}-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.

Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Plešinger, M.

2015-01-01

Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015

Note on twisted elliptic genus of K3 surface

Energy Technology Data Exchange (ETDEWEB)

Eguchi, Tohru, E-mail: eguchi@yukawa.kyoto-u.ac.j [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Hikami, Kazuhiro, E-mail: KHikami@gmail.co [Department of Mathematics, Naruto University of Education, Tokushima 772-8502 (Japan)

2011-01-03

We discuss the possibility of Mathieu group M{sub 24} acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M{sub 24} so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M{sub 24}. In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

Near-infrared photometry of bright elliptical galaxies

NARCIS (Netherlands)

Peletier, R. F.; Valentijn, E. A.; Jameson, R. F.

High-quality visual-infrared color profiles have been determined for elliptical galaxies for the first time. Surface photometry in J and K is presented for 12 bright elliptical galaxies, and the results have been combined with CCD data in visual passbands. It is shown that the galaxies become bluer

Type-2 fuzzy elliptic membership functions for modeling uncertainty

DEFF Research Database (Denmark)

Kayacan, Erdal; Sarabakha, Andriy; Coupland, Simon

2018-01-01

Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs...... in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance...... advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem...

Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case

OpenAIRE

Kösters, Holger

2009-01-01

We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are g...

Energy and the Elliptical Orbit

Science.gov (United States)

Nettles, Bill

2009-03-01

In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.

Hydrodynamic simulation of elliptic flow

CERN Document Server

Kolb, P F; Ruuskanen, P V; Heinz, Ulrich W

1999-01-01

We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of radial and elliptic flow. We show that at high energies elliptic flow is generated only during the initial stages of the expansion while radial flow continues to grow until freeze-out. Quantitative comparisons with SPS data from semiperipheral Pb+Pb collisions suggest the applicability of hydrodynamical concepts already $\\approx$ 1 fm/c after impact.

Numerical analysis of turbulent flow and heat transfer in a square sectioned U-bend duct by elliptic-blending second moment closure

International Nuclear Information System (INIS)

Shin, Jong Keun; Choi, Young Don; An, Jeong Soo

2007-01-01

A second moment turbulence closure using the elliptic-blending equation is introduced to analyze the turbulence and heat transfer in a square sectioned U-bend duct flow. The turbulent heat flux model based on the elliptic concept satisfies the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also has the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. Also, the traditional GGDH heat flux model is compared with the present elliptic concept-based heat flux model. The turbulent heat flux models are closely linked to the elliptic blending second moment closure which is used for the prediction of Reynolds stresses. The predicted results show their reasonable agreement with experimental data for a square sectioned U-bend duct flow field adopted in the present study

Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

KAUST Repository

Waheed, Umair bin

2014-05-01

Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media

KAUST Repository

Waheed, Umair bin; Alkhalifah, Tariq Ali

2014-01-01

Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.

Generation of an elliptic hollow beam using Mathieu and Bessel functions.

Science.gov (United States)

Chakraborty, Rijuparna; Ghosh, Ajay

2006-09-01

A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.

Random source generating far field with elliptical flat-topped beam profile

International Nuclear Information System (INIS)

Zhang, Yongtao; Cai, Yangjian

2014-01-01

Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively. (paper)

On reflectionless equi-transmitting matrices

Directory of Open Access Journals (Sweden)

Pavel Kurasov

2014-01-01

Full Text Available Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.

An investigation into the vector ellipticity of extremely low frequency magnetic fields from appliances in UK homes

International Nuclear Information System (INIS)

Ainsbury, Elizabeth A; Conein, Emma; Henshaw, Denis L

2005-01-01

Elliptically polarized magnetic fields induce higher currents in the body compared with their plane polarized counterparts. This investigation examines the degree of vector ellipticity of extremely low frequency magnetic fields (ELF-MFs) in the home, with regard to the adverse health effects reportedly associated with ELF-MFs, for instance childhood leukaemia. Tri-axial measurements of the magnitude and phase of the 0-3000 Hz magnetic fields, produced by 226 domestic mains-fed appliances of 32 different types, were carried out in 16 homes in Worcestershire in the summer of 2004. Magnetic field strengths were low, with average (RMS) values of 0.03 ± 0.02 μT across all residences. In contrast, background field ellipticities were high, on average 47 ± 11%. Microwave and electric ovens produced the highest ellipticities: mean respective values of 21 ± 21% and 21 ± 17% were observed 20 cm away from these appliances. There was a negative correlation between field strength and field polarization, which we attribute to the higher relative field contribution close to each individual (single-phase) appliance. The measurements demonstrate that domestic magnetic fields are extremely complex and cannot simply be characterized by traditional measurements such as time-weighted average or peak exposure levels. We conclude that ellipticity should become a relevant metric for future epidemiological studies of health and ELF-MF exposure

Superconducting elliptical cavities

CERN Document Server

Sekutowicz, J K

2011-01-01

We give a brief overview of the history, state of the art, and future for elliptical superconducting cavities. Principles of the cell shape optimization, criteria for multi-cell structures design, HOM damping schemes and other features are discussed along with examples of superconducting structures for various applications.

Interstellar matter within elliptical galaxies

Science.gov (United States)

Jura, Michael

1988-01-01

Multiwavelength observations of elliptical galaxies are reviewed, with an emphasis on their implications for theoretical models proposed to explain the origin and evolution of the interstellar matter. Particular attention is given to interstellar matter at T less than 100 K (atomic and molecular gas and dust), gas at T = about 10,000 K, and gas at T = 10 to the 6th K or greater. The data are shown to confirm the occurrence of mass loss from evolved stars, significant accretion from companion galaxies, and cooling inflows; no evidence is found for large mass outflow from elliptical galaxies.

Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?

Science.gov (United States)

Genzel, R.; Tacconi, L. J.; Rigopoulou, D.; Lutz, D.; Tecza, M.

2001-12-01

We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~0.5" resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are ``ellipticals in formation.'' Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrotsini/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history. Based on observations at the European Southern Observatory, Chile (ESO 65.N-0266, 65.N-0289), and on observations at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, The University of California, and the National Aeronautics and Space Administration. The Keck Observatory was made possible by the general financial support by the W. M. Keck Foundation.

Newton flows for elliptic functions: A pilot study

NARCIS (Netherlands)

Twilt, F.; Helminck, G.F.; Snuverink, M.; van den Brug, L.

2008-01-01

Elliptic Newton flows are generated by a continuous, desingularized Newton method for doubly periodic meromorphic functions on the complex plane. In the special case, where the functions underlying these elliptic Newton flows are of second-order, we introduce various, closely related, concepts of

Centrality dependence of directed and elliptic flow at the SPS

International Nuclear Information System (INIS)

Poskanzer, A.M.; Voloshin, S.A.; Baechler, J.; Barna, D.; Barnby, L.S.; Bartke, J.; Barton, R.A.; Betev, L.; Bialkowska, H.; Billmeier, A.; Blume, C.; Blyth, C.O.; Boimska, B.; Bracinik, J.; Brady, F.P.; Brockmann, R.; Brun, R.; Buncic, P.; Carr, L.; Cebra, D.; Cooper, G.E.; Cramer, J.G.; Csato, P.; Eckardt, V.; Eckhardt, F.; Ferenc, D.; Fischer, H.G.; Fodor, Z.; Foka, P.; Freund, P.; Friese, V.; Ftacnik, J.; Gal, J.; Ganz, R.; Gazdzicki, M.; Gladysz, E.; Grebieszkow, J.; Harris, J.W.; Hegyi, S.; Hlinka, V.; Hoehne, C.; Igo, G.; Ivanov, M.; Jacobs, P.; Janik, R.; Jones, P.G.; Kadija, K.; Kolesnikov, V.I.; Kowalski, M.; Lasiuk, B.; Levai, P.; Malakhov, A.I.; Margetis, S.; Markert, C.; Mayes, B.W.; Melkumov, G.L.; Molnar, J.; Nelson, J.M.; Odyniec, G.; Oldenburg, M.D.; Palla, G.; Panagiotou, A.D.; Petridis, A.; Pikna, M.; Pinsky, L.; Poskanzer, A.M.; Prindle, D.J.; Puehlhofer, F.; Reid, J.G.; Renfordt, R.; Retyk, W.; Ritter, H.G.; Roehrich, D.; Roland, C.; Roland, G.; Rybicki, A.; Sammer, T.; Sandoval, A.; Sann, H.; Semenov, A.Yu.; Schaefer, E.; Schmitz, N.; Seyboth, P.; Sikler, F.; Sitar, B.; Skrzypczak, E.; Snellings, R.; Squier, G.T.A.; Stock, R.; Strmen, P.; Stroebele, H.; Susa, T.; Szarka, I.; Szentpetery, I.; Sziklai, J.; Toy, M.; Trainor, T.A.; Trentalange, S.; Ullrich, T.; Varga, D.; Vassiliou, M.; Veres, G.I.; Vesztergombi, G.; Voloshin, S.; Vranic, D.; Wang, F.; Weerasundara, D.D.; Wenig, S.; Whitten, C.; Xu, N.; Yates, T.A.; Yoo, I.K.; Zimanyi, J.

1999-01-01

New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models

X-ray Point Source Populations in Spiral and Elliptical Galaxies

Science.gov (United States)

Colbert, E.; Heckman, T.; Weaver, K.; Strickland, D.

2002-01-01

The hard-X-ray luminosity of non-active galaxies has been known to be fairly well correlated with the total blue luminosity since the days of the Einstein satellite. However, the origin of this hard component was not well understood. Some possibilities that were considered included X-ray binaries, extended upscattered far-infrared light via the inverse-Compton process, extended hot 107 K gas (especially in ellipitical galaxies), or even an active nucleus. Chandra images of normal, elliptical and starburst galaxies now show that a significant amount of the total hard X-ray emission comes from individual point sources. We present here spatial and spectral analyses of the point sources in a small sample of Chandra obervations of starburst galaxies, and compare with Chandra point source analyses from comparison galaxies (elliptical, Seyfert and normal galaxies). We discuss possible relationships between the number and total hard luminosity of the X-ray point sources and various measures of the galaxy star formation rate, and discuss possible options for the numerous compact sources that are observed.

Thickness shear mode quartz crystal resonators with optimized elliptical electrodes

International Nuclear Information System (INIS)

Ma Ting-Feng; Feng Guan-Ping; Zhang Chao; Jiang Xiao-Ning

2011-01-01

Quartz crystal resonators (QCRs) with circular electrodes have been widely used for various liquid and gas sensing applications. In this work, quartz crystal resonators with elliptical electrodes were studied and tested for liquid property measurement. Mindlin's theory was used to optimize the dimension and geometry of the electrodes and a 5-MHz QCR with minimum series resistance and without any spurious modes was obtained. A series of AT-cut QCRs with elliptical electrodes of different sizes were fabricated and their sensing performances were compared to devices with circular electrodes. The experimental result shows that the device with elliptical electrodes can obtain lower resonance impedance and a higher Q factor, which results in a better loading capability. Even though the sensitivities of devices with elliptical and circular electrodes are found to be similar, the sensor with elliptical electrodes has much higher resolution due to a better frequency stability. The study indicates that the performance of QCRs with elliptical electrodes is superior to that of traditional QCRs with circular electrodes. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

Hadron correlations from recombination

Energy Technology Data Exchange (ETDEWEB)

Fries, Rainer J [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States)

2005-01-01

Quark recombination is a successful model to describe the hadronization of a deconfined quark gluon plasma. Jet-like dihadron correlations measured at RHIC provide a challenge for this picture. We discuss how correlations between hadrons can arise from correlations between partons before hadronization. An enhancement of correlations through the recombination process, similar to the enhancement of elliptic flow is found. Hot spots from completely or partially quenched jets are a likely source of such parton correlations.

Elliptical cross section fuel rod study II

International Nuclear Information System (INIS)

Taboada, H.; Marajofsky, A.

1996-01-01

In this paper it is continued the behavior analysis and comparison between cylindrical fuel rods of circular and elliptical cross sections. Taking into account the accepted models in the literature, the fission gas swelling and release were studied. An analytical comparison between both kinds of rod reveals a sensible gas release reduction in the elliptical case, a 50% swelling reduction due to intragranular bubble coalescence mechanism and an important swelling increase due to migration bubble mechanism. From the safety operation point of view, for the same linear power, an elliptical cross section rod is favored by lower central temperatures, lower gas release rates, greater gas store in ceramic matrix and lower stored energy rates. (author). 6 refs., 8 figs., 1 tab

Index profile measurement of asymmetrical elliptical preforms or fibers

NARCIS (Netherlands)

Blitterswijk, van W.; Smit, M.K.

1987-01-01

An extension of the beam-deflection method to the case of elliptical preforms with eccentric core (asymmetrical elliptical preforms) is presented, which can be easily implemented on automatic measurement equipment

Electron energy spectrum in core-shell elliptic quantum wire

Directory of Open Access Journals (Sweden)

V.Holovatsky

2007-01-01

Full Text Available The electron energy spectrum in core-shell elliptic quantum wire and elliptic semiconductor nanotubes are investigated within the effective mass approximation. The solution of Schrodinger equation based on the Mathieu functions is obtained in elliptic coordinates. The dependencies of the electron size quantization spectrum on the size and shape of the core-shell nanowire and nanotube are calculated. It is shown that the ellipticity of a quantum wire leads to break of degeneration of quasiparticle energy spectrum. The dependences of the energy of odd and even electron states on the ratio between semiaxes are of a nonmonotonous character. The anticrosing effects are observed at the dependencies of electron energy spectrum on the transversal size of the core-shell nanowire.

Reliability and Validity of Colored Progressive Matrices for 4-6 Age Children

Directory of Open Access Journals (Sweden)

Ahmet Bildiren

2017-06-01

Full Text Available In this research, it was aimed to test the reliability and validity of Colored Progressive Matrices for children between the ages of 4 to 6 from 15 schools. The sample of the study consisted of 640 kindergarten children. Test-retest and parallel form were used for reliability analyses. For the validity analysis, the relations between the Colored Progressive Matrices Test and Bender Gestalt Visual Motor Sensitivity Test, WISC-R and TONI-3 tests were examined. The results showed that there was a significant relation between the test-retest results and the parallel forms in all the age groups. Validity analyses showed strong correlations between the Colored Progressive Matrices and all the other measures.

Characterizing protein conformations by correlation analysis of coarse-grained contact matrices

Science.gov (United States)

Lindsay, Richard J.; Siess, Jan; Lohry, David P.; McGee, Trevor S.; Ritchie, Jordan S.; Johnson, Quentin R.; Shen, Tongye

2018-01-01

We have developed a method to capture the essential conformational dynamics of folded biopolymers using statistical analysis of coarse-grained segment-segment contacts. Previously, the residue-residue contact analysis of simulation trajectories was successfully applied to the detection of conformational switching motions in biomolecular complexes. However, the application to large protein systems (larger than 1000 amino acid residues) is challenging using the description of residue contacts. Also, the residue-based method cannot be used to compare proteins with different sequences. To expand the scope of the method, we have tested several coarse-graining schemes that group a collection of consecutive residues into a segment. The definition of these segments may be derived from structural and sequence information, while the interaction strength of the coarse-grained segment-segment contacts is a function of the residue-residue contacts. We then perform covariance calculations on these coarse-grained contact matrices. We monitored how well the principal components of the contact matrices is preserved using various rendering functions. The new method was demonstrated to assist the reduction of the degrees of freedom for describing the conformation space, and it potentially allows for the analysis of a system that is approximately tenfold larger compared with the corresponding residue contact-based method. This method can also render a family of similar proteins into the same conformational space, and thus can be used to compare the structures of proteins with different sequences.

Signal and noise in financial correlation matrices

Science.gov (United States)

Burda, Zdzisław; Jurkiewicz, Jerzy

2004-12-01

Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to analyze a particular case of the correlations in financial series and to show that contrary to earlier claims, correlations can be measured also in the “random” part of the spectrum. Implications for the portfolio optimization are briefly discussed.

Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations

International Nuclear Information System (INIS)

Yu Jianping; Sun Yongli

2008-01-01

This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations

Hot interstellar matter in elliptical galaxies

CERN Document Server

Kim, Dong-Woo

2012-01-01

Based on a number of new discoveries resulting from 10 years of Chandra and XMM-Newton observations and corresponding theoretical works, this is the first book to address significant progress in the research of the Hot Interstellar Matter in Elliptical Galaxies. A fundamental understanding of the physical properties of the hot ISM in elliptical galaxies is critical, because they are directly related to the formation and evolution of elliptical galaxies via star formation episodes, environmental effects such as stripping, infall, and mergers, and the growth of super-massive black holes. Thanks to the outstanding spatial resolution of Chandra and the large collecting area of XMM-Newton, various fine structures of the hot gas have been imaged in detail and key physical quantities have been accurately measured, allowing theoretical interpretations/predictions to be compared and tested against observational results. This book will bring all readers up-to-date on this essential field of research.

Multiparticle azimuthal correlations

Indian Academy of Sciences (India)

In §2, we recall the definition of elliptic flow and explain the mechanism producing ..... Taking this effect into account, one is led to revise significantly the values of the ... non-flow correlations, one can show under very general assumptions that ...

Stellar populations as a function of radius in giant elliptical galaxies

NARCIS (Netherlands)

Peletier, Reynier F.; Valentijn, Edwin A.

Accurate surface photometry has been obtained in J and K for 12 giant elliptical galaxies. Ellipses have been fitted, to obtain luminosity, ellipticity, and major axis position angle profiles. The results have been combined with visual profiles from CCD observations. It is found that elliptical

Instanton geometry and quantum A∞ structure on the elliptic curve

International Nuclear Information System (INIS)

Herbst, M.; Lerche, W.; Nemeschansky, D.

2006-03-01

We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the 'long-diagonal branes' on the elliptic curve. We verify that they satisfy the relevant A ∞ consistency relations at both classical and quantum levels. In particular we find that the A ∞ relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A ∞ relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields. (orig.)

An investigation into the vector ellipticity of extremely low frequency magnetic fields from appliances in UK homes

Science.gov (United States)

Ainsbury, Elizabeth A.; Conein, Emma; Henshaw, Denis L.

2005-07-01

Elliptically polarized magnetic fields induce higher currents in the body compared with their plane polarized counterparts. This investigation examines the degree of vector ellipticity of extremely low frequency magnetic fields (ELF-MFs) in the home, with regard to the adverse health effects reportedly associated with ELF-MFs, for instance childhood leukaemia. Tri-axial measurements of the magnitude and phase of the 0-3000 Hz magnetic fields, produced by 226 domestic mains-fed appliances of 32 different types, were carried out in 16 homes in Worcestershire in the summer of 2004. Magnetic field strengths were low, with average (RMS) values of 0.03 ± 0.02 µT across all residences. In contrast, background field ellipticities were high, on average 47 ± 11%. Microwave and electric ovens produced the highest ellipticities: mean respective values of 21 ± 21% and 21 ± 17% were observed 20 cm away from these appliances. There was a negative correlation between field strength and field polarization, which we attribute to the higher relative field contribution close to each individual (single-phase) appliance. The measurements demonstrate that domestic magnetic fields are extremely complex and cannot simply be characterized by traditional measurements such as time-weighted average or peak exposure levels. We conclude that ellipticity should become a relevant metric for future epidemiological studies of health and ELF-MF exposure. This work is supported by the charity CHILDREN with LEUKAEMIA, registered charity number 298405.

Investigation on computation of elliptical microwave plasma cavity

Science.gov (United States)

Liao, Xiaoli; Liu, Hua; Zhang, Kai

2008-12-01

In recent years, the advance of the elliptical resonant cavity and focus cavity is known by many people. There are homogeneous and multipatternal virtues in the focus dimensional microwave field of the elliptical resonant cavity. It is very suitable for applying the low power microwave biological effect equipment. However, when designing the elliptical resonant cavity may meet the problems of complex and huge computation need to be solved. This paper proposed the simple way of approximate processing the Mathieu function. It can greatly simplify the difficulty and decrease the scale of computation. This method can satisfy the requirements of research and development within project permitted precision.

Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model

International Nuclear Information System (INIS)

Langmann, Edwin

2006-01-01

We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter λ, we also obtain 'dual' relations involving 'mixed' correlation functions of anyons with two different statistics parameters λ and 1/λ. We also give alternative, elementary proofs of these identities by direct computations

Structure and Formation of Elliptical and Spheroidal Galaxies

Science.gov (United States)

Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf

2009-05-01

New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sérsic log I vprop r 1/n functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes MVT 4 uncorrelated with MVT . They also are α-element enhanced, implying short star-formation timescales. And their stellar populations have a variety of ages but mostly are very old. Extra light ellipticals generally rotate rapidly, are more isotropic than core Es, and have disky isophotes. We show that they have n sime 3 ± 1 almost uncorrelated with MVT and younger and less α-enhanced stellar populations. These are new clues to galaxy formation. We suggest that extra light ellipticals got their low Sérsic indices by forming in relatively few binary mergers, whereas giant ellipticals have n > 4 because they formed in larger numbers of mergers of more galaxies at once plus later heating during hierarchical clustering. We confirm that core Es contain X-ray-emitting gas whereas extra light Es generally do not. This leads us to suggest why the E-E dichotomy arose. If energy feedback from active galactic nuclei (AGNs) requires a "working surface" of hot gas, then this is present in core galaxies but absent in extra light galaxies. We suggest that AGN energy feedback is a strong function of galaxy mass: it is weak enough in small Es not to prevent merger starbursts but strong enough in giant Es and their progenitors to make dry mergers dry and to protect old stellar populations from late star formation. Finally, we verify that there is a strong

Electromagnetic Invisibility of Elliptic Cylinder Cloaks

International Nuclear Information System (INIS)

Kan, Yao; Chao, Li; Fang, Li

2008-01-01

Structures with unique electromagnetic properties are designed based on the approach of spatial coordinate transformations of Maxwell's equations. This approach is applied to scheme out invisible elliptic cylinder cloaks, which provide more feasibility for cloaking arbitrarily shaped objects. The transformation expressions for the anisotropic material parameters and the field distribution are derived. The cloaking performances of ideal and lossy elliptic cylinder cloaks are investigated by finite element simulations. It is found that the cloaking performance will degrade in the forward direction with increasing loss. (fundamental areas of phenomenology (including applications))

Quantum W-algebras and elliptic algebras

International Nuclear Information System (INIS)

Feigin, B.; Kyoto Univ.; Frenkel, E.

1996-01-01

We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

Vortex precession in thin elliptical ferromagnetic nanodisks

Energy Technology Data Exchange (ETDEWEB)

Zaspel, C.E., E-mail: craig.zaspel@umwestern.edu

2017-07-01

Highlights: • A general form for the magnetostatic energy is calculated for the vortex state in a ferromagnetic ellipse. • The ellipse magnetostatic energy is minimized by conformal mapping the circular disk onto the ellipse. • The gyrotropic precession frequency is obtained in general for a range of ellipticities. - Abstract: The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk. It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.

Rank reduction of correlation matrices by majorization

NARCIS (Netherlands)

R. Pietersz (Raoul); P.J.F. Groenen (Patrick)

2004-01-01

textabstractIn this paper a novel method is developed for the problem of finding a low-rank correlation matrix nearest to a given correlation matrix. The method is based on majorization and therefore it is globally convergent. The method is computationally efficient, is straightforward to implement,

Influences of magma chamber ellipticity on ring fracturing and eruption at collapse calderas

International Nuclear Information System (INIS)

Holohan, Eoghan P; Walsh, John J; Vries, Benjamin van Wyk de; Troll, Valentin R; Walter, Thomas R

2008-01-01

Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.

Influences of magma chamber ellipticity on ring fracturing and eruption at collapse calderas

Energy Technology Data Exchange (ETDEWEB)

Holohan, Eoghan P; Walsh, John J [Fault Analysis Group, School of Geological Sciences, University College Dublin, Belfield, Dublin 4 (Ireland); Vries, Benjamin van Wyk de [Laboratoire Magmas et Volcans, 5 rue Kessler, 63038 Clermont-Ferrand (France); Troll, Valentin R [Department of Earth Sciences, Uppsala University, SE-752 36, Uppsala (Sweden); Walter, Thomas R [GFZ Potsdam, Telegrafenberg, Potsdam, D-14473 (Germany)], E-mail: Eoghan.Holohan@ucd.ie

2008-10-01

Plan-view ellipticity of a pre-caldera magma reservoir, and its influence on the development of caldera ring fracturing and eruptive behaviour, have not previously been subjected to dedicated evaluation. We experimentally simulated caldera collapse into elliptical magma chambers and found that collapse into highly-elliptical chambers produced a characteristic pattern of ring-fault localization and lateral propagation. Although results are preliminary, the general deformation pattern for elliptical resurgence shows strong similarities to elliptical collapse. Ring faults accommodating uplift again initiate around the chamberos short axis and are reverse, but dip inward. Field and geophysical observations at several elliptical calderas of varying scale (e.g. Long Valley, Katmai, and Rabaul calderas) are consistent with a control from elliptical magma chamber geometry on ring fracturing and eruption, as predicted from our experiments.

Polarization characteristics of double-clad elliptical fibers.

Science.gov (United States)

Zhang, F; Lit, J W

1990-12-20

A scalar variational analysis based on a Gaussian approximation of the fundamental mode of a double-clad elliptical fiber with a depressed inner cladding is studied. The polarization properties and graphic results are presented; they are given in terms of three parameters: the ratio of the major axis to the minor axis of the core, the ratio of the inner cladding major axis to the core major axis, and the difference between the core index and the inner cladding index. The variations of both the spot size and the field intensity with core ellipticity are examined. It is shown that high birefringence and dispersion-free orthogonal polarization modes can be obtained within the single-mode region and that the field intensity distribution may be more confined to the fiber center than in a single-clad elliptical fiber.

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices

Structural Analysis of Covariance and Correlation Matrices.

Science.gov (United States)

Joreskog, Karl G.

1978-01-01

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

Elliptic Diophantine equations a concrete approach via the elliptic logarithm

CERN Document Server

Tzanakis, Nikos

2013-01-01

This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages, like Magma. This book is suitable for students in mathematics, as well as professional mathematicians.

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

Science.gov (United States)

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

The elliptic model for communication fluxes

International Nuclear Information System (INIS)

Herrera-Yagüe, C; Schneider, C M; González, M C; Smoreda, Z; Couronné, T; Zufiria, P J

2014-01-01

In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry of transportation models, the new model considers that the number of relationships between two locations is inversely proportional to the population in the ellipse whose foci are in these two locations. The elliptic model is evaluated by considering the anonymous communications patterns of 25 million users from three different countries, where a location has been assigned to each user based on their most used phone tower or billing zip code. With this information, spatial social networks are built at three levels of resolution: tower, city and region for each of the three countries. The elliptic model achieves a similar performance when predicting communication fluxes as transportation models do when predicting trips. This shows that human relationships are influenced at least as much by geography as is human mobility. (paper)

Elliptical Galaxies: Rotationally Distorted, After All

Directory of Open Access Journals (Sweden)

Caimmi, R.

2009-12-01

Full Text Available On the basis of earlier investigations onhomeoidally striated Mac Laurin spheroids and Jacobi ellipsoids (Caimmi and Marmo2005, Caimmi 2006a, 2007, different sequences of configurations are defined and represented in the ellipticity-rotation plane, $({sf O}hat{e}chi_v^2$. The rotation parameter, $chi_v^2$, is defined as the ratio, $E_mathrm{rot}/E_mathrm{res}$, of kinetic energy related to the mean tangential equatorial velocity component, $M(overline{v_phi}^2/2$, to kineticenergy related to tangential equatorial component velocity dispersion, $Msigma_{phiphi}^2/2$, andresidual motions, $M(sigma_{ww}^2+sigma_{33}^2/2$.Without loss of generality (above a thresholdin ellipticity values, the analysis is restricted to systems with isotropic stress tensor, whichmay be considered as adjoint configurationsto any assigned homeoidally striated density profile with anisotropic stress tensor, different angular momentum, and equal remaining parameters.The description of configurations in the$({sf O}hat{e}chi_v^2$ plane is extendedin two respects, namely (a from equilibriumto nonequilibrium figures, where the virialequations hold with additional kinetic energy,and (b from real to imaginary rotation, wherethe effect is elongating instead of flattening,with respect to the rotation axis.An application is made toa subsample $(N=16$ of elliptical galaxies extracted from richer samples $(N=25,~N=48$of early type galaxies investigated within theSAURON project (Cappellari et al. 2006, 2007.Sample objects are idealized as homeoidallystriated MacLaurinspheroids and Jacobi ellipsoids, and theirposition in the $({sf O}hat{e}chi_v^2$plane is inferred from observations followinga procedure outlined in an earlier paper(Caimmi 2009b. The position of related adjoint configurations with isotropic stresstensor is also determined. With a singleexception (NGC 3379, slow rotators arecharacterized by low ellipticities $(0lehat{e}<0.2$, low anisotropy parameters$(0ledelta<0

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

Interplay between Coulomb-focusing and non-dipole effects in strong-field ionization with elliptical polarization

Science.gov (United States)

Daněk, J.; Klaiber, M.; Hatsagortsyan, K. Z.; Keitel, C. H.; Willenberg, B.; Maurer, J.; Mayer, B. W.; Phillips, C. R.; Gallmann, L.; Keller, U.

2018-06-01

We study strong-field ionization and rescattering beyond the long-wavelength limit of the dipole approximation with elliptically polarized mid-IR laser pulses. Full three-dimensional photoelectron momentum distributions (PMDs) measured with velocity map imaging and tomographic reconstruction revealed an unexpected sharp ridge structure in the polarization plane (2018 Phys. Rev. A 97 013404). This thin line-shaped ridge structure for low-energy photoelectrons is correlated with the ellipticity-dependent asymmetry of the PMD along the beam propagation direction. The peak of the projection of the PMD onto the beam propagation axis is shifted from negative to positive values when the sharp ridge fades away with increasing ellipticity. With classical trajectory Monte Carlo simulations and analytical analysis, we study the underlying physics of this feature. The underlying physics is based on the interplay between the lateral drift of the ionized electron, the laser magnetic field induced drift in the laser propagation direction, and Coulomb focusing. To apply our observations to emerging techniques relying on strong-field ionization processes, including time-resolved holography and molecular imaging, we present a detailed classical trajectory-based analysis of our observations. The analysis leads to the explanation of the fine structure of the ridge and its non-dipole behavior upon rescattering while introducing restrictions on the ellipticity. These restrictions as well as the ionization and recollision phases provide additional observables to gain information on the timing of the ionization and recollision process and non-dipole properties of the ionization process.

C1,1 regularity for degenerate elliptic obstacle problems

Science.gov (United States)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

Lambda-matrices and vibrating systems

CERN Document Server

Lancaster, Peter; Stark, M; Kahane, J P

1966-01-01

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with late

Abundance ratios in dwarf elliptical galaxies

Science.gov (United States)

Şen, Ş.; Peletier, R. F.; Boselli, A.; den Brok, M.; Falcón-Barroso, J.; Hensler, G.; Janz, J.; Laurikainen, E.; Lisker, T.; Mentz, J. J.; Paudel, S.; Salo, H.; Sybilska, A.; Toloba, E.; van de Ven, G.; Vazdekis, A.; Yesilyaprak, C.

2018-04-01

We determine abundance ratios of 37 dwarf ellipticals (dEs) in the nearby Virgo cluster. This sample is representative of the early-type population of galaxies in the absolute magnitude range -19.0 originate from late-type dwarfs or small spirals. Na-yields appear to be very metal-dependent, in agreement with studies of giant ellipticals, probably due to the large dependence on the neutron-excess in stars. We conclude that dEs have undergone a considerable amount of chemical evolution, they are therefore not uniformly old, but have extended SFH, similar to many of the Local Group galaxies.

Elliptic fibrations of maximal rank on a supersingular K3 surface

International Nuclear Information System (INIS)

Shioda, Tetsuji

2013-01-01

We study a class of elliptic K3 surfaces defined by an explicit Weierstrass equation to find elliptic fibrations of maximal rank on K3 surface in positive characteristic. In particular, we show that the supersingular K3 surface of Artin invariant 1 (unique by Ogus) admits at least one elliptic fibration with maximal rank 20 in every characteristic p>7, p≠13, and further that the number, say N(p), of such elliptic fibrations (up to isomorphisms), is unbounded as p → ∞; in fact, we prove that lim p→∞ N(p)/p 2 ≥(1/12) 2 .

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

2017-01-01

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications

KAUST Repository

Elkhalil, Khalil

2017-07-31

This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.

Manin matrices and Talalaev's formula

International Nuclear Information System (INIS)

Chervov, A; Falqui, G

2008-01-01

In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation properties, considered by Yu I Manin some 20 years ago at the beginning of quantum group theory. These are the commutation properties of matrix elements of linear homomorphisms between polynomial rings; more explicitly these read: (1) elements of the same column commute; (2) commutators of the cross terms are equal: [M ij , M kl ] [M kj , M il ] (e.g. [M 11 , M 22 ] = [M 21 , M 12 ]). The main aim of this paper is twofold: on the one hand we observe and prove that such matrices (which we call Manin matrices in short) behave almost as well as matrices with commutative elements. Namely, the theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) have a straightforward counterpart in the case of Manin matrices. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation 'RTT=TTR' and the so-called Cartier-Foata matrices. Also, they enter Talalaev's remarkable formulae: det(∂ z -L gaudin (z)), det(1-e -∂z T Yangian (z)) for the 'quantum spectral curve', and appear in the separation of variables problem and Capelli identities. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g. in the construction of new generators in Z(U crit (gl-hat n )) (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We propose, in the appendix, a construction of quantum separated variables for the XXX-Heisenberg system

Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method

OpenAIRE

Banerjee, Subhabrata; Jacobi, Anthony M.

2012-01-01

The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-01-01

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-12-05

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

Science.gov (United States)

Wang, Gang-Jin; Xie, Chi; Chen, Shou; Yang, Jiao-Jiao; Yang, Ming-Yan

2013-09-01

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko-Pastur distribution.

Electromagnetic fields and Green functions in elliptical vacuum chambers

CERN Document Server

AUTHOR|(CDS)2084216; Biancacci, Nicolo; Migliorati, Mauro; Palumbo, Luigi; Vaccaro, Vittorio; CERN. Geneva. ATS Department

2017-01-01

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be diffe...

Efficient Rank Reduction of Correlation Matrices

NARCIS (Netherlands)

I. Grubisic (Igor); R. Pietersz (Raoul)

2005-01-01

textabstractGeometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with the Lagrange multiplier method is established,

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD

Directory of Open Access Journals (Sweden)

N. A. Balonin

2014-05-01

Full Text Available Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.; calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research. Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.. Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels. Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by

Holomorphic bundles over elliptic manifolds

International Nuclear Information System (INIS)

Morgan, J.W.

2000-01-01

In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves

Sensitivity of Rayleigh wave ellipticity and implications for surface wave inversion

Science.gov (United States)

Cercato, Michele

2018-04-01

The use of Rayleigh wave ellipticity has gained increasing popularity in recent years for investigating earth structures, especially for near-surface soil characterization. In spite of its widespread application, the sensitivity of the ellipticity function to the soil structure has been rarely explored in a comprehensive and systematic manner. To this end, a new analytical method is presented for computing the sensitivity of Rayleigh wave ellipticity with respect to the structural parameters of a layered elastic half-space. This method takes advantage of the minor decomposition of the surface wave eigenproblem and is numerically stable at high frequency. This numerical procedure allowed to retrieve the sensitivity for typical near surface and crustal geological scenarios, pointing out the key parameters for ellipticity interpretation under different circumstances. On this basis, a thorough analysis is performed to assess how ellipticity data can efficiently complement surface wave dispersion information in a joint inversion algorithm. The results of synthetic and real-world examples are illustrated to analyse quantitatively the diagnostic potential of the ellipticity data with respect to the soil structure, focusing on the possible sources of misinterpretation in data inversion.

The effects of axis ratio on laminar fluid flow around an elliptical cylinder

International Nuclear Information System (INIS)

Faruquee, Zakir; Ting, David S-K.; Fartaj, Amir; Barron, Ronald M.; Carriveau, Rupp

2007-01-01

An elliptical cylinder is a generic shape which represents a flat plate at its minor to major axis ratio (AR) limits of zero and infinity, and a circular cylinder at AR of unity. While incompressible flows over a streamwise flat plate (AR = 0), a cross-stream flat plate (AR = ∞), and a circular cylinder have been studied extensively, the role of AR on the detailed flow structure is still not well understood. Therefore, a numerical study was conducted to examine the flow field around an elliptical cylinder over a range of ARs from 0.3 to 1, with the major axis parallel to the free-stream, at a Reynolds number of 40 based on the hydraulic diameter. The control volume approach of FLUENT was used to solve the fluid flow equations, assuming the flow over the cylinder is unbounded, steady, incompressible and two-dimensional. It has been found that a pair of steady vortices forms when AR reaches a critical value of 0.34; below this value no vortices are formed behind the elliptical cylinder. Various wake parameters, drag coefficient, pressure and velocity distributions, have been characterized as functions of AR. The wake size and the drag coefficient are found to increase with the increase of AR. Quadratic correlations have been obtained to describe the relations of wake length and drag coefficient with axis ratio

Correlation matrices of two-mode bosonic systems

International Nuclear Information System (INIS)

Pirandola, Stefano; Serafini, Alessio; Lloyd, Seth

2009-01-01

We present a detailed analysis of all the algebraic conditions an arbitrary 4x4 symmetric matrix must satisfy in order to represent the correlation matrix of a two-mode bosonic system. Then, we completely clarify when this arbitrary matrix can represent the correlation matrix of a separable or entangled Gaussian state. In this analysis, we introduce alternative sets of conditions, which are expressed in terms of local symplectic invariants.

Nonlinear elliptic equations of the second order

CERN Document Server

Han, Qing

2016-01-01

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

Radial, sideward and elliptic flow at AGS energies

Indian Academy of Sciences (India)

the sideward flow, the elliptic flow and the radial transverse mass distribution of protons data at. AGS energies. In order to ... data on both sideward and elliptic flow, NL3 model is better at 2 A¡GeV, while NL23 model is at 4–8. A¡GeV. ... port approach RBUU which is based on a coupled set of covariant transport equations for.

Can elliptical galaxies be equilibrium systems

Energy Technology Data Exchange (ETDEWEB)

Caimmi, R [Padua Univ. (Italy). Ist. di Astronomia

1980-08-01

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational + centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes with n = 0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Young et al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical galaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

Multilevel quadrature of elliptic PDEs with log-normal diffusion

KAUST Repository

Harbrecht, Helmut

2015-01-07

We apply multilevel quadrature methods for the moment computation of the solution of elliptic PDEs with lognormally distributed diffusion coefficients. The computation of the moments is a difficult task since they appear as high dimensional Bochner integrals over an unbounded domain. Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number of quadrature points times the complexity for a single elliptic PDE solve. The multilevel idea is to reduce this complexity by combining quadrature methods with different accuracies with several spatial discretization levels in a sparse grid like fashion.

Type A Jacobi Elliptic One-Monopole

International Nuclear Information System (INIS)

Teh, Rosy; Wong, Khai-Ming

2010-01-01

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with Θ-winding number m = 1 and φ-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing. This solution is a regular non-BPS finite energy solution.

Intrinsic character of Stokes matrices

Science.gov (United States)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.

Hierarchical matrices algorithms and analysis

CERN Document Server

Hackbusch, Wolfgang

2015-01-01

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists ...

Kerr ellipticity effect in a birefringent optical fiber

International Nuclear Information System (INIS)

Ishiekwene, G.C.; Mensah, S.Y.; Brown, C.S.

2004-09-01

An intensity-dependent change in the ellipticity of an input light beam leads to a characteristic shift in polarization instability. Dichroism gives rise to a self-induced ellipticity effect in the polarization state of an intense input light oriented along the fast axis of a birefringent optical fiber. The critical power at which the fiber effective beat length becomes infinite is reduced considerably in the presence of dichroism. (author)

Beam energy dependence of elliptic flow in heavy-ion collision

International Nuclear Information System (INIS)

Otuka, Naohiko; Isse, Masatsugu; Ohnishi, Akira; Pradip Kumar Sahu; Nara, Yasushi

2002-01-01

We study radial flow and elliptic flow in relativistic heavy-ion collisions at energies from GSI-SIS to BNL-RHIC energies using hadronic cascade model JAM. The excitation function of radial flow shows the softening of hadronic matter from BNL-AGS to CERN-SPS energies. JAM model reproduces transverse mass spectra at BNL-AGS, CERN-SPS at BNL-RHIC energies as well as elliptic flow upto CERN-SPS. For elliptic flow at BNL-RHIC energy (√s=130 GeV), while JAM gives the enough flow at fragment region, it fails at mid rapidity. (author)

Multiple solutions for a quasilinear (p,q-elliptic system

Directory of Open Access Journals (Sweden)

Seyyed Mohsen Khalkhali

2013-06-01

Full Text Available In this article we show the existence of three weak solutions of a Dirichlet quasilinear elliptic system of differential equations which involves a general (p,q-elliptic operator in divergence, with $1

Elliptical Orbit [arrow right] 1/r[superscript 2] Force

Science.gov (United States)

Prentis, Jeffrey; Fulton, Bryan; Hesse, Carol; Mazzino, Laura

2007-01-01

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

Special matrices of mathematical physics stochastic, circulant and Bell matrices

CERN Document Server

Aldrovandi, R

2001-01-01

This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co

Elliptic Tales Curves, Counting, and Number Theory

CERN Document Server

Ash, Avner

2012-01-01

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from

Nonlinear elliptic partial differential equations an introduction

CERN Document Server

Le Dret, Hervé

2018-01-01

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Structure and stellar content of dwarf elliptical galaxies

International Nuclear Information System (INIS)

Caldwell, N.

1983-01-01

A small number of low-luminosity elliptical galaxies in the Virgo cluster and around other prominent galaxies have been studied using photoelectric and photographic techniques. The color-magnitude relation for ellipticals now extends from M/sub v/ = -23 to -15, and is linear over that range with a slope of 0.10 in U-V per visual magnitude. Galaxies which are known to contain a large number of young stars (''extreme cases'') are from 0.10 to 0.20 mag bluer in U-V than the lower envelope of the dwarf elliptical color-magnitude relation. This difference can be accounted for if the dwarf elliptical galaxies are young, but do not contain the massive blue stars that probably exist in the young populations of the extreme cases. Surface brightness profiles of the dwarfs have revealed some interesting distinctions between themselves and the brighter E's. In general, their intensity profiles are shallower than those of the bright E's, meaning they are of lower mean density. These mean densities are also a function of the total luminosity. Unlike the bright E's, the surface brightnesses near the centers are also a strong function of the total luminosity. The presence of a nucleation, which can be as much as 2 mag brighter than what the outer envelope would predict, does not appear to depend on any other measurable property of the galaxies. The variation in surface brightness profiles at the same total luminosity is suggestive that the low-luminosity dwarfs formed in more than one way. The flattening distribution of the dwarfs is like that of the bright ellipticals, and is also similar to the flattening distribution of field irregular galaxies

Optimization of elliptic neutron guides for triple-axis spectroscopy

International Nuclear Information System (INIS)

Janoschek, M.; Boeni, P.; Braden, M.

2010-01-01

In the last decade the performance of neutron guides for the transport of neutrons has been significantly increased. The most recent developments have shown that elliptic guide systems can be used to focus neutron beams while simultaneously reducing the number of neutron reflections, hence, leading to considerable gains in neutron flux. We have carried out Monte-Carlo simulations for a new triple-axis spectrometer that will be built at the end position of the conventional cold guide NL-1 in the neutron guide hall of the research reactor FRM-II in Munich, Germany. Our results demonstrate that an elliptic guide section at the end of a conventional guide can be used to at least maintain the total neutron flux onto the sample, while significantly improving the energy resolution of the spectrometer. The simulation further allows detailed insight how the defining parameters of an elliptic guide have to be chosen to obtain optimum results. Finally, we show that the elliptic guide limits losses in the neutron flux that generally arise at the gaps, where the monochromator system of the upstream instrument is situated.

Raven's matrices and working memory: a dual-task approach.

Science.gov (United States)

Rao, K Venkata; Baddeley, Alan

2013-01-01

Raven's Matrices Test was developed as a "pure" measure of Spearman's concept of general intelligence, g. Subsequent research has attempted to specify the processes underpinning performance, some relating it to the concept of working memory and proposing a crucial role for the central executive, with the nature of other components currently unclear. Up to this point, virtually all work has been based on correlational analysis of number of correct solutions, sometimes related to possible strategies. We explore the application to this problem of the concurrent task methodology used widely in developing the concept of multicomponent working memory. Participants attempted to solve problems from the matrices under baseline conditions, or accompanied by backward counting or verbal repetition tasks, assumed to disrupt the central executive and phonological loop components of working memory, respectively. As in other uses of this method, number of items correct showed little effect, while solution time measures gave very clear evidence of an important role for the central executive, but no evidence for phonological loop involvement. We conclude that this and related concurrent task techniques hold considerable promise for the analysis of Raven's matrices and potentially for other established psychometric tests.

Elliptic flow based on a relativistic hydrodynamic model

Energy Technology Data Exchange (ETDEWEB)

Hirano, Tetsufumi [Department of Physics, Waseda Univ., Tokyo (Japan)

1999-08-01

Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution of hot and dense nuclear matter produced in non-central relativistic heavy-ion collisions is discussed. The elliptic flow parameter v{sub 2} is obtained by Fourier analysis of the azimuthal distribution of pions and protons which are emitted from the freeze-out hypersurface. As a function of rapidity, the pion and proton elliptic flow parameters both have a peak at midrapidity. (author)

Vertical elliptic operator for efficient wave propagation in TTI media

KAUST Repository

Waheed, Umair bin; Alkhalifah, Tariq Ali

2015-01-01

Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

Vertical elliptic operator for efficient wave propagation in TTI media

KAUST Repository

Waheed, Umair bin

2015-08-19

Elliptic wave extrapolation operators require significantly less computational cost than the ones for transversely isotropic (TI) media. However, it does not provide accurate wavefield representation or imaging for the prevalent TI media. We propose a new vertical elliptically anisotropic (VEA) wave equation by decomposing the acoustic TI pseudo-differential wave equation. The decomposition results in a vertical elliptic differential equation and a scalar operator. The new VEA-like wave equation shares the same dispersion relation as that of the original acoustic TI wave equation. Therefore, the kinematic contents are correctly matched to the original equation. Moreover, the proposed decomposition yields better amplitude properties than the isotropic decomposition without increasing the computational load. Therefore, it exhibits better cost versus accuracy tradeoff compared to the isotropic or the tilted elliptic decompositions. We demonstrate with numerical examples that the proposed methodology is numerically stable for complex models and is free from shear-wave artifacts.

Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies.

Science.gov (United States)

McConnell, Nicholas J; Ma, Chung-Pei; Gebhardt, Karl; Wright, Shelley A; Murphy, Jeremy D; Lauer, Tod R; Graham, James R; Richstone, Douglas O

2011-12-08

Observational work conducted over the past few decades indicates that all massive galaxies have supermassive black holes at their centres. Although the luminosities and brightness fluctuations of quasars in the early Universe suggest that some were powered by black holes with masses greater than 10 billion solar masses, the remnants of these objects have not been found in the nearby Universe. The giant elliptical galaxy Messier 87 hosts the hitherto most massive known black hole, which has a mass of 6.3 billion solar masses. Here we report that NGC 3842, the brightest galaxy in a cluster at a distance from Earth of 98 megaparsecs, has a central black hole with a mass of 9.7 billion solar masses, and that a black hole of comparable or greater mass is present in NGC 4889, the brightest galaxy in the Coma cluster (at a distance of 103 megaparsecs). These two black holes are significantly more massive than predicted by linearly extrapolating the widely used correlations between black-hole mass and the stellar velocity dispersion or bulge luminosity of the host galaxy. Although these correlations remain useful for predicting black-hole masses in less massive elliptical galaxies, our measurements suggest that different evolutionary processes influence the growth of the largest galaxies and their black holes.

Dynamics of elliptic breathers in saturable nonlinear media with linear anisotropy

International Nuclear Information System (INIS)

Liang, Guo; Guo, Qi; Shou, Qian; Ren, Zhanmei

2014-01-01

We have introduced a class of dynamic elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behavior for the dynamic breathers, rotations and molecule-like librations, are both predicted by the variational approach, and confirmed in numerical simulations. The dynamic elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). As the media are linear anisotropic, OAM is no longer conserved, and hence the angular velocity is not constant but a periodic function of the propagation distance. When the linear anisotropy is large enough, the dynamic elliptic breathers librate like molecules. The dynamic elliptic breathers are present in media with not only saturable nonlinearity but also nonlocal nonlinearity; indeed, they are universal in nonlinear media with linear anisotropy. (paper)

Power law deformation of Wishart–Laguerre ensembles of random matrices

International Nuclear Information System (INIS)

Akemann, Gernot; Vivo, Pierpaolo

2008-01-01

We introduce a one-parameter deformation of the Wishart–Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1,2 and 4. Our generalized model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three values of β, in terms of the orthogonal polynomials of the standard Wishart–Laguerre ensembles. For large N in a certain double-scaling limit we obtain a generalized Marčenko–Pastur distribution on the macroscopic scale, and a generalized Bessel law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power law tails, where the microscopic limit depends on β and the difference M−N. In the limit where our parameter governing the power law goes to infinity we recover the correlations of the Wishart–Laguerre ensembles. To illustrate these findings, the generalized Marčenko–Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

Science.gov (United States)

Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Effect of an elliptical orbit on SPECT resolution and image uniformity

International Nuclear Information System (INIS)

Gottschalk, S.; Salem, D.

1982-01-01

This paper studies the impact of elliptical motion on SPECT resolution and detector flood correction as implemented in a Technicare Omega 500. Bringing the detector closer to the object improves detector resolution in each view, which results in improved resolution in the reconstructed image. In the Omega 500 the elliptical orbit is realized by a succession of translational and rotational motions of the detector head. This introduces motion of the detector center relative to the object center. Statistical fluctuations in the flood correction matrix due to the finite acquisition time result in ring artifacts for the circular orbit. The relative center motion of an elliptical orbit results in an averaging of the flood correction noise and a significant reduction in artifacts. These two aspects of SPECT spatial resolution and flood correction response improvement in elliptical orbit have been analyzed through computer simulations for point sources and a uniform activity 20 x 30 cm ellipse. Results compared a 35 cm diameter circular orbit to a 35 x 25 cm elliptical orbit

Standard Errors for Matrix Correlations.

Science.gov (United States)

Ogasawara, Haruhiko

1999-01-01

Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

A transmission line model for propagation in elliptical core optical fibers

Science.gov (United States)

Georgantzos, E.; Papageorgiou, C.; Boucouvalas, A. C.

2015-12-01

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell's equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.

A transmission line model for propagation in elliptical core optical fibers

International Nuclear Information System (INIS)

Georgantzos, E.; Boucouvalas, A. C.; Papageorgiou, C.

2015-01-01

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method

Instanton geometry and quantum A{sub {infinity}} structure on the elliptic curve

Energy Technology Data Exchange (ETDEWEB)

Herbst, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Lerche, W. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Nemeschansky, D. [University of Southern California, Los Angeles, CA (United States). Dept. of Physics

2006-03-15

We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the 'long-diagonal branes' on the elliptic curve. We verify that they satisfy the relevant A{sub {infinity}} consistency relations at both classical and quantum levels. In particular we find that the A{sub {infinity}} relation for the annulus provides a reconstruction of annulus instantons out of disk instantons. We note in passing that the naive application of the Cardy-constraint does not hold for our correlators, confirming expectations. Moreover, we analyze various analytical properties of the correlators, including instanton flops and the mixing of correlators with different numbers of legs under monodromy. The classical and quantum A{sub {infinity}} relations turn out to be compatible with such homotopy transformations. They lead to a non-invariance of the effective action under modular transformations, unless compensated by suitable contact terms which amount to redefinitions of the tachyon fields. (orig.)

Symmetry of anomalous dimension matrices for colour evolution of hard scattering processes

International Nuclear Information System (INIS)

Seymour, Michael H.

2005-01-01

In a recent paper, Dokshitzer and Marchesini rederived the anomalous dimension matrix for colour evolution of gg→gg scattering, first derived by Kidonakis, Oderda and Sterman. They noted a weird symmetry that it possesses under interchange of internal (colour group) and external (scattering angle) degrees of freedom and speculated that this may be related to an embedding into a context that correlates internal and external variables such as string theory. In this short note, I point out another symmetry possessed by all the colour evolution anomalous dimension matrices calculated to date. It is more prosaic, but equally unexpected, and may also point to the fact that colour evolution might be understood in some deeper theoretical framework. To my knowledge it has not been pointed out elsewhere, or anticipated by any of the authors calculating these matrices. It is simply that, in a suitably chosen colour basis, they are complex symmetric matrices

three solutions for a semilinear elliptic boundary value problem

Indian Academy of Sciences (India)

69

Keywords: The Laplacian operator, elliptic problem, Nehari man- ifold, three critical points, weak solution. 1. Introduction. Let Ω be a smooth bounded domain in RN , N ≥ 3 . In this work, we show the existence of at least three solutions for the semilinear elliptic boundary- value problem: (Pλ).. −∆u = f(x)|u(x)|p−2u(x) + ...

Generation of Elliptically Polarized Terahertz Waves from Antiferromagnetic Sandwiched Structure.

Science.gov (United States)

Zhou, Sheng; Zhang, Qiang; Fu, Shu-Fang; Wang, Xuan-Zhang; Song, Yu-Ling; Wang, Xiang-Guang; Qu, Xiu-Rong

2018-04-01

The generation of elliptically polarized electromagnetic wave of an antiferromagnetic (AF)/dielectric sandwiched structure in the terahertz range is studied. The frequency and external magnetic field can change the AF optical response, resulting in the generation of elliptical polarization. An especially useful geometry with high levels of the generation of elliptical polarization is found in the case where an incident electromagnetic wave perpendicularly illuminates the sandwiched structure, the AF anisotropy axis is vertical to the wave-vector and the external magnetic field is pointed along the wave-vector. In numerical calculations, the AF layer is FeF2 and the dielectric layers are ZnF2. Although the effect originates from the AF layer, it can be also influenced by the sandwiched structure. We found that the ZnF2/FeF2/ZnF2 structure possesses optimal rotation of the principal axis and ellipticity, which can reach up to about thrice that of a single FeF2 layer.

Correlation and Entanglement in Elliptically Deformed Two-Electron Quantum Dots

International Nuclear Information System (INIS)

Okopinska, A.; Koscik, P.

2011-01-01

We study quantum correlation in a two-dimensional system of two Coulombically interacting electrons trapped in an anisotropic harmonic potential in dependence on the interaction strength. The linear entropy and von Neumann entropy that measure the entanglement between the electrons are compared with the correlation energy and the statistical correlation coefficient. We observe that the entanglement properties are dramatically influenced by the anisotropy of the confining potential. We observe that the energetic and statistical correlations get stronger, whereas the entropic measures show weakening of the correlations with anisotropy. (author)

Hörmander spaces, interpolation, and elliptic problems

CERN Document Server

Mikhailets, Vladimir A; Malyshev, Peter V

2014-01-01

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients

Energy Technology Data Exchange (ETDEWEB)

Wagner, C.

1996-12-31

In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.

Hadron correlations in CMS

CERN Document Server

Maguire, Charles Felix

2012-01-01

The measurements of the anisotropic flow of single particles and particle pairs have provided some of the most compelling evidence for the creation of a strongly interacting quark-gluon plasma (sQGP) in relativistic heavy ion collisions, first at RHIC, and more recently at the LHC. Using PbPb collision data taken in the 2010 and 2011 heavy ion runs at the LHC, the CMS experiment has investigated a broad scope of these flow phenomena. The $v_2$ elliptic flow coefficient has been extracted with four different methods to cross-check contributions from initial state fluctuations and non-flow correlations. The measurements of the $v_2$ elliptic anisotropy have been extended to a transverse momentum of 60 GeV/c, which will enable the placement of new quantitative constraints on parton energy loss models as a function of path length in the sQGP medium. Additionally, for the first time at the LHC, the CMS experiment has extracted precise elliptic anisotropy coefficients for the neutral $\\pi$ meson ($\\pi^0$) in the c...

Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2012-01-01

Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

Invisible anti-cloak with elliptic cross section using phase complement

International Nuclear Information System (INIS)

Yang Yu-Qi; Zhang Min; Yue Jian-Xiang

2011-01-01

Based on the theory of phase complement, an anti-cloak with circular cross section can be made invisible to an object outside its domain. As the cloak with elliptic cross section is more effective to make objects invisible than that with circular cross section, a scaled coordinate system is proposed to design equivalent materials of invisible anti-cloak with elliptic cross section using phase complement. The cloaks with conventional dielectric and double negative parameters are both simulated with the geometrical transformations. The results show that the cloak with elliptic cross section through phase complement can effectively hide the outside objects. (classical areas of phenomenology)

Short-Term Comparison of Several Solutinos of Elliptic Relative Motion

Directory of Open Access Journals (Sweden)

Jung Hyun Jo

2007-12-01

Full Text Available Recently introduced, several explicit solutions of relative motion between neighboring elliptic satellite orbits are reviewed. The performance of these solutions is compared with an analytic solution of the general linearized equation of motion. The inversion solution by the Hill-Clohessy-Wiltshire equations is used to produce the initial condition of numerical results. Despite the difference of the reference orbit, the relative motion with the relatively small eccentricity shows the similar results on elliptic case and circular case. In case of the 'chief' satellite with the relatively large eccentricity, HCW equation with the circular reference orbit has relatively larger error than other elliptic equation of motion does.

Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies

Science.gov (United States)

Temi, P.; Brighenti, F.; Mathews, W. G.; Amblard, A.; Riguccini, L.

2013-01-01

Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.

Efficient method for finding square roots for elliptic curves over OEF

CSIR Research Space (South Africa)

Abu-Mahfouz, Adnan M

2009-01-01

Full Text Available Elliptic curve cryptosystems like others public key encryption schemes, require computing a square roots modulo a prime number. The arithmetic operations in elliptic curve schemes over Optimal Extension Fields (OEF) can be efficiently computed...

Single inclusive spectra, Hanburg–Brown–Twiss and elliptic flow: A ...

Indian Academy of Sciences (India)

The constraints due to the measurements of the single particle inclusive spectra, the ... flow and HBT vs. the reaction plane with a hydro-motivated blast wave model. .... different mass particles allows the extraction of the elliptic component of the transverse ... Moreover, the details of the dependence of elliptic flow on particle.

The auxiliary elliptic-like equation and the exp-function method

Indian Academy of Sciences (India)

exact solutions of the nonlinear evolution equations are derived with the aid of auxiliary elliptic-like equation. ... (NEE) have been paid attention by many researchers, especially the investigations of exact solutions for ... elliptic-like equation with the aid of the travelling wave reduction are introduced. The exact solutions of ...

Hyper-and-elliptic-curve cryptography

NARCIS (Netherlands)

Bernstein, D.J.; Lange, T.

2014-01-01

This paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast

Iron abundance evolution in spiral and elliptical galaxies

International Nuclear Information System (INIS)

Matteucci, F.

1987-01-01

Chemical evolution models for the Galaxy and ellipticals, which take into account the most recent developments on theories of nucleosynthesis and supernova progenitors, are presented. The evolution of the abundance of iron in these systems, under the assumption that this element is mainly produced by type I SNe, originating from white dwarfs in binary systems, has been computed and the results have been compared with the observations. Overabundances of O, Si, Ne and Mg with respect to iron have been predicted for halo stars in their Galaxy. The existence of an Fe - total mass relation with a slope steeper than the corresponding relations for Mg and O has been predicted for ellipticals. The masses of Fe ejected by ellipticals of various masses into the intergalactic medium have also been computed in detail. The general agreement obtained between these theoretical models and the observations for galaxies of different morphological type supports the assumptions made about the origin of iron

Dirac Particles Emission from An Elliptical Black Hole

Directory of Open Access Journals (Sweden)

Yuant Tiandho

2017-03-01

Full Text Available According to the general theory of relativiy, a black hole is defined as a region of spacetime with super-strong gravitational effects and there is nothing can escape from it. So in the classical theory of relativity, it is safe to say that black hole is a "dead" thermodynamical object. However, by using quantum mechanics theory, Hawking has shown that a black hole may emit particles. In this paper, calculation of temperature of an elliptical black hole when emitting the Dirac particles was presented. By using the complexpath method, radiation can be described as emission process in the tunneling pictures. According to relationship between probability of outgoing particle with the spectrum of black body radiation for fermion particles, temperature of the elliptical black hole can be obtained and it depend on the azimuthal angle. This result also showed that condition on the surface of elliptical black hole is not in thermal equilibrium.

Modern cryptography and elliptic curves a beginner's guide

CERN Document Server

Shemanske, Thomas R

2017-01-01

This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the...

Comparison of elliptical and spherical mirrors for the grasshopper monochromators at SSRL

International Nuclear Information System (INIS)

Waldhauer, A.P.

1989-01-01

A comparison of the performance of a spherical and elliptical mirror in the grasshopper monochromator is presented. The problem was studied by ray tracing and then tested using visible (λ=633 nm) laser light. Calculations using ideal optics yield an improvement in flux by a factor of up to 2.7, while tests with visible light show an increase by a factor of 5 because the old spherical mirror is compared to a new, perfect elliptical one. The FWHM of the measured focus is 90 μm with a spherical mirror, and 25 μm with an elliptical one. Elliptical mirrors have been acquired and are now being installed in the two grasshoppers at SSRL

Pathological rate matrices: from primates to pathogens

Directory of Open Access Journals (Sweden)

Knight Rob

2008-12-01

Full Text Available Abstract Background Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. Results We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability, both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Pad

Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Kolb, Peter F.; Heinz, Ulrich; Huovinen, Pasi; Eskola, Kari J.; Tuominen, Kimmo

2001-03-21

The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p{sub T}-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p{sub T}-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initialization.

Jacobian elliptic wave solutions for the Wadati-Segur-Ablowitz equation

International Nuclear Information System (INIS)

Teh, C.G.R.; Koo, W.K.; Lee, B.S.

1996-07-01

Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By a mere variation of the Jacobian elliptic parameter k 2 from zero to one, these solutions are transformed from a trivial one to the known solitary wave solutions. (author). 9 refs

Spectra of sparse random matrices

International Nuclear Information System (INIS)

Kuehn, Reimer

2008-01-01

We compute the spectral density for ensembles of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of that suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaussians. It gives rise to a pair of integral equations which can be solved by a stochastic population-dynamics algorithm. Remarkably our representation allows us to identify pure-point contributions to the spectral density related to the existence of normalizable eigenstates. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows us to unfold the total density of states into contributions coming from vertices of different local coordinations and an example of such an unfolding is presented. Our results are well corroborated by numerical diagonalization studies of large finite random matrices

Elliptic interpretation of black holes and quantum mechanics

International Nuclear Information System (INIS)

Gibbons, G.W.

1987-01-01

The lectures as delivered contained an elementary introduction to the classical theory of black holes together with an account of Hawking's original derivation of the thermal emission from black holes in the quantum theory. Also described here is what is here called the elliptic interpretation partly because of its possible relevance to the lectures of Professor 't Hooft. A rather more detailed account of the elliptic interpretation is given and the reader is referred to the original literature for the elementary material. 22 references

Elliptic flow in Au+Au collisions at RHIC

Science.gov (United States)

Vale, Carla M.; PHOBOS Collaboration; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Budzanowski, A.; Busza, W.; Carroll, A.; Decowski, M. P.; García, E.; George, N.; Gulbrandsen, K.; Gushue, S.; Halliwell, C.; Hamblen, J.; Heintzelman, G. A.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holynski, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Katzy, J.; Khan, N.; Kucewicz, W.; Kulinich, P.; Kuo, C. M.; Lin, W. T.; Manly, S.; McLeod, D.; Mignerey, A. C.; Ngyuen, M.; Nouicer, R.; Olszewski, A.; Pak, R.; Park, I. C.; Pernegger, H.; Reed, C.; Remsberg, L. P.; Reuter, M.; Roland, C.; Roland, G.; Rosenberg, L.; Sagerer, J.; Sarin, P.; Sawicki, P.; Skulski, W.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tang, J.-L.; Tonjes, M. B.; Trzupek, A.; van Nieuwenhuizen, G. J.; Verdier, R.; Veres, G.; Wolfs, F. L. H.; Wosiek, B.; Wozniak, K.; Wuosmaa, A. H.; Wyslouch, B.

2005-04-01

Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.

Newton flows for elliptic functions

NARCIS (Netherlands)

Helminck, G.F.; Twilt, F.

2015-01-01

Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational (complex) and the elliptic (i.e., doubly

Second order degenerate elliptic equations

International Nuclear Information System (INIS)

Duong Minh Duc.

1988-08-01

Using an improved Sobolev inequality we study a class of elliptic operators which is degenerate inside the domain and strongly degenerate near the boundary of the domain. Our results are applicable to the L 2 -boundary value problem and the mixed boundary problem. (author). 18 refs

The chiral Gaussian two-matrix ensemble of real asymmetric matrices

International Nuclear Information System (INIS)

Akemann, G; Phillips, M J; Sommers, H-J

2010-01-01

We solve a family of Gaussian two-matrix models with rectangular N x (N + ν) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter μ. Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalizing the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed ν at strong and weak non-Hermiticity.

Applications of elliptic Carleman inequalities to Cauchy and inverse problems

CERN Document Server

Choulli, Mourad

2016-01-01

This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

Design of an elliptical solenoid magnet for transverse beam matching to the spiral inflector

International Nuclear Information System (INIS)

Goswami, A.; Sing Babu, P.; Pandit, V.S.

2013-01-01

In this work, we present the design study of an elliptical solenoid magnet to be used for transverse beam matching at the input of a spiral inflector for efficient transmission. We have studied the dependence of axial field and gradients in the transverse directions of the elliptical solenoid magnet with ellipticity of the aperture. Using the beam envelope equations we have studied the feasibility of using an elliptical solenoid for transverse beam matching to the acceptance of a spiral inflector. (author)

ZZ RRDF-98, Cross-sections and covariance matrices for 22 neutron induced dosimetry reactions

International Nuclear Information System (INIS)

Zolotarev, K.I.; Ignatyuk, A.V.; Mahokhin, V.N.; Pashchenko, A.B.

2005-01-01

1 - Description of program or function: Format: ENDF-6 format; Number of groups: Continuous energy; Dosimetry reactions: 6-C-12(n,2n), 8-O-16(n,2n), 9-F-19(n,2n), 12-Mg-24(n,p), 22-Ti-46(n,2n), 22-Ti-46(n,p), 22-Ti-47(n,x), 22-Ti-48(n,p), 22-Ti-48(n,x), 22-Ti-49(n,x), 23-V-51(n,alpha), 26-Fe-54(n,2n), 26-Fe-54(n,alpha), 26-Fe-56(n,p), 27-Co-59(n,alpha), 29-Cu-63(n,alpha), 33-As-75(n,2n), 41-Nb-93(n,2n), 41-Nb-93(n,n'), 45-Rh-103(n,n'), 49-In-115(n,n'), 59-Pr-141(n,2n); Origin: Russian Federation; Weighting spectrum: None. RRDF-98 contains original evaluations of cross section data performed at the Institute of Physics and Power Engineering, Obninsk, for 22 neutron induced dosimetry reactions. The dataset also contains the corresponding covariance matrices. 2 - Methods: The evaluation of excitation functions was performed on the basis of statistical analysis of corrected experimental data in the framework of generalized least squares method and taking into account the results of optical-statistical STAPRE and GNASH calculations. The experimental cross section data including the most recent results were critically reviewed and processed in this study. If necessary, the data were normalized in order to make adjustments in relevant cross sections and decay schemes. The covariance matrices were prepared and the evaluated cross section data are presented in ENDF-6 format (Files 3, 33). For estimation of correlations between experimental data the total uncertainties of measured cross sections have been separated into statistical and systematic parts and correlation coefficients between components of systematic parts were assigned according to information given in the original publications and EXFOR library. Then the correlation matrix of cross sections measured within one experiment was calculated and approximated by matrix with a constant (average) correlation coefficient. The overall correlation matrix was composed of such sub-matrices in the assumption that the cross

Solitons and separable elliptic solutions of the sine-Gordon equation

International Nuclear Information System (INIS)

Bryan, A.C.; Haines, C.R.; Stuart, A.E.G.

1979-01-01

It is pointed out that the two-soliton (antisoliton) solutions of the sine-Gordon equation may be obtained as limiting cases of a separable, two-parameter family of elliptic solutions. The solitons are found on the boundary of the parameter space for the elliptic solutions when the latter are considered over their usual complex domain. (Auth.)

Rotational magnetization of anisotropic media: Lag angle, ellipticity and accommodation

International Nuclear Information System (INIS)

Kahler, G.R.; Della Torre, E.

2006-01-01

This paper discusses the change in the ellipticity of two-dimensional magnetization trajectories as the applied field rotates from the easy axis to the hard axis of a material. Furthermore, the impact that the reversible magnetization has on the ellipticity is discussed, including the relationship between the magnetization squareness and the reversible component of the magnetization

COMPUTER-AIDED DESIGN, MANUFACTURE AND EXPERIMENTAL ANALYSIS OF A PAIR OF ELLIPTICAL SPUR GEARS

Directory of Open Access Journals (Sweden)

Mehmet YAZAR

2016-12-01

Full Text Available ABSTRACT In this study, geometrical equations of elliptical spur gears, which are too difficult to manufacture by traditional methods and which require specific machines equipped with special techniques, are developed using the methods in the literature. Using these equations, a LISP program on AutoLISP is created to model elliptical spur gears on AutoCAD with desired tooth number and modules. Elliptical spur gears are manufactured with 5 different modules by Wire EDM through the above-mentioned package program. The variations in the center distances of elliptical spur gears, the most important parameter for workability of gears, are experimentally determined by a simple test unit designed and manufactured within the context this study. In addition, the surface roughness and hardness of elliptical spur gears are obtained and hydraulic pump and noise analysis results are discussed. The experimental and computer-aided results show that the elliptical spur gears may widely be used in many industrial and mechanical applications in the future.

UV Visibility of Moderate-Redshift Giant Elliptical Galaxies

Directory of Open Access Journals (Sweden)

Myung-Hyun Rhee

1998-06-01

Full Text Available We show quantitatively whether giant elliptical galaxies would be visible at far UV wavelengths if they were placed at moderate redshift of 0.4-0.5. On the basis of simple cosmological tests, we conclude that giant elliptical galaxies can be detectable upto the redshift of 0.4-0.5 in the proposed GALEX (Galaxy Evolution Explorer Deep Imaging Survey. We also show that obtaining UV color index such as m_1550 - V from upcoming GALEX and SDSS (Sloan Digital Sky Survey observations should be feasible.

An electrostatic elliptical mirror for neutral polar molecules.

Science.gov (United States)

González Flórez, A Isabel; Meek, Samuel A; Haak, Henrik; Conrad, Horst; Santambrogio, Gabriele; Meijer, Gerard

2011-11-14

Focusing optics for neutral molecules finds application in shaping and steering molecular beams. Here we present an electrostatic elliptical mirror for polar molecules consisting of an array of microstructured gold electrodes deposited on a glass substrate. Alternating positive and negative voltages applied to the electrodes create a repulsive potential for molecules in low-field-seeking states. The equipotential lines are parallel to the substrate surface, which is bent in an elliptical shape. The mirror is characterized by focusing a beam of metastable CO molecules and the results are compared to the outcome of trajectory simulations.

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution

OpenAIRE

Han, Fang; Liu, Han

2016-01-01

Correlation matrices play a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, it is not an effective estimator when facing heavy-tailed distributions. As a robust alternative, Han and Liu [J. Am. Stat. Assoc. 109 (2015) 275-2...

Chitosan-Based Matrices Prepared by Gamma Irradiation for Tissue Regeneration: Structural Properties vs. Preparation Method.

Science.gov (United States)

Casimiro, Maria Helena; Lancastre, Joana J H; Rodrigues, Alexandra P; Gomes, Susana R; Rodrigues, Gabriela; Ferreira, Luís M

2017-02-01

In the last decade, new generations of biopolymer-based materials have attracted attention, aiming its application as scaffolds for tissue engineering. These engineered three-dimensional scaffolds are designed to improve or replace damaged, missing, or otherwise compromised tissues or organs. Despite the number of promising methods that can be used to generate 3D cell-instructive matrices, the innovative nature of the present work relies on the application of ionizing radiation technology to form and modify surfaces and matrices with advantage over more conventional technologies (room temperature reaction, absence of harmful initiators or solvents, high penetration through the bulk materials, etc.), and the possibility of preparation and sterilization in one single step. The current chapter summarizes the work done by the authors in the gamma radiation processing of biocompatible and biodegradable chitosan-based matrices for skin regeneration. Particular attention is given to the correlation between the different preparation conditions and the final polymeric matrices' properties. We therefore expect to demonstrate that instructive matrices produced and improved by radiation technology bring to the field of skin regenerative medicine a supplemental advantage over more conservative techniques.

ON ELLIPTICALLY POLARIZED ANTENNAS IN THE PRESENCE OF GROUND

Science.gov (United States)

The effect of ground reflections upon the far field of an elliptically polarized antenna of ar itrary orientation with r spect to ground is...investigated. The equation of the polarization ellipse produced by an elliptically polarized antenna in the presence of ground is derived, AND SEVERAL...EXAMPLES ILLUSTRATE THE VARIATION IN THE AXIS RATIO OF THE POLARIZATION ELLIPSE AS A FUNCTION OF THE GEOMETRY OF THE MEASURING SETUP. A method is presented

Ellipticity and the offset angle of high harmonics generated by homonuclear diatomic molecules

International Nuclear Information System (INIS)

Odzak, S; Milosevic, D B

2011-01-01

In our recent paper (2010 Phys. Rev. A 82 023412) we introduced a theory of high-order harmonic generation by diatomic molecules exposed to an elliptically polarized laser field and have shown that the nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we now develop a theoretical approach for calculating ellipticity and the offset angle of high harmonics. We show that the emitted harmonics generated by aligned molecules are elliptically polarized even if the applied field is linearly polarized. Using examples of N 2 , O 2 and Ar 2 molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment and explain them by the destructive two-centre interference. Taking into account that the aligned molecules are an anisotropic medium for high harmonic generation, we introduce elliptic dichroism as a measure of this anisotropy, for both components of the T-matrix element. We propose that the measurement of the elliptic dichroism may reveal further information about the molecular structure.

Elliptic Flow in Au+Au Collisions at √sNN = 130 GeV

Science.gov (United States)

Ackermann, K. H.; Adams, N.; Adler, C.; Ahammed, Z.; Ahmad, S.; Allgower, C.; Amsbaugh, J.; Anderson, M.; Anderssen, E.; Arnesen, H.; Arnold, L.; Averichev, G. S.; Baldwin, A.; Balewski, J.; Barannikova, O.; Barnby, L. S.; Baudot, J.; Beddo, M.; Bekele, S.; Belaga, V. V.; Bellwied, R.; Bennett, S.; Bercovitz, J.; Berger, J.; Betts, W.; Bichsel, H.; Bieser, F.; Bland, L. C.; Bloomer, M.; Blyth, C. O.; Boehm, J.; Bonner, B. E.; Bonnet, D.; Bossingham, R.; Botlo, M.; Boucham, A.; Bouillo, N.; Bouvier, S.; Bradley, K.; Brady, F. P.; Braithwaite, E. S.; Braithwaite, W.; Brandin, A.; Brown, R. L.; Brugalette, G.; Byrd, C.; Caines, H.; Calderón de La Barca Sánchez, M.; Cardenas, A.; Carr, L.; Carroll, J.; Castillo, J.; Caylor, B.; Cebra, D.; Chatopadhyay, S.; Chen, M. L.; Chen, W.; Chen, Y.; Chernenko, S. P.; Cherney, M.; Chikanian, A.; Choi, B.; Chrin, J.; Christie, W.; Coffin, J. P.; Conin, L.; Consiglio, C.; Cormier, T. M.; Cramer, J. G.; Crawford, H. J.; Danilov, V. I.; Dayton, D.; Demello, M.; Deng, W. S.; Derevschikov, A. A.; Dialinas, M.; Diaz, H.; Deyoung, P. A.; Didenko, L.; Dimassimo, D.; Dioguardi, J.; Dominik, W.; Drancourt, C.; Draper, J. E.; Dunin, V. B.; Dunlop, J. C.; Eckardt, V.; Edwards, W. R.; Efimov, L. G.; Eggert, T.; Emelianov, V.; Engelage, J.; Eppley, G.; Erazmus, B.; Etkin, A.; Fachini, P.; Feliciano, C.; Ferenc, D.; Ferguson, M. I.; Fessler, H.; Finch, E.; Fine, V.; Fisyak, Y.; Flierl, D.; Flores, I.; Foley, K. J.; Fritz, D.; Gagunashvili, N.; Gans, J.; Gazdzicki, M.; Germain, M.; Geurts, F.; Ghazikhanian, V.; Gojak, C.; Grabski, J.; Grachov, O.; Grau, M.; Greiner, D.; Greiner, L.; Grigoriev, V.; Grosnick, D.; Gross, J.; Guilloux, G.; Gushin, E.; Hall, J.; Hallman, T. J.; Hardtke, D.; Harper, G.; Harris, J. W.; He, P.; Heffner, M.; Heppelmann, S.; Herston, T.; Hill, D.; Hippolyte, B.; Hirsch, A.; Hjort, E.; Hoffmann, G. W.; Horsley, M.; Howe, M.; Huang, H. Z.; Humanic, T. J.; Hümmler, H.; Hunt, W.; Hunter, J.; Igo, G. J.; Ishihara, A.; Ivanshin, Yu. I.; Jacobs, P.; Jacobs, W. W.; Jacobson, S.; Jared, R.; Jensen, P.; Johnson, I.; Jones, P. G.; Judd, E.; Kaneta, M.; Kaplan, M.; Keane, D.; Kenney, V. P.; Khodinov, A.; Klay, J.; Klein, S. R.; Klyachko, A.; Koehler, G.; Konstantinov, A. S.; Kormilitsyne, V.; Kotchenda, L.; Kotov, I.; Kovalenko, A. D.; Kramer, M.; Kravtsov, P.; Krueger, K.; Krupien, T.; Kuczewski, P.; Kuhn, C.; Kunde, G. J.; Kunz, C. L.; Kutuev, R. Kh.; Kuznetsov, A. A.; Lakehal-Ayat, L.; Lamas-Valverde, J.; Lamont, M. A.; Landgraf, J. M.; Lange, S.; Lansdell, C. P.; Lasiuk, B.; Laue, F.; Lebedev, A.; Lecompte, T.; Leonhardt, W. J.; Leontiev, V. M.; Leszczynski, P.; Levine, M. J.; Li, Q.; Li, Q.; Li, Z.; Liaw, C.-J.; Lin, J.; Lindenbaum, S. J.; Lindenstruth, V.; Lindstrom, P. J.; Lisa, M. A.; Liu, H.; Ljubicic, T.; Llope, W. J.; Locurto, G.; Long, H.; Longacre, R. S.; Lopez-Noriega, M.; Lopiano, D.; Love, W. A.; Lutz, J. R.; Lynn, D.; Madansky, L.; Maier, R.; Majka, R.; Maliszewski, A.; Margetis, S.; Marks, K.; Marstaller, R.; Martin, L.; Marx, J.; Matis, H. S.; Matulenko, Yu. A.; Matyushevski, E. A.; McParland, C.; McShane, T. S.; Meier, J.; Melnick, Yu.; Meschanin, A.; Middlekamp, P.; Mikhalin, N.; Miller, B.; Milosevich, Z.; Minaev, N. G.; Minor, B.; Mitchell, J.; Mogavero, E.; Moiseenko, V. A.; Moltz, D.; Moore, C. F.; Morozov, V.; Morse, R.; de Moura, M. M.; Munhoz, M. G.; Mutchler, G. S.; Nelson, J. M.; Nevski, P.; Ngo, T.; Nguyen, M.; Nguyen, T.; Nikitin, V. A.; Nogach, L. V.; Noggle, T.; Norman, B.; Nurushev, S. B.; Nussbaum, T.; Nystrand, J.; Odyniec, G.; Ogawa, A.; Ogilvie, C. A.; Olchanski, K.; Oldenburg, M.; Olson, D.; Ososkov, G. A.; Ott, G.; Padrazo, D.; Paic, G.; Pandey, S. U.; Panebratsev, Y.; Panitkin, S. Y.; Pavlinov, A. I.; Pawlak, T.; Pentia, M.; Perevotchikov, V.; Peryt, W.; Petrov, V. A.; Pinganaud, W.; Pirogov, S.; Platner, E.; Pluta, J.; Polk, I.; Porile, N.; Porter, J.; Poskanzer, A. M.; Potrebenikova, E.; Prindle, D.; Pruneau, C.; Puskar-Pasewicz, J.; Rai, G.; Rasson, J.; Ravel, O.; Ray, R. L.; Razin, S. V.; Reichhold, D.; Reid, J.; Renfordt, R. E.; Retiere, F.; Ridiger, A.; Riso, J.; Ritter, H. G.; Roberts, J. B.; Roehrich, D.; Rogachevski, O. V.; Romero, J. L.; Roy, C.; Russ, D.; Rykov, V.; Sakrejda, I.; Sanchez, R.; Sandler, Z.; Sandweiss, J.; Sappenfield, P.; Saulys, A. C.; Savin, I.; Schambach, J.; Scharenberg, R. P.; Scheblien, J.; Scheetz, R.; Schlueter, R.; Schmitz, N.; Schroeder, L. S.; Schulz, M.; Schüttauf, A.; Sedlmeir, J.; Seger, J.; Seliverstov, D.; Seyboth, J.; Seyboth, P.; Seymour, R.; Shakaliev, E. I.; Shestermanov, K. E.; Shi, Y.; Shimanskii, S. S.; Shuman, D.; Shvetcov, V. S.; Skoro, G.; Smirnov, N.; Smykov, L. P.; Snellings, R.; Solberg, K.; Sowinski, J.; Spinka, H. M.; Srivastava, B.; Stephenson, E. J.; Stock, R.; Stolpovsky, A.; Stone, N.; Stone, R.; Strikhanov, M.; Stringfellow, B.; Stroebele, H.; Struck, C.; Suaide, A. A.; Sugarbaker, E.; Suire, C.; Symons, T. J.; Takahashi, J.; Tang, A. H.; Tarchini, A.; Tarzian, J.; Thomas, J. H.; Tikhomirov, V.; Szanto de Toledo, A.; Tonse, S.; Trainor, T.; Trentalange, S.; Tokarev, M.; Tonjes, M. B.; Trofimov, V.; Tsai, O.; Turner, K.; Ullrich, T.; Underwood, D. G.; Vakula, I.; van Buren, G.; Vandermolen, A. M.; Vanyashin, A.; Vasilevski, I. M.; Vasiliev, A. N.; Vigdor, S. E.; Visser, G.; Voloshin, S. A.; Vu, C.; Wang, F.; Ward, H.; Weerasundara, D.; Weidenbach, R.; Wells, R.; Wells, R.; Wenaus, T.; Westfall, G. D.; Whitfield, J. P.; Whitten, C.; Wieman, H.; Willson, R.; Wilson, K.; Wirth, J.; Wisdom, J.; Wissink, S. W.; Witt, R.; Wolf, J.; Wood, L.; Xu, N.; Xu, Z.; Yakutin, A. E.; Yamamoto, E.; Yang, J.; Yepes, P.; Yokosawa, A.; Yurevich, V. I.; Zanevski, Y. V.; Zhang, J.; Zhang, W. M.; Zhu, J.; Zimmerman, D.; Zoulkarneev, R.; Zubarev, A. N.

2001-01-01

Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at sNN = 130 GeV using the STAR Time Projection Chamber at the Relativistic Heavy Ion Collider. The elliptic flow signal, v2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.

A note on the conditional correlation between energy prices: Evidence from future markets

International Nuclear Information System (INIS)

Marzo, Massimiliano; Zagaglia, Paolo

2008-01-01

We model the joint movements of daily returns on one-month futures for crude oil, heating oil and natural gas through the multivariate GARCH with dynamic conditional correlations and elliptical distributions introduced by Pelagatti and Rondena [Pelagatti, M.M., Rondena, S., 2007. 'Dynamic Conditional Correlation with Elliptical Distributions', unpublished manuscript. Universita di Milano - Bicocca, August]. Futures prices of crude and heating oil covary strongly. The conditional correlation between the futures prices of natural gas and crude oil has been rising over the last 5 years. However, this correlation has been low on average over two thirds of the sample, suggesting that future markets have no established tradition of pricing natural gas as a function of developments on oil markets. (author)

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

2012-01-01

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

CERN Document Server

Grimm, Thomas W.; Klevers, Denis

2016-01-01

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional ...

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...

L∞-error estimate for a system of elliptic quasivariational inequalities

Directory of Open Access Journals (Sweden)

M. Boulbrachene

2003-01-01

Full Text Available We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs. Under W2,p(Ω-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs.

Positive solutions with single and multi-peak for semilinear elliptic ...

Indian Academy of Sciences (India)

LI WANG

2018-04-24

Apr 24, 2018 ... [2] Bahri A and Lions P, On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 14(3) (1997) 365–413. [3] Cao D, and Noussair E, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN , Ann. Inst. H.

Major and minor axis kinematics of 22 ellipticals

International Nuclear Information System (INIS)

Franx, M.; Illingworth, G.; Heckman, T.

1989-01-01

Rotation curves and velocity dispersion profiles have been determined for the major and the minor axes of 22 elliptical galaxies. Rotation was detected in all but one galaxy, even though the sample was biased toward round ellipticals. Minor axis rotation larger than major axis rotation was measured in two galaxies, NGC 4406 and NGC 7507. Roughly 10 percent of ellipticals may show large minor axis velocities relative to those on the major axis. A simple model is used to derive a rotational axis from the observed minor and major axis velocities to a typical accuracy of 6 deg. The rotational and photometric minor axes aligned to better than 10 deg for 60 percent of the sample, implying that the direction of the angular momentum is related to the orientation of the figure of the galaxy. IC 1459 has a kinematically distinct core with its angular momentum opposite to the angular momentum of the outer parts, and NGC 4406 has a core with its angular momentum perpendicular to that of the outer parts. 46 refs

ERRORJ, Multigroup covariance matrices generation from ENDF-6 format

International Nuclear Information System (INIS)

Chiba, Go

2007-01-01

1 - Description of program or function: ERRORJ produces multigroup covariance matrices from ENDF-6 format following mainly the methods of the ERRORR module in NJOY94.105. New version differs from previous version in the following features: Additional features in ERRORJ with respect to the NJOY94.105/ERRORR module: - expands processing for the covariance matrices of resolved and unresolved resonance parameters; - processes average cosine of scattering angle and fission spectrum; - treats cross-correlation between different materials and reactions; - accepts input of multigroup constants with various forms (user input, GENDF, etc.); - outputs files with various formats through utility NJOYCOVX (COVERX format, correlation matrix, relative error and standard deviation); - uses a 1% sensitivity method for processing of resonance parameters; - ERRORJ can process the JENDL-3.2 and 3.3 covariance matrices. Additional features of the version 2 with respect to the previous version of ERRORJ: - Since the release of version 2, ERRORJ has been modified to increase its reliability and stability, - calculation of the correlation coefficients in the resonance region, - Option for high-speed calculation is implemented, - Perturbation amount is optimised in a sensitivity calculation, - Effect of the resonance self-shielding can be considered, - a compact covariance format (LCOMP=2) proposed by N. M. Larson can be read. Additional features of the version 2.2.1 with respect to the previous version of ERRORJ: - Several routines were modified to reduce calculation time. The new one needs shorter calculation time (50-70%) than the old version without changing results. - In the U-233 and Pu-241 files of JENDL-3.3 an inconsistency between resonance parameters in MF=32 and those in MF=2 was corrected. NEA-1676/06: This version differs from the previous one (NEA-1676/05) in the following: ERRORJ2.2.1 was modified to treat the self-shielding effect accurately. NEA-1676/07: This version

System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow

Science.gov (United States)

Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Hołyński, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.

2007-06-01

This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Directory of Open Access Journals (Sweden)

Yanpeng Zheng

2015-01-01

Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.

Central $L$-values of elliptic curves and local polynomials

OpenAIRE

Ehlen, Stephan; Guerzhoy, Pavel; Kane, Ben; Rolen, Larry

2018-01-01

Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves in terms of finite sums over canonical binary quadratic forms. This yields vastly simpler formulas related to work of Birch and Swinnerton-Dyer for such $L$-values, and extends beyond their framework to special non-CM elliptic curves.

Enhancing Understanding of Transformation Matrices

Science.gov (United States)

Dick, Jonathan; Childrey, Maria

2012-01-01

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

The demagnetizing energies of a uniformly magnetized cylinder with an elliptic cross-section

International Nuclear Information System (INIS)

Goode, D.A.; Rowlands, G.

2003-01-01

Analytic expressions for the demagnetizing energies are obtained in the form of partial series, for long elliptic cylinders and for squat ones where the ellipticity of the cross-section is unrestrained. This leaves just a small range where the demagnetizing energies are not well defined. It is found that by replacing the elliptic cylinders with rectangular blocks, a good approximation to the demagnetizing energy may be made in this small range

Halo ellipticity of GAMA galaxy groups from KiDS weak lensing

Science.gov (United States)

van Uitert, Edo; Hoekstra, Henk; Joachimi, Benjamin; Schneider, Peter; Bland-Hawthorn, Joss; Choi, Ami; Erben, Thomas; Heymans, Catherine; Hildebrandt, Hendrik; Hopkins, Andrew M.; Klaes, Dominik; Kuijken, Konrad; Nakajima, Reiko; Napolitano, Nicola R.; Schrabback, Tim; Valentijn, Edwin; Viola, Massimo

2017-06-01

We constrain the average halo ellipticity of ˜2600 galaxy groups from the Galaxy And Mass Assembly (GAMA) survey, using the weak gravitational lensing signal measured from the overlapping Kilo Degree Survey (KiDS). To do so, we quantify the azimuthal dependence of the stacked lensing signal around seven different proxies for the orientation of the dark matter distribution, as it is a priori unknown which one traces the orientation best. On small scales, the major axis of the brightest group/cluster member (BCG) provides the best proxy, leading to a clear detection of an anisotropic signal. In order to relate that to a halo ellipticity, we have to adopt a model density profile. We derive new expressions for the quadrupole moments of the shear field given an elliptical model surface mass density profile. Modelling the signal with an elliptical Navarro-Frenk-White profile on scales R < 250 kpc, and assuming that the BCG is perfectly aligned with the dark matter, we find an average halo ellipticity of ɛh = 0.38 ± 0.12, in fair agreement with results from cold dark matter only simulations. On larger scales, the lensing signal around the BCGs becomes isotropic and the distribution of group satellites provides a better proxy for the halo's orientation instead, leading to a 3σ-4σ detection of a non-zero halo ellipticity at 250 < R < 750 kpc. Our results suggest that the distribution of stars enclosed within a certain radius forms a good proxy for the orientation of the dark matter within that radius, which has also been observed in hydrodynamical simulations.

Exponential smoothing weighted correlations

Science.gov (United States)

Pozzi, F.; Di Matteo, T.; Aste, T.

2012-06-01

In many practical applications, correlation matrices might be affected by the "curse of dimensionality" and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson's ρ and Kendall's τ correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.

The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces

KAUST Repository

Chen, Yujia; Macdonald, Colin B.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general

Exact solution and thermodynamics of a spin chain with long-range elliptic interactions

International Nuclear Information System (INIS)

Finkel, Federico; González-López, Artemio

2014-01-01

We solve in closed form the simplest (su(1|1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1|1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane–Shastry chain. (paper)

OPTICAL-NEAR-INFRARED COLOR GRADIENTS AND MERGING HISTORY OF ELLIPTICAL GALAXIES

International Nuclear Information System (INIS)

Kim, Duho; Im, Myungshin

2013-01-01

It has been suggested that merging plays an important role in the formation and the evolution of elliptical galaxies. While gas dissipation by star formation is believed to steepen metallicity and color gradients of the merger products, mixing of stars through dissipation-less merging (dry merging) is believed to flatten them. In order to understand the past merging history of elliptical galaxies, we studied the optical-near-infrared (NIR) color gradients of 204 elliptical galaxies. These galaxies are selected from the overlap region of the Sloan Digital Sky Survey (SDSS) Stripe 82 and the UKIRT Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS). The use of optical and NIR data (g, r, and K) provides large wavelength baselines, and breaks the age-metallicity degeneracy, allowing us to derive age and metallicity gradients. The use of the deep SDSS Stripe 82 images makes it possible for us to examine how the color/age/metallicity gradients are related to merging features. We find that the optical-NIR color and the age/metallicity gradients of elliptical galaxies with tidal features are consistent with those of relaxed ellipticals, suggesting that the two populations underwent a similar merging history on average and that mixing of stars was more or less completed before the tidal features disappeared. Elliptical galaxies with dust features have steeper color gradients than the other two types, even after masking out dust features during the analysis, which can be due to a process involving wet merging. More importantly, we find that the scatter in the color/age/metallicity gradients of the relaxed and merging feature types decreases as their luminosities (or masses) increase at M > 10 11.4 M ☉ but stays large at lower luminosities. Mean metallicity gradients appear nearly constant over the explored mass range, but a possible flattening is observed at the massive end. According to our toy model that predicts how the distribution of metallicity gradients

Plasma blob generation due to cooperative elliptic instability.

Science.gov (United States)

Manz, P; Xu, M; Müller, S H; Fedorczak, N; Thakur, S C; Yu, J H; Tynan, G R

2011-11-04

Using fast-camera measurements the generation mechanism of plasma blobs is investigated in the linear device CSDX. During the ejection of plasma blobs the plasma is dominated by an m=1 mode, which is a counterrotating vortex pair. These flows are known to be subject to the cooperative elliptic instability, which is characterized by a cooperative disturbance of the vortex cores and results in a three-dimensional breakdown of two-dimensional flows. The first experimental evidence of a cooperative elliptic instability preceding the blob-ejection is provided in terms of the qualitative evolution of the vortex geometries and internal wave patterns.

Group inverses of M-matrices and their applications

CERN Document Server

Kirkland, Stephen J

2013-01-01

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

Science.gov (United States)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral

FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions

Directory of Open Access Journals (Sweden)

Allaberen Ashyralyev

2012-01-01

Full Text Available A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition. The first and second-orders of accuracy stable difference schemes for the approximate solution of this nonlocal boundary value problem are presented. The stability estimates, coercivity, and almost coercivity inequalities for solution of these schemes are established. The theoretical statements for the solutions of these nonlocal elliptic problems are supported by results of numerical examples.

The Ising model: from elliptic curves to modular forms and Calabi-Yau equations

International Nuclear Information System (INIS)

Bostan, A; Boukraa, S; Hassani, S; Zenine, N; Van Hoeij, M; Maillard, J-M; Weil, J-A

2011-01-01

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions of the susceptibility of the Ising model for n ≤ 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z 2 , F 2 , F 3 , L-tilde 3 can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-4 globally nilpotent linear differential operator is not reducible to this elliptic curve, modular form scheme. This operator is shown to actually correspond to a natural generalization of this elliptic curve, modular form scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected 4 F 3 hypergeometric function. This hypergeometric function can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back (square root extension), the corresponding Calabi-Yau fourth order differential operator having a symplectic differential Galois group SP(4,C). The mirror maps and higher order Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms, in particular an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2,Z) symmetry group.

Elliptic flow from Coulomb interaction and low density elastic scattering

Science.gov (United States)

Sun, Yuliang; Li, Qingfeng; Wang, Fuqiang

2018-04-01

In high energy heavy ion collisions and interacting cold atom systems, large elliptic flow anisotropies have been observed. For the large opacity (ρ σ L ˜103 ) of the latter hydrodynamics is a natural consequence, but for the small opacity (ρ σ L ˜1 ) of the former the hydrodynamic description is questionable. To shed light onto the situation, we simulate the expansion of a low density argon ion (or atom) system, initially trapped in an elliptical region, under the Coulomb interaction (or elastic scattering). Significant elliptic anisotropy is found in both cases, and the anisotropy depends on the initial spatial eccentricity and the density of the system. The results may provide insights into the physics of anisotropic flow in high energy heavy ion collisions and its role in the study of quantum chromodynamics.

Correlations in the Parton Recombination Model

Energy Technology Data Exchange (ETDEWEB)

Bass, S.A. [Department of Physics, Duke University, Durham, NC 27708-0305 (United States); RIKEN BNL Research Center, Brookhaven Nat. Lab., Upton, NY 11973 (United States); Fries, R.J. [School of Physics and Astronomy, Univ. of Minnesota, Minneapolis, MN 55455 (United States); Mueller, B. [Department of Physics, Duke University, Durham, NC 27708-0305 (United States)

2006-08-07

We describe how parton recombination can address the recent measurement of dynamical jet-like two particle correlations. In addition we discuss the possible effect realistic light-cone wave-functions including higher Fock-states may have on the well-known elliptic flow valence-quark number scaling law.

Local identities involving Jacobi elliptic functions

Indian Academy of Sciences (India)

systematize the local identities by deriving four local 'master identities' analogous to the ... involving Jacobi elliptic functions can be explicitly evaluated and a number of .... most of these integrals do not seem to be known in the literature. In §6 ...

Temporal evolution of financial-market correlations

Science.gov (United States)

Fenn, Daniel J.; Porter, Mason A.; Williams, Stacy; McDonald, Mark; Johnson, Neil F.; Jones, Nick S.

2011-08-01

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007-2008 credit and liquidity crisis.

Effects of elliptical burner geometry on partially premixed gas jet flames in quiescent surroundings

Science.gov (United States)

Baird, Benjamin

This study is the investigation of the effect of elliptical nozzle burner geometry and partial premixing, both 'passive control' methods, on a hydrogen/hydrocarbon flame. Both laminar and turbulent flames for circular, 3:1, and 4:1 aspect ratio (AR) elliptical burners are considered. The amount of air mixed with the fuel is varied from fuel-lean premixed flames to fuel-rich partially premixed flames. The work includes measurements of flame stability, global pollutant emissions, flame radiation, and flame structure for the differing burner types and fuel conditions. Special emphasis is placed on the near-burner region. Experimentally, both conventional (IR absorption, chemiluminecent, and polarographic emission analysis,) and advanced (laser induced fluorescence, planar laser induced fluorescence, Laser Doppler Velocimetry (LDV), Rayleigh scattering) diagnostic techniques are used. Numerically, simulations of 3-dimensional laminar and turbulent reacting flow are conducted. These simulations are run with reduced chemical kinetics and with a Reynolds Stress Model (RSM) for the turbulence modeling. It was found that the laminar flames were similar in appearance and overall flame length for the 3:1 AR elliptical and the circular burner. The laminar 4:1 AR elliptical burner flame split into two sub-flames along the burner major axis. This splitting had the effect of greatly shortening the 4:1 AR elliptical burner flame to have an overall flame length about half of that of the circular and 3:1 AR elliptical burner flames. The length of all three burners flames increased with increasing burner exit equivalence ratio. The blowout velocity for the three burners increased with increase in hydrogen mass fraction of the hydrogen/propane fuel mixture. For the rich premixed flames, the circular burner was the most stable, the 3:1 AR elliptical burner, was the least stable, and the 4:1 AR elliptical burner was intermediate to the two other burners. This order of stability was due

Elliptic curves and primality proving

Science.gov (United States)

Atkin, A. O. L.; Morain, F.

1993-07-01

The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret.

Duality relations between SU(N)k and SU(k)NWZW models and their braid matrices

International Nuclear Information System (INIS)

Naculich, S.G.; Schnitzer, H.J.

1990-01-01

Dual relations are found between the primary fields, correlators, and conformal blocks of SU(N) k and SU(k) N WZW models, which in turn imply dual relations between the braid matrices of the two theories. These results are a consequence of the fact that the spaces of conformal blocks of SU(N) k and SU(k) N correlation functions are dual. (orig.)

Phenomenological mass matrices with a democratic warp

International Nuclear Information System (INIS)

Kleppe, A.

2018-01-01

Taking into account all available data on the mass sector, we obtain unitary rotation matrices that diagonalize the quark matrices by using a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. In this way, we find mass matrices for the up- and down-quark sectors of a specific, symmetric form, with traces of a democratic texture.

Nonlinear elliptic equations and nonassociative algebras

CERN Document Server

Nadirashvili, Nikolai; Vlăduţ, Serge

2014-01-01

This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions...

Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

KAUST Repository

Castrillon, Julio; Nobile, Fabio; Tempone, Raul

2016-01-01

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem

Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

OpenAIRE

Berglund, P.; Henningson, M.

1994-01-01

We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirr...

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)

Universality for 1d Random Band Matrices: Sigma-Model Approximation

Science.gov (United States)

Shcherbina, Mariya; Shcherbina, Tatyana

2018-02-01

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.

Elliptic flow in Au+Au collisions at square root(S)NN = 130 GeV.

Science.gov (United States)

Ackermann, K H; Adams, N; Adler, C; Ahammed, Z; Ahmad, S; Allgower, C; Amsbaugh, J; Anderson, M; Anderssen, E; Arnesen, H; Arnold, L; Averichev, G S; Baldwin, A; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Beddo, M; Bekele, S; Belaga, V V; Bellwied, R; Bennett, S; Bercovitz, J; Berger, J; Betts, W; Bichsel, H; Bieser, F; Bland, L C; Bloomer, M; Blyth, C O; Boehm, J; Bonner, B E; Bonnet, D; Bossingham, R; Botlo, M; Boucham, A; Bouillo, N; Bouvier, S; Bradley, K; Brady, F P; Braithwaite, E S; Braithwaite, W; Brandin, A; Brown, R L; Brugalette, G; Byrd, C; Caines, H; Calderón de la Barca Sánchez, M; Cardenas, A; Carr, L; Carroll, J; Castillo, J; Caylor, B; Cebra, D; Chatopadhyay, S; Chen, M L; Chen, W; Chen, Y; Chernenko, S P; Cherney, M; Chikanian, A; Choi, B; Chrin, J; Christie, W; Coffin, J P; Conin, L; Consiglio, C; Cormier, T M; Cramer, J G; Crawford, H J; Danilov, V I; Dayton, D; DeMello, M; Deng, W S; Derevschikov, A A; Dialinas, M; Diaz, H; DeYoung, P A; Didenko, L; Dimassimo, D; Dioguardi, J; Dominik, W; Drancourt, C; Draper, J E; Dunin, V B; Dunlop, J C; Eckardt, V; Edwards, W R; Efimov, L G; Eggert, T; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Etkin, A; Fachini, P; Feliciano, C; Ferenc, D; Ferguson, M I; Fessler, H; Finch, E; Fine, V; Fisyak, Y; Flierl, D; Flores, I; Foley, K J; Fritz, D; Gagunashvili, N; Gans, J; Gazdzicki, M; Germain, M; Geurts, F; Ghazikhanian, V; Gojak, C; Grabski, J; Grachov, O; Grau, M; Greiner, D; Greiner, L; Grigoriev, V; Grosnick, D; Gross, J; Guilloux, G; Gushin, E; Hall, J; Hallman, T J; Hardtke, D; Harper, G; Harris, J W; He, P; Heffner, M; Heppelmann, S; Herston, T; Hill, D; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horsley, M; Howe, M; Huang, H Z; Humanic, T J; Hümmler, H; Hunt, W; Hunter, J; Igo, G J; Ishihara, A; Ivanshin, Y I; Jacobs, P; Jacobs, W W; Jacobson, S; Jared, R; Jensen, P; Johnson, I; Jones, P G; Judd, E; Kaneta, M; Kaplan, M; Keane, D; Kenney, V P; Khodinov, A; Klay, J; Klein, S R; Klyachko, A; Koehler, G; Konstantinov, A S; Kormilitsyne, V; Kotchenda, L; Kotov, I; Kovalenko, A D; Kramer, M; Kravtsov, P; Krueger, K; Krupien, T; Kuczewski, P; Kuhn, C; Kunde, G J; Kunz, C L; Kutuev, R K; Kuznetsov, A A; Lakehal-Ayat, L; Lamas-Valverde, J; Lamont, M A; Landgraf, J M; Lange, S; Lansdell, C P; Lasiuk, B; Laue, F; Lebedev, A; LeCompte, T; Leonhardt, W J; Leontiev, V M; Leszczynski, P; LeVine, M J; Li, Q; Li, Q; Li, Z; Liaw, C J; Lin, J; Lindenbaum, S J; Lindenstruth, V; Lindstrom, P J; Lisa, M A; Liu, H; Ljubicic, T; Llope, W J; LoCurto, G; Long, H; Longacre, R S; Lopez-Noriega, M; Lopiano, D; Love, W A; Lutz, J R; Lynn, D; Madansky, L; Maier, R; Majka, R; Maliszewski, A; Margetis, S; Marks, K; Marstaller, R; Martin, L; Marx, J; Matis, H S; Matulenko, Y A; Matyushevski, E A; McParland, C; McShane, T S; Meier, J; Melnick, Y; Meschanin, A; Middlekamp, P; Mikhalin, N; Miller, B; Milosevich, Z; Minaev, N G; Minor, B; Mitchell, J; Mogavero, E; Moiseenko, V A; Moltz, D; Moore, C F; Morozov, V; Morse, R; de Moura, M M; Munhoz, M G; Mutchler, G S; Nelson, J M; Nevski, P; Ngo, T; Nguyen, M; Nguyen, T; Nikitin, V A; Nogach, L V; Noggle, T; Norman, B; Nurushev, S B; Nussbaum, T; Nystrand, J; Odyniec, G; Ogawa, A; Ogilvie, C A; Olchanski, K; Oldenburg, M; Olson, D; Ososkov, G A; Ott, G; Padrazo, D; Paic, G; Pandey, S U; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Pentia, M; Perevotchikov, V; Peryt, W; Petrov, V A; Pinganaud, W; Pirogov, S; Platner, E; Pluta, J; Polk, I; Porile, N; Porter, J; Poskanzer, A M; Potrebenikova, E; Prindle, D; Pruneau, C; Puskar-Pasewicz, J; Rai, G; Rasson, J; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J; Renfordt, R E; Retiere, F; Ridiger, A; Riso, J; Ritter, H G; Roberts, J B; Roehrich, D; Rogachevski, O V; Romero, J L; Roy, C; Russ, D; Rykov, V; Sakrejda, I; Sanchez, R; Sandler, Z; Sandweiss, J; Sappenfield, P; Saulys, A C; Savin, I; Schambach, J; Scharenberg, R P; Scheblien, J; Scheetz, R; Schlueter, R; Schmitz, N; Schroeder, L S; Schulz, M; Schüttauf, A; Sedlmeir, J; Seger, J; Seliverstov, D; Seyboth, J; Seyboth, P; Seymour, R; Shakaliev, E I; Shestermanov, K E; Shi, Y; Shimanskii, S S; Shuman, D; Shvetcov, V S; Skoro, G; Smirnov, N; Smykov, L P; Snellings, R; Solberg, K; Sowinski, J; Spinka, H M; Srivastava, B; Stephenson, E J; Stock, R; Stolpovsky, A; Stone, N; Stone, R; Strikhanov, M; Stringfellow, B; Stroebele, H; Struck, C; Suaide, A A; Sugarbaker, E; Suire, C; Symons, T J; Takahashi, J; Tang, A H; Tarchini, A; Tarzian, J; Thomas, J H; Tikhomirov, V; Szanto De Toledo, A; Tonse, S; Trainor, T; Trentalange, S; Tokarev, M; Tonjes, M B; Trofimov, V; Tsai, O; Turner, K; Ullrich, T; Underwood, D G; Vakula, I; Van Buren, G; VanderMolen, A M; Vanyashin, A; Vasilevski, I M; Vasiliev, A N; Vigdor, S E; Visser, G; Voloshin, S A; Vu, C; Wang, F; Ward, H; Weerasundara, D; Weidenbach, R; Wells, R; Wells, R; Wenaus, T; Westfall, G D; Whitfield, J P; Whitten, C; Wieman, H; Willson, R; Wilson, K; Wirth, J; Wisdom, J; Wissink, S W; Witt, R; Wolf, J; Wood, L; Xu, N; Xu, Z; Yakutin, A E; Yamamoto, E; Yang, J; Yepes, P; Yokosawa, A; Yurevich, V I; Zanevski, Y V; Zhang, J; Zhang, W M; Zhu, J; Zimmerman, D; Zoulkarneev, R; Zubarev, A N

2001-01-15

Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at square root(S)NN = 130 GeV using the STAR Time Projection Chamber at the Relativistic Heavy Ion Collider. The elliptic flow signal, v2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.

The analytical solution of wake-fields in an elliptical pillbox cavity

International Nuclear Information System (INIS)

Yang, J.S.; Chen, K.W.

1991-01-01

The wake potential of a bunch of relativistic charged particles traversing an elliptical pillbox cavity is derived analytically in the limit of vanishing aperture. It is found that the resonant modes of an elliptical cavity can be expressed in terms of Mathieu functions. Calculation results are presented and compared with numerical ones. (author) 10 refs., 10 figs., 2 tabs

The construction of factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

We study the relationships between factorized S-matrices given as representations of the Zamolodchikov algebra and exactly solvable models constructed using the Baxter method. Several new examples of symmetric and non-symmetric factorized S-matrices are proposed. (orig.)

Coexistence of a General Elliptic System in Population Dynamics

DEFF Research Database (Denmark)

Pedersen, Michael

2004-01-01

This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross-diffusion......This paper is concerned with a strongly-coupled elliptic system representing a competitive interaction between two species. We give a sufficient condition for the existence of positive solutions. An example is also given to show that there is a coexistence of a steady state if the cross...

Large N elliptic genus and AdS/CFT Correspondence

International Nuclear Information System (INIS)

Boer, Jan de

1998-01-01

According to one of Maldacena's dualities, type IIB string theory on AdS 3 x S 3 x K3 is equivalent to a certain N = (4, 4) superconformal field theory. In this note we compute the elliptic genus of the boundary theory in the supergravity approximation. A finite quantity is obtained once we introduce a particular exclusion principle. In the regime where the supergravity approximation is reliable, we find exact agreement with the elliptic genus of a sigma model with target space K3 N /S N

Inflation of polymer melts into elliptic and circular cylinders

DEFF Research Database (Denmark)

Rasmussen, Henrik Koblitz; Christensen, Jens Horslund; Gøttsche, Søren

2000-01-01

A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top of the infla......A thin sheet (membrane) of the polymeric material is clamped between a Teflon-coated thermostated plate and a thermostated aluminium cylinder. By applying thermostated air through the plate, the polymer membrane deforms into an elliptic or a circular cylinder. The position of the top...

Color gradients in elliptical galaxies

International Nuclear Information System (INIS)

Franx, M.; Illingworth, G.

1990-01-01

The relationship of the color gradients within ellipticals and the color differences between them are studied. It is found that the local color appears to be strongly related to the escape velocity. This suggests that the local escape velocity is the primary factor that determines the metallicity of the stellar population. Models with and without dark halos give comparable results. 27 refs

Impedances in lossy elliptical vacuum chambers

International Nuclear Information System (INIS)

Piwinski, A.

1994-04-01

The wake fields of a bunched beam caused by the resistivity of the chamber walls are investigated for a vacuum chamber with elliptical cross section. The longitudinal and transverse impedances are calculated for arbitrary energies and for an arbitrary position of the beam in the chamber. (orig.)

Equivalent operator preconditioning for elliptic problems

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Karátson, J.

2009-01-01

Roč. 50, č. 3 (2009), s. 297-380 ISSN 1017-1398 Institutional research plan: CEZ:AV0Z30860518 Keywords : Elliptic problem * Conjugate gradient method * preconditioning * equivalent operators * compact operators Subject RIV: BA - General Mathematics Impact factor: 0.716, year: 2009 http://en.scientificcommons.org/42514649

Matrices in Engineering Problems

CERN Document Server

Tobias, Marvin

2011-01-01

This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo

Convective heat transfer from a heated elliptic cylinder at uniform wall temperature

Energy Technology Data Exchange (ETDEWEB)

Kaprawi, S.; Santoso, Dyos [Mechanical Department of Sriwijaya University, Jl. Raya Palembang-Prabumulih Km. 32 Inderalaya 50062 Ogan Ilir (Indonesia)

2013-07-01

This study is carried out to analyse the convective heat transfer from a circular and an elliptic cylinders to air. Both circular and elliptic cylinders have the same cross section. The aspect ratio of cylinders range 0-1 are studied. The implicit scheme of the finite difference is applied to obtain the discretized equations of hydrodynamic and thermal problem. The Choleski method is used to solve the discretized hydrodynamic equation and the iteration method is applied to solve the discretized thermal equation. The circular cylinder has the aspect ratio equal to unity while the elliptical cylinder has the aspect ratio less than unity by reducing the minor axis and increasing the major axis to obtain the same cross section as circular cylinder. The results of the calculations show that the skin friction change significantly, but in contrast with the elliptical cylinders have greater convection heat transfer than that of circular cylinder. Some results of calculations are compared to the analytical solutions given by the previous authors.

A FUNDAMENTAL LINE FOR ELLIPTICAL GALAXIES

International Nuclear Information System (INIS)

Nair, Preethi; Van den Bergh, Sidney; Abraham, Roberto G.

2011-01-01

Recent studies have shown that massive galaxies in the distant universe are surprisingly compact, with typical sizes about a factor of three smaller than equally massive galaxies in the nearby universe. It has been suggested that these massive galaxies grow into systems resembling nearby galaxies through a series of minor mergers. In this model the size growth of galaxies is an inherently stochastic process, and the resulting size-luminosity relationship is expected to have considerable environmentally dependent scatter. To test whether minor mergers can explain the size growth in massive galaxies, we have closely examined the scatter in the size-luminosity relation of nearby elliptical galaxies using a large new database of accurate visual galaxy classifications. We demonstrate that this scatter is much smaller than has been previously assumed, and may even be so small as to challenge the plausibility of the merger-driven hierarchical models for the formation of massive ellipticals.

Elliptic differential equations theory and numerical treatment

CERN Document Server

Hackbusch, Wolfgang

2017-01-01

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Detecting genuine multipartite correlations in terms of the rank of coefficient matrix

International Nuclear Information System (INIS)

Li Bo; Kwek, Leong Chuan; Fan Heng

2012-01-01

We propose a method to detect genuine quantum correlation for arbitrary quantum states in terms of the rank of coefficient matrices associated with the pure state. We then derive a necessary and sufficient condition for a quantum state to possess genuine correlation, namely that all corresponding coefficient matrices have rank larger than 1. We demonstrate an approach to decompose the genuine quantum correlated state with high rank coefficient matrix into the form of product states with no genuine quantum correlation for a pure state. (paper)

A Brief Historical Introduction to Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

Strategy use fully mediates the relationship between working memory capacity and performance on Raven's matrices.

Science.gov (United States)

Gonthier, Corentin; Thomassin, Noémylle

2015-10-01

Working memory capacity consistently correlates with fluid intelligence. It has been suggested that this relationship is partly attributable to strategy use: Participants with high working memory capacity would use more effective strategies, in turn leading to higher performance on fluid intelligence tasks. However, this idea has never been directly investigated. In 2 experiments, we tested this hypothesis by directly manipulating strategy use in a combined experimental-correlational approach (Experiment 1; N = 250) and by measuring strategy use with a self-report questionnaire (Experiment 2; N = 93). Inducing all participants to use an effective strategy in Raven's matrices decreased the correlation between working memory capacity and performance; the strategy use measure fully mediated the relationship between working memory capacity and performance on the matrices task. These findings indicate that individual differences in strategic behavior drive the predictive utility of working memory. We interpret the results within a theoretical framework integrating the multiple mediators of the relationship between working memory capacity and high-level cognition. (c) 2015 APA, all rights reserved).

Optical asymmetric cryptography based on amplitude reconstruction of elliptically polarized light

Science.gov (United States)

Cai, Jianjun; Shen, Xueju; Lei, Ming

2017-11-01

We propose a novel optical asymmetric image encryption method based on amplitude reconstruction of elliptically polarized light, which is free from silhouette problem. The original image is analytically separated into two phase-only masks firstly, and then the two masks are encoded into amplitudes of the orthogonal polarization components of an elliptically polarized light. Finally, the elliptically polarized light propagates through a linear polarizer, and the output intensity distribution is recorded by a CCD camera to obtain the ciphertext. The whole encryption procedure could be implemented by using commonly used optical elements, and it combines diffusion process and confusion process. As a result, the proposed method achieves high robustness against iterative-algorithm-based attacks. Simulation results are presented to prove the validity of the proposed cryptography.

Carleman estimates for some elliptic systems

International Nuclear Information System (INIS)

Eller, M

2008-01-01

A Carleman estimate for a certain first order elliptic system is proved. The proof is elementary and does not rely on pseudo-differential calculus. This estimate is used to prove Carleman estimates for the isotropic Lame system as well as for the isotropic Maxwell system with C 1 coefficients

Hypercyclic Abelian Semigroups of Matrices on Cn

International Nuclear Information System (INIS)

Ayadi, Adlene; Marzougui, Habib

2010-07-01

We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

2013-01-01

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

Determination of Rayleigh wave ellipticity using single-station and array-based processing of ambient seismic noise

Science.gov (United States)

Workman, Eli Joseph

We present a single-station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 sec the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 sec, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher ( 2%) and significantly higher (>20%), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e., Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves.

Mechanism of unconventional aerodynamic characteristics of an elliptic airfoil

Directory of Open Access Journals (Sweden)

Sun Wei

2015-06-01

Full Text Available The aerodynamic characteristics of elliptic airfoil are quite different from the case of conventional airfoil for Reynolds number varying from about 104 to 106. In order to reveal the fundamental mechanism, the unsteady flow around a stationary two-dimensional elliptic airfoil with 16% relative thickness has been simulated using unsteady Reynolds-averaged Navier–Stokes equations and the γ-Reθt‾ transition turbulence model at different angles of attack for flow Reynolds number of 5 × 105. The aerodynamic coefficients and the pressure distribution obtained by computation are in good agreement with experimental data, which indicates that the numerical method works well. Through this study, the mechanism of the unconventional aerodynamic characteristics of airfoil is analyzed and discussed based on the computational predictions coupled with the wind tunnel results. It is considered that the boundary layer transition at the leading edge and the unsteady flow separation vortices at the trailing edge are the causes of the case. Furthermore, a valuable insight into the physics of how the flow behavior affects the elliptic airfoil’s aerodynamics is provided.

Uniformization of elliptic curves

OpenAIRE

Ülkem, Özge; Ulkem, Ozge

2015-01-01

Every elliptic curve E defined over C is analytically isomorphic to C*=qZ for some q ∊ C*. Similarly, Tate has shown that if E is defined over a p-adic field K, then E is analytically isomorphic to K*=qZ for some q ∊ K . Further the isomorphism E(K) ≅ K*/qZ respects the action of the Galois group GK/K, where K is the algebraic closure of K. I will explain the construction of this isomorphism.

Formation of S0s via disc accretion around high-redshift compact ellipticals

Science.gov (United States)

Diaz, Jonathan; Bekki, Kenji; Forbes, Duncan A.; Couch, Warrick J.; Drinkwater, Michael J.; Deeley, Simon

2018-06-01

We present hydrodynamical N-body models which demonstrate that elliptical galaxies can transform into S0s by acquiring a disc. In particular, we show that the merger with a massive gas-rich satellite can lead to the formation of a baryonic disc around an elliptical. We model the elliptical as a massive, compact galaxy which could be observed as a `red nugget' in the high-z universe. This scenario contrasts with existing S0 formation scenarios in the literature in two important ways. First, the progenitor is an elliptical galaxy whereas scenarios in the literature typically assume a spiral progenitor. Secondly, the physical conditions underlying our proposed scenario can exist in low-density environments such as the field, in contrast to scenarios in the literature which typically address dense environments like clusters and groups. As a consequence, S0s in the field may be the most likely candidates to have evolved from elliptical progenitors. Our scenario also naturally explains recent observations which indicate that field S0s may have older bulges than discs, contrary to cluster S0s which seem to have older discs than bulges.

Formal matrices

CERN Document Server

Krylov, Piotr

2017-01-01

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...

On the application of correlation function matrices in OMA

DEFF Research Database (Denmark)

Brincker, Rune

2017-01-01

In this paper the theoretical solution for the correlation function matrix of the random response of a structural system is re-visited. It is shown that using the classical definition of the correlation functions, the row space is defined by the mode shapes of the system, whereas the column space...

The arithmetic of elliptic fibrations in gauge theories on a circle

Energy Technology Data Exchange (ETDEWEB)

Grimm, Thomas W. [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Institute for Theoretical Physics,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Center for Extreme Matter and Emergent Phenomena,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Kapfer, Andreas [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)

2016-06-20

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

The arithmetic of elliptic fibrations in gauge theories on a circle

Science.gov (United States)

Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

2016-06-01

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

The arithmetic of elliptic fibrations in gauge theories on a circle

International Nuclear Information System (INIS)

Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

2016-01-01

The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

Mechanical properties and drug release of venlafaxine HCl solid mini matrices prepared by hot-melt extrusion and hot or ambient compression.

Science.gov (United States)

Avgerinos, Theodoros; Kantiranis, Nikolaos; Panagopoulou, Athanasia; Malamataris, Stavros; Kachrimanis, Kyriakos; Nikolakakis, Ioannis

2018-02-01

Objective/significance: To elucidate the role of plasticizers in different mini matrices and correlate mechanical properties with drug release. Cylindrical pellets were prepared by hot-melt extrusion (HME) and mini tablets by hot (HC) and ambient compression (AC). Venlafaxine HCl was the model drug, Eudragit ® RSPO the matrix former and citric acid or Lutrol ® F127 the plasticizers. The matrices were characterized for morphology, crystallinity, and mechanical properties. The influence of plasticizer's type and content on the extrusion pressure (P e ) during HME and ejection during tableting was examined and the mechanical properties were correlated with drug release parameters. Resistance to extrusion and tablet ejection force were reduced by Lutrol ® F127 which also produced softer and weaker pellets with faster release, but harder and stronger HC tablets with slower release. HME pellets showed greater tensile strength (T) and 100 times slower release than tablets. P e correlated with T and resistance to deformation of the corresponding pellets (r 2  = 0.963 and 0.945). For both HME and HC matrices the decrease of drug release with T followed a single straight line (r 2  = 0.990) and for HME the diffusion coefficient (D e ) and retreat rate constant (k b ) decreased linearly with T (r 2  = 0.934 and 0.972). Lutrol ® F127 and citric acid are efficient plasticizers and Lutrol ® F127 is a thermal binder/lubricant in HC compression. The different bonding mechanisms of the matrices were reflected in the mechanical strength and drug release. Relationships established between T and drug release parameters for HME and HC matrices may be useful during formulation work.

Stress concentration factors for pressurized elliptic crossbores in blocks

International Nuclear Information System (INIS)

Badr, Elie A.

2006-01-01

Intersecting bore geometries are used in a number of industrial applications including heavy-walled pressure vessels containing oil holes for lubrication, ports for valves and fluid ends of reciprocating pumps. The bore intersection location is a stress concentration point where the maximum hoop stress can be many times the fluid pressure in the bores. Intersecting circular holes in heavy-walled cylinders and rectangular blocks have been extensively investigated. Specifically, stress/pressure concentration curves for intersecting circular bores in rectangular blocks were presented by Sorem et al. [Sorem JR, Shadley JR, Tipton SM. Design curves for maximum stresses in blocks containing pressurized bore intersections. ASME J Mech Des 1990; 113: 427-31.]. However, stress/pressure concentrations due to intersecting elliptic bores have not been broadly investigated. With the availability of computer numerical control (CNC) machinery, bores with elliptic crosssection can be produced with relative ease. In this paper, hoop stress concentration ratios are developed for elliptic crossbores in rectangular blocks. Results indicate that introducing elliptic crossbores, rather than circular ones, significantly reduces the hoop stress concentration factor at the crossbore intersection. Also, the presence of intersecting crossbores has a major effect on the fatigue life of pressure vessels [Badr EA, Sorem JR, Jr Tipton SM. Evaluation of the autofrettage effect on fatigue lives of steel blocks with crossbores using a statistical and a strain-based method. ASTM J Test Eval 2000; 28: 181-8.] and the reduction of hoop stress concentration is expected to enhance the fatigue life of pressure vessels containing crossbores

Abundance Ratios in Dwarf Elliptical Galaxies

NARCIS (Netherlands)

Sen, Seyda; Peletier, Reynier F.; Toloba, Elisa; Mentz, Jaco J.

The aim of this study is to determine abundance ratios and star formation histories (SFH) of dwarf ellipticals in the nearby Virgo cluster. We perform a stellar population analysis of 39 dEs and study them using index-index and scaling relations. We find an unusual behaviour where [Na/Fe] is

Spatial scan statistics using elliptic windows

DEFF Research Database (Denmark)

Christiansen, Lasse Engbo; Andersen, Jens Strodl; Wegener, Henrik Caspar

2006-01-01

The spatial scan statistic is widely used to search for clusters. This article shows that the usually applied elimination of secondary clusters as implemented in SatScan is sensitive to smooth changes in the shape of the clusters. We present an algorithm for generation of a set of confocal elliptic...

THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Directory of Open Access Journals (Sweden)

Y. N. Balonin

2013-05-01

Full Text Available The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch matrices (C-matrices, conference matrices and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.

COLORS OF ELLIPTICALS FROM GALEX TO SPITZER

Energy Technology Data Exchange (ETDEWEB)

Schombert, James M., E-mail: jschombe@uoregon.edu [Department of Physics, University of Oregon, Eugene, OR 97403 (United States)

2016-12-01

Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

COLORS OF ELLIPTICALS FROM GALEX TO SPITZER

International Nuclear Information System (INIS)

Schombert, James M.

2016-01-01

Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer ( GALEX ), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV , ugri , JHK and 3.6 μ m. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color–magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from −0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

In-line photonic microcells based on the elliptical microfibers for refractive index sensors applications

Science.gov (United States)

Jin, Wa; Liu, Xuejing; Jin, Wei

2017-10-01

We report the fabrication of in-line photonic microcells (PMCs) by encapsulating tapered elliptical microfibers (MFs) inside glass tubes. The encapsulation does not change the optical property of the MF but protects the elliptical MF from external disturbance and contamination and makes the micro-laboratory robust. Such micro-laboratory can be easily integrated into standard fiber-optic circuits with low loss, making the elliptical MF-based devices more practical for real-world applications. Evanescent field sensing is realized by fabricating micro-channel on the PMC for ingress/egress of sample liquids/gas. Based on the encapsulated elliptical MF PMCs, we demonstrated RI sensitivity of 2024 nm per refractive index unit (nm/RIU) in gaseous environment and 21231 nm/RIU in water.

Generalized canonical correlation analysis with missing values

NARCIS (Netherlands)

M. van de Velden (Michel); Y. Takane

2012-01-01

textabstractGeneralized canonical correlation analysis is a versatile technique that allows the joint analysis of several sets of data matrices. The generalized canonical correlation analysis solution can be obtained through an eigenequation and distributional assumptions are not required. When

Elliptic Genera of Symmetric Products and Second Quantized Strings

CERN Document Server

Dijkgraaf, R; Verlinde, Erik; Verlinde, Herman L

1997-01-01

In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $M^N/S_N$ of a manifold $M$ to the partition function of a second quantized string theory on the space $M \\times S^1$. The generating function of these elliptic genera is shown to be (almost) an automorphic form for $O(3,2,\\Z)$. In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.

Transfer coefficients for plate fin and elliptical tube heat exchangers

International Nuclear Information System (INIS)

Saboya, S.M.; Saboya, F.E.M.

1981-01-01

In order to determine transfer coefficients for plate fin and elliptical tube exchangers, mass transfer experiments have been performed using the naphthalene sublimation technique. By means of the heat-mass transfer analogy, the results can be converted to heat transfer results. The transfer coefficients were compared with those for circular tube exchangers and the comparison revealed no major differences. This is a positive outcome, since the use of elliptical tubes may reduce substantially the pressure drop, without affecting the transfer characteristics.(Author) [pt

Waveguide elliptic polarizers for ECH at down-shifted frequencies on PLT

International Nuclear Information System (INIS)

Doane, J.L.

1986-01-01

ECH experiments on PLT with resonance frequencies of 80 to 90 GHz at the plasma center use 60 GHz extraordinary mode (X-mode) propagation at 30 0 from the toroidal field. Efficient excitation of this mode requires elliptic polarization of the incident wave at the plasma edge. On PLT the elliptic polarization is achieved outside the vacuum vessel in an elliptically deformed section of circular waveguide propagating TM11, a mode that is intermediate between TE01 and HE11 (which has an ideal radiation pattern). The squeeze and orientation of the TM11 polarizer are adjusted to compensate both for the birefringence of a corrugated bend propagating HE11 and for a flat mirror inside PLT that reverses the sense of rotation of the polarization. 11 refs., 8 figs

Two-dimensional optical correlation spectroscopy applied to liquid/glass dynamics

OpenAIRE

Lazonder, Kees; Pshenichnikov, Maxim S.; Wiersma, Douwe A.; Corkum, Paul; Jonas, David M.; Miller, R.J. Dwayne.; Weiner, Andrew M.

2007-01-01

Correlation spectroscopy was used to study the effects of temperature and phase changes on liquid and glass solvent dynamics. By assessing the eccentricity of the elliptic shape of a 2D optical correlation spectrum the value of the underlying frequency-frequency correlation function can be retrieved through a very simple relationship. This method yielded both intuitive clues and a quantitative measure of the dynamics of the system.

Observation of long-range elliptic azimuthal anisotropies in √s = 13 and 2.76 TeV pp collisions with the ATLAS detector

Czech Academy of Sciences Publication Activity Database

Aad, G.; Abbott, B.; Abdallah, J.; Chudoba, Jiří; Havránek, Miroslav; Hejbal, Jiří; Jakoubek, Tomáš; Kepka, Oldřich; Kupčo, Alexander; Kůs, Vlastimil; Lokajíček, Miloš; Lysák, Roman; Marčišovský, Michal; Mikeštíková, Marcela; Němeček, Stanislav; Penc, Ondřej; Šícho, Petr; Staroba, Pavel; Svatoš, Michal; Taševský, Marek; Vrba, Václav

2016-01-01

Roč. 116, č. 17 (2016), 1-20, č. článku 172301. ISSN 0031-9007 Institutional support: RVO:68378271 Keywords : CERN LHC Coll * factorization * enhancement * correlation * long-range * elliptic flow * modulation * anisotropy * tracks: multi plicity Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 8.462, year: 2016

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

Statistics about elliptic curves over finite prime fields

OpenAIRE

Gekeler, Ernst-Ulrich

2006-01-01

We derive formulas for the probabilities of various properties (cyclicity, squarefreeness, generation by random points) of the point groups of randomly chosen elliptic curves over random prime fields.

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.

The ellipticity of galaxy cluster haloes from satellite galaxies and weak lensing

Science.gov (United States)

Shin, Tae-hyeon; Clampitt, Joseph; Jain, Bhuvnesh; Bernstein, Gary; Neil, Andrew; Rozo, Eduardo; Rykoff, Eli

2018-04-01

We study the ellipticity of galaxy cluster haloes as characterized by the distribution of cluster galaxies and as measured with weak lensing. We use Monte Carlo simulations of elliptical cluster density profiles to estimate and correct for Poisson noise bias, edge bias and projection effects. We apply our methodology to 10 428 Sloan Digital Sky Survey clusters identified by the redMaPPer algorithm with richness above 20. We find a mean ellipticity =0.271 ± 0.002 (stat) ±0.031 (sys) corresponding to an axis ratio = 0.573 ± 0.002 (stat) ±0.039 (sys). We compare this ellipticity of the satellites to the halo shape, through a stacked lensing measurement using optimal estimators of the lensing quadrupole based on Clampitt and Jain (2016). We find a best-fitting axis ratio of 0.56 ± 0.09 (stat) ±0.03 (sys), consistent with the ellipticity of the satellite distribution. Thus, cluster galaxies trace the shape of the dark matter halo to within our estimated uncertainties. Finally, we restack the satellite and lensing ellipticity measurements along the major axis of the cluster central galaxy's light distribution. From the lensing measurements, we infer a misalignment angle with an root-mean-square of 30° ± 10° when stacking on the central galaxy. We discuss applications of halo shape measurements to test the effects of the baryonic gas and active galactic nucleus feedback, as well as dark matter and gravity. The major improvements in signal-to-noise ratio expected with the ongoing Dark Energy Survey and future surveys from Large Synoptic Survey Telescope, Euclid, and Wide Field Infrared Survey Telescope will make halo shapes a useful probe of these effects.

Abel-grassmann's groupoids of modulo matrices

International Nuclear Information System (INIS)

Javaid, Q.; Awan, M.D.; Naqvi, S.H.A.

2016-01-01

The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z/sub n/ of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n >≥ 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Z/sub n/ is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Z/sub n/ of Type-II is a T/sup 3/-AG-groupoid. (iii) An AG-groupoid of matrices over Z/sub n/ ; G /sub nAG/(t,u), is an AG-band, if t+u=1(mod n). (author)

Free probability and random matrices

CERN Document Server

Mingo, James A

2017-01-01

This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces

Science.gov (United States)

Kimura, Yusuke

2018-03-01

F-theory/heterotic duality is formulated in the stable degeneration limit of a K3 fibration on the F-theory side. In this note, we analyze the structure of the stable degeneration limit. We discuss whether stable degeneration exists for pairs of rational elliptic surfaces. We demonstrate that, when two rational elliptic surfaces have an identical complex structure, stable degeneration always exists. We provide an equation that systematically describes the stable degeneration of a K3 surface into a pair of isomorphic rational elliptic surfaces. When two rational elliptic surfaces have different complex structures, whether their sum glued along a smooth fiber admits deformation to a K3 surface can be determined by studying the structure of the K3 lattice. We investigate the lattice theoretic condition to determine whether a deformation to a K3 surface exists for pairs of extremal rational elliptic surfaces. In addition, we discuss the configurations of singular fibers under stable degeneration. The sum of two isomorphic rational elliptic surfaces glued together admits a deformation to a K3 surface, the singular fibers of which are twice that of the rational elliptic surface. For special situations, singular fibers of the resulting K3 surface collide and they are enhanced to a fiber of another type. Some K3 surfaces become attractive in these situations. We determine the complex structures and the Weierstrass forms of these attractive K3 surfaces. We also deduce the gauge groups in F-theory compactifications on these attractive K3 surfaces times a K3. E 6, E 7, E 8, SU(5), and SO(10) gauge groups arise in these compactifications.

Elliptic flow in a hadron-string cascade model at 130 GeV energy

Indian Academy of Sciences (India)

vectors b. The elliptic flow v2 is the anisotropy of particle emission in- and out-of reaction plane. ... However, recent observation at SPS shows similar behaviour of the elliptic flow like RHIC as a ..... hadron gas [18]. Large spatial eccentricity ε is ...

Quantum matrices in two dimensions

International Nuclear Information System (INIS)

Ewen, H.; Ogievetsky, O.; Wess, J.

1991-01-01

Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)

A physico-mathematical analysis of elliptical nerve and muscle fibres

International Nuclear Information System (INIS)

Bonsignori, F.

1977-01-01

In the framework of the tridimensional core conductor model, the current flow field of an elliptical nerve or muscle fibre in a volume conductor is studied. As the quasi-static conditions are valid, the Laplace equation applies. Expressions for the intracellular and extra cellular potential fields and the membrane current are exactly derived. As a limit the solutions for the circular case are recovered. Finally a sketch of an approximate method of calculation is outlined and the first elliptical correction to the usual membrane current is evaluated

L-series of elliptic curves with CM by √-3

International Nuclear Information System (INIS)

Qiu Derong; Zhang Xianke

2001-09-01

Let E:y 2 =x 3 -2 4 3 3 D 2 be elliptic curves defined over the quadratic field Q(√-3). Hecke L-series attached to E are studied, formulae for the values of the L-series at s=1 are given, and the bound of 3-adic valuations of these values are obtained. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer, and generalize results in recent literature about elliptic curves defined over rationals. (author)

Performance of penalized maximum likelihood in estimation of genetic covariances matrices

Directory of Open Access Journals (Sweden)

Meyer Karin

2011-11-01

Full Text Available Abstract Background Estimation of genetic covariance matrices for multivariate problems comprising more than a few traits is inherently problematic, since sampling variation increases dramatically with the number of traits. This paper investigates the efficacy of regularized estimation of covariance components in a maximum likelihood framework, imposing a penalty on the likelihood designed to reduce sampling variation. In particular, penalties that "borrow strength" from the phenotypic covariance matrix are considered. Methods An extensive simulation study was carried out to investigate the reduction in average 'loss', i.e. the deviation in estimated matrices from the population values, and the accompanying bias for a range of parameter values and sample sizes. A number of penalties are examined, penalizing either the canonical eigenvalues or the genetic covariance or correlation matrices. In addition, several strategies to determine the amount of penalization to be applied, i.e. to estimate the appropriate tuning factor, are explored. Results It is shown that substantial reductions in loss for estimates of genetic covariance can be achieved for small to moderate sample sizes. While no penalty performed best overall, penalizing the variance among the estimated canonical eigenvalues on the logarithmic scale or shrinking the genetic towards the phenotypic correlation matrix appeared most advantageous. Estimating the tuning factor using cross-validation resulted in a loss reduction 10 to 15% less than that obtained if population values were known. Applying a mild penalty, chosen so that the deviation in likelihood from the maximum was non-significant, performed as well if not better than cross-validation and can be recommended as a pragmatic strategy. Conclusions Penalized maximum likelihood estimation provides the means to 'make the most' of limited and precious data and facilitates more stable estimation for multi-dimensional analyses. It should

Seiberg-Witten curves and double-elliptic integrable systems

International Nuclear Information System (INIS)

Aminov, G.; Braden, H.W.; Mironov, A.; Morozov, A.; Zotov, A.

2015-01-01

An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the N-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven.

Fully plastic solutions of semi-elliptical surface cracks

International Nuclear Information System (INIS)

Yagawa, Genki; Yoshimura, Shinobu; Kitajima, Yasumi; Ueda, Hiroyoshi.

1990-01-01

Nonlinear finite element analyses of semi-elliptical surface cracks are performed under the fully plastic condition. The power-law hardening materials and the deformation theory of plasticity are assumed. Either the penalty function method or the Uzawa's algorithm is utilized to treat the incompressibility of plastic strains. The local and global J-integral values are obtained using a virtual crack extension technique for plates and cylinders with semi-elliptical surface cracks subjected to uniform tensions. The fully plastic solutions for surface cracked plates are given in the form of polynominals with geometric parameters a/t, a/c and the strain hardening exponent (n). In addition, the effects of curvature on fully plastic solutions are discussed through the comparison between the results of plates and cylinders. (author)

Thermodynamics of Inozemtsev's elliptic spin chain

International Nuclear Information System (INIS)

Klabbers, Rob

2016-01-01

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

Realm of Matrices

Indian Academy of Sciences (India)

IAS Admin

harmonic analysis and complex analysis, in ... gebra describes not only the study of linear transforma- tions and .... special case of the Jordan canonical form of matrices. ..... Richard Bronson, Schaum's Outline Series Theory And Problems Of.

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Elastic plastic buckling of elliptical vessel heads

International Nuclear Information System (INIS)

Alix, M.; Roche, R.L.

1981-08-01

The risks of buckling of dished vessel head increase when the vessel is thin walled. This paper gives the last results on experimental tests of 3 elliptical heads and compares all the results with some empirical formula dealing with elastic and plastic buckling

A holomorphic anomaly in the elliptic genus

International Nuclear Information System (INIS)

Murthy, Sameer

2014-01-01

We consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2,2) superconformal field theories in the infra-red, a prototype of which is the SL(2,ℝ)/U(1) (cigar) coset. We compute the elliptic genus of the GLSMs as a path-integral on the torus using supersymmetric localization. We find that the result is a Jacobi-like form that is non-holomorphic in the modular parameter τ of the torus, with mock modular behavior. This agrees with a previously-computed expression in the cigar coset. We show that the lack of holomorphicity of the elliptic genus arises from the contributions of a compact boson carrying momentum and winding excitations. This boson has an axionic shift symmetry and plays the role of a compensator field that is needed to cancel the chiral anomaly in the rest of the theory.

On rotational solutions for elliptically excited pendulum

International Nuclear Information System (INIS)

Belyakov, Anton O.

2011-01-01

The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact rotational solutions in the case of circular pivot trajectory and zero gravity. The conditions for existence and stability of such solutions are derived. Assuming that the amplitudes of excitations are not small while the pivot trajectory has small ellipticity the approximate solutions are found both for high and small linear dampings. Comparison between approximate and numerical solutions is made for different values of the damping parameter. -- Highlights: → We study rotations of the mathematical pendulum when its pivot moves along an ellipse. → There are stable exact solutions for a circular pivot trajectory and zero gravity. → Asymptotic solutions are found for an elliptical pivot trajectory

The dynamical fingerprint of core scouring in massive elliptical galaxies

International Nuclear Information System (INIS)

Thomas, J.; Saglia, R. P.; Bender, R.; Erwin, P.; Fabricius, M.

2014-01-01

The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r b , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

International Nuclear Information System (INIS)

Lee, Wei-Ming

2012-01-01

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

The different star formation histories of blue and red spiral and elliptical galaxies

Science.gov (United States)

Tojeiro, Rita; Masters, Karen L.; Richards, Joshua; Percival, Will J.; Bamford, Steven P.; Maraston, Claudia; Nichol, Robert C.; Skibba, Ramin; Thomas, Daniel

2013-06-01

We study the spectral properties of intermediate mass galaxies (M* ˜ 1010.7 M⊙) as a function of colour and morphology. We use Galaxy Zoo to define three morphological classes of galaxies, namely early types (ellipticals), late-type (disc-dominated) face-on spirals and early-type (bulge-dominated) face-on spirals. We classify these galaxies as blue or red according to their Sloan Digital Sky Survey (SDSS) g - r colour and use the spectral fitting code Versatile Spectral Analyses to calculate time-resolved star formation histories, metallicity and total starlight dust extinction from their SDSS fibre spectra. We find that red late-type spirals show less star formation in the last 500 Myr than blue late-type spirals by up to a factor of 3, but share similar star formation histories at earlier times. This decline in recent star formation explains their redder colour: their chemical and dust content are the same. We postulate that red late-type spirals are recent descendants of blue late-type spirals, with their star formation curtailed in the last 500 Myr. The red late-type spirals are however still forming stars ≃17 times faster than red ellipticals over the same period. Red early-type spirals lie between red late-type spirals and red ellipticals in terms of recent-to-intermediate star formation and dust content. Therefore, it is plausible that these galaxies represent an evolutionary link between these two populations. They are more likely to evolve directly into red ellipticals than red late-type spirals, which show star formation histories and dust content closer to blue late-type spirals. Blue ellipticals show similar star formation histories as blue spirals (regardless of type), except that they have formed less stars in the last 100 Myr. However, blue ellipticals have different dust content, which peaks at lower extinction values than all spiral galaxies. Therefore, many blue ellipticals are unlikely to be descendants of blue spirals, suggesting there may

Semihard scattering unraveled from collective dynamics by two-pion azimuthal correlations in 158A GeV/c Pb+Au collisions.

Science.gov (United States)

Agakichiev, G; Appelshäuser, H; Baur, R; Bielcikova, J; Braun-Munzinger, P; Cherlin, A; Drees, A; Esumi, S I; Filimonov, K; Fraenkel, Z; Fuchs, Ch; Glässel, P; Hering, G; Huovinen, P; Lenkeit, B; Marín, A; Messer, F; Messer, M; Milosevic, J; Miśkowiec, D; Nix, O; Panebrattsev, Yu; Petrácek, V; Pfeiffer, A; Rak, J; Ravinovich, I; Razin, S; Rehak, P; Sako, H; Saveljic, N; Schmitz, W; Shimansky, S; Socol, E; Specht, H J; Stachel, J; Tilsner, H; Tserruya, I; Voigt, C; Voloshin, S; Weber, C; Wessels, J P; Wurm, J P; Yurevich, V

2004-01-23

Elliptic flow and two-particle azimuthal correlations of charged hadrons and high-p(T) pions (p(T)>1 GeV/c) have been measured close to midrapidity in 158A GeV/c Pb+Au collisions by the CERES experiment. Elliptic flow (v(2)) rises linearly with p(T) to a value of about 10% at 2 GeV/c. Beyond p(T) approximately 1.5 GeV/c, the slope decreases considerably, possibly indicating a saturation of v(2) at high p(T). Two-pion azimuthal anisotropies for p(T)>1.2 GeV/c exceed the elliptic flow values by about 60% in midcentral collisions. These nonflow contributions are attributed to nearside and back-to-back jetlike correlations, the latter exhibiting centrality dependent broadening.

Semihard scattering unraveled from collective dynamics by two-pion azimuthal correlations in 158A GeV/c Pb + Au collisions

CERN Document Server

Agakichiev, G; Baur, R; Bielcikova, J; Braun-Munzinger, P; Cherlin, A; Drees, A; Esumi, S I; Filimonov, K; Fraenkel, Zeev; Fuchs, C; Glässel, P; Hering, G; Huovinen, P; Lenkeit, B C; Marin, A; Messer, F; Messer, M; Milosevic, J; Miskowiec, D; Nix, O; Panebratsev, Yu A; Petracek, V; Pfeiffer, A; Rak, J; Ravinovich, I; Razin, S; Rehak, P; Sako, H; Saveljic, N; Schmitz, W; Shimansky, S S; Socol, E; Specht, H J; Stachel, J; Tilsner, H; Tserruya, Itzhak; Voigt, C A; Voloshin, S A; Weber, C; Wessels, J P; Wurm, J P; Yurevich, V

2004-01-01

Elliptic flow and two-particle azimuthal correlations of charged hadrons and high-$p_{T}$ pions ($p_{T}>$1 GeV/c) have been measured close to midrapidity in 158A GeV/c Pb + Au collisions by the CERES experiment. Elliptic flow ($v_{2}$) rises linearly with $p_{T}$ to a value of about 10% at 2 GeV/c. Beyond $p_{T} \\approx $1.5 Ge V/c, the slope decreases considerably, possibly indicating a saturation of $v_{2}$ at high $p_{T}$. Two-pion azimuthal anisotropies for $p_{T} >$1.2 GeV/c exceed the elliptic flow values by about 60% in midcentral collisions. These nonflow contributions are attributed to nearside and back-to-back jetlike correlations, the latter exhibiting centrality dependent broadening.

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)

Constraints on stellar populations in elliptical galaxies

International Nuclear Information System (INIS)

Rose, J.A.

1985-01-01

Photographic image-tube spectra in the wavelength interval 3400--4500 A have been obtained for 12 elliptical galaxy nuclei and for a number of Galactic globular and open clusters in integrated light. The spectra have a wavelength resolution of 2.5 A and a high signal-to-noise ratio. A new quantitative three-dimensional spectral-classification system that has been calibrated on a sample of approx.200 individual stars (Rose 1984) is used to analyze the integrated spectra of the ellipical galaxy nuclei and to compare them with those of the globular clusters. This system is based on spectral indices that are formed by comparing neighborhood spectral features and is unaffected by reddening. The following results have been found: (1) Hot stars (i.e., spectral types A and B) contribute only 2% to the integrated spectra of elliptical galaxies at approx.4000 A, except in the nucleus of NGC 205, where the hot component dominates. This finding is based on a spectral index formed from the relative central intensities in the Ca II H+Hepsilon and Ca II K lines, which is shown to be constant for late-type (i.e., F, G, and K) stars, but changes drastically at earlier types. The observed Ca II H+Hepsilon/Ca II K indices in ellipticals can be reproduced by the inclusion of a small metal-poor population (as in the globular cluster M5) that contributes approx.8% of the light at 4000 A. Such a contribution is qualitatively consistent with the amount of

Calculation of complete or incomplete elliptic integrals of the first and second kind

International Nuclear Information System (INIS)

Guillermin, J.M.; Guerin, M.

1968-01-01

The structure of the article is as following: inversion of the Jacobi function Sn (U, K), definition of the functions F (PHI, K) and E (PHI, K), Landen transformation, calculation of elliptic integrals F (PHI, K) and E (PHI, K), particular case of complete elliptic integrals, realised programs [fr

Orbits in general relativity: the Jacobian elliptic function

Energy Technology Data Exchange (ETDEWEB)

Miro Rodriguez, C

1987-03-11

The Jacobian elliptic functions are applied to the motion of nonzero-rest-mass particles in the Schwarzschild geometry. The bound and unbound trajectories are analysed together with their classical and special-relativity limits.

Mergers of elliptical galaxies and the fundamental plane

NARCIS (Netherlands)

Gonzalez-Garcia, AC; van Albada, TS; AvilaReese,; Firmani, C; Frenk, CS; Allen, YC

2003-01-01

N-body simulations have been carried out in order to explore the final state of elliptical galaxies after encounters and more expecifically whether the Fundamental Plane (FP hereafter) relation is affected by merging.

Intrinsic Density Matrices of the Nuclear Shell Model

International Nuclear Information System (INIS)

Deveikis, A.; Kamuntavichius, G.

1996-01-01

A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code. (author). 11 refs., 2 tabs

Random matrix approach to cross correlations in financial data

Science.gov (United States)

Plerou, Vasiliki; Gopikrishnan, Parameswaran; Rosenow, Bernd; Amaral, Luís A.; Guhr, Thomas; Stanley, H. Eugene

2002-06-01

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues λi of C against a ``null hypothesis'' - a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [λ-,λ+] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these ``deviating eigenvectors'' are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

Fission yield correlation generation and impact on nuclear problems - 15570

International Nuclear Information System (INIS)

Fiorito, L.; Stankovskiy, A.; Van den Eynde, G.

2015-01-01

In our work we defined a scheme to update fission yields and their covariance matrices. We implemented a Generalised Linear Least Square (GLLS) updating procedure to produce inter-isotope fission yield correlations. At each update, a constraining equation was selected and the related set of observables calculated using the prior knowledge of the fission yield data and uncertainties. Then, available extra information on each observable was introduced into the system - e.g. a data set of direct measurements or uncertainties. Our GLLS-based updating tool calculates best-estimate posterior fission yields and covariance matrices which merge both the extra and prior data. The major result of the update is the generation of fission yield correlations. We created complete updated covariance matrices for 6 nuclides (Th 232 , U 233 , U 235 , U 238 , Pu 239 and Pu 241 ) and a total of 14 fissioning systems using the JEFF-3.1.1 files. The fission yield covariance matrices were tested against the criticality and nuclide inventory calculations of the REBUS single pin benchmark after one irradiation cycle. It appears that fission yield correlations reduce the uncertainties to a very great extent, which in many cases are 4 times smaller than those obtained with uncorrelated data

Nontrivial correlation between the CKM and MNS matrices

International Nuclear Information System (INIS)

Xing Zhizhong

2005-01-01

We point out that the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix V CKM and the Maki-Nakagawa-Sakata (MNS) lepton mixing matrix V MNS can naturally be correlated in a class of seesaw models if the Dirac neutrino mass matrix and the up-type quark mass matrix are symmetric and identical, but the texture of their correlation matrix F ν is rather nontrivial. The bimaximal mixing pattern of F ν is disfavored by current data, and other special forms of F ν may suffer from fine-tuning of the free phase parameters in fitting the so-called quark-lepton complementarity relation. A straightforward calculation of F ν in terms of V CKM and V MNS reveals a striking feature of F ν : its (1,3) element cannot be zero or too small, no matter whether the (1,3) elements of V CKM and V MNS are vanishing or not. We also add some brief comments on possible radiative corrections to V CKM and V MNS

Eliminating line of sight in elliptic guides using gravitational curving

International Nuclear Information System (INIS)

Kleno, Kaspar H.; Willendrup, Peter K.; Knudsen, Erik; Lefmann, Kim

2011-01-01

Eliminating fast neutrons (λ<0.5A) by removing direct line of sight between the source and the target sample is a well established technique. This can be done with little loss of transmission for a straight neutron guide by horizontal curving. With an elliptic guide shape, however, curving the guide would result in a breakdown of the geometrical focusing mechanism inherent to the elliptical shape, resulting in unwanted reflections and loss of transmission. We present a new and yet untried idea by curving a guide in such a way as to follow the ballistic curve of a neutron in the gravitational field, while still retaining the elliptic shape seen from the accelerated reference frame of the neutron. Analytical calculations and ray-tracing simulations show that this method is useful for cold neutrons at guide lengths in excess of 100 m. We will present some of the latest results for guide optimization relevant for instrument design at the ESS, in particular an off-backscattering spectrometer which utilizes the gravitational curving, for 6.66 A neutrons over a guide length of 300 m.

Parallelization of elliptic solver for solving 1D Boussinesq model

Science.gov (United States)

Tarwidi, D.; Adytia, D.

2018-03-01

In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.

Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

Science.gov (United States)

Cho, Yumi

2018-05-01

We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

Skin equivalent tissue-engineered construct: co-cultured fibroblasts/ keratinocytes on 3D matrices of sericin hope cocoons.

Directory of Open Access Journals (Sweden)

Sunita Nayak

Full Text Available The development of effective and alternative tissue-engineered skin replacements to autografts, allografts and xenografts has became a clinical requirement due to the problems related to source of donor tissue and the perceived risk of disease transmission. In the present study 3D tissue engineered construct of sericin is developed using co-culture of keratinocytes on the upper surface of the fabricated matrices and with fibroblasts on lower surface. Sericin is obtained from "Sericin Hope" silkworm of Bombyx mori mutant and is extracted from cocoons by autoclave. Porous sericin matrices are prepared by freeze dried method using genipin as crosslinker. The matrices are characterized biochemically and biophysically. The cell proliferation and viability of co-cultured fibroblasts and keratinocytes on matrices for at least 28 days are observed by live/dead assay, Alamar blue assay, and by dual fluorescent staining. The growth of the fibroblasts and keratinocytes in co-culture is correlated with the expression level of TGF-β, b-FGF and IL-8 in the cultured supernatants by enzyme-linked immunosorbent assay. The histological analysis further demonstrates a multi-layered stratified epidermal layer of uninhibited keratinocytes in co-cultured constructs. Presence of involucrin, collagen IV and the fibroblast surface protein in immuno-histochemical stained sections of co-cultured matrices indicates the significance of paracrine signaling between keratinocytes and fibroblasts in the expression of extracellular matrix protein for dermal repair. No significant amount of pro inflammatory cytokines (TNF-α, IL-1β and nitric oxide production are evidenced when macrophages grown on the sericin matrices. The results all together depict the potentiality of sericin 3D matrices as skin equivalent tissue engineered construct in wound repair.

Random matrices and random difference equations

International Nuclear Information System (INIS)

Uppuluri, V.R.R.

1975-01-01

Mathematical models leading to products of random matrices and random difference equations are discussed. A one-compartment model with random behavior is introduced, and it is shown how the average concentration in the discrete time model converges to the exponential function. This is of relevance to understanding how radioactivity gets trapped in bone structure in blood--bone systems. The ideas are then generalized to two-compartment models and mammillary systems, where products of random matrices appear in a natural way. The appearance of products of random matrices in applications in demography and control theory is considered. Then random sequences motivated from the following problems are studied: constant pulsing and random decay models, random pulsing and constant decay models, and random pulsing and random decay models

Quantum Entanglement and Reduced Density Matrices

Science.gov (United States)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.

Performance of an elliptically tapered neutron guide

International Nuclear Information System (INIS)

Muehlbauer, Sebastian; Stadlbauer, Martin; Boeni, Peter; Schanzer, Christan; Stahn, Jochen; Filges, Uwe

2006-01-01

Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics

Experimental Validation of Elliptical Fin-Opening Behavior

Directory of Open Access Journals (Sweden)

James M. Garner

2003-01-01

Full Text Available An effort to improve the performance of ordnance has led to the consideration of the use of folding elliptical fins for projectile stabilization. A second order differential equation was used to model elliptical fin deployment history and accounts for: deployment with respect to the geometric properties of the fin, the variation in fin aerodynamics during deployment, the initial yaw effect on fin opening, and the variation in deployment speed based on changes in projectile spin. This model supports tests conducted at the Transonic Experimental Facility, Aberdeen Proving Ground examining the opening behavior of these uniquely shaped fins. The fins use the centrifugal force from the projectile spin to deploy. During the deployment, the fin aerodynamic forces vary with angle-of-attack changes to the free stream. Model results indicate that projectile spin dominates the initial opening rates and aerodynamics dominate near the fully open state. The model results are examined to explain the observed behaviors, and suggest improvements for later designs.

Can mergers make slowly rotating elliptical galaxies

International Nuclear Information System (INIS)

White, S.D.M.

1979-01-01

The results of numerical experiments are used to guide an analytic discussion of hyperbolic mergers among an uncorrelated galaxy population. The expected merger rate is derived as a function of progenitor mass and relative angular momentum, and is used to predict the distribution of the parameter V/sub c//sigma 0 for merger products where V/sub c/ is the maximum observed rotation velocity in a galaxy and sigma 0 is its central velocity dispersion. The median value of this parameter for mergers between comparable galaxies is estimated to be 0.65 and is higher than the observed value in any of the 14 galaxies for which data are available. It seems unlikely that most elliptical galaxies are the result of single or multiple mergers between initially unbound stellar systems; further observational and theoretical work is suggested which should lead to a conclusive test of this picture. The present arguments cannot, however, exclude formation from low angular momentum elliptical orbits

Estimates of azimuthal numbers associated with elementary elliptic cylinder wave functions

Science.gov (United States)

Kovalev, V. A.; Radaev, Yu. N.

2014-05-01

The paper deals with issues related to the construction of solutions, 2 π-periodic in the angular variable, of the Mathieu differential equation for the circular elliptic cylinder harmonics, the associated characteristic values, and the azimuthal numbers needed to form the elementary elliptic cylinder wave functions. A superposition of the latter is one possible form for representing the analytic solution of the thermoelastic wave propagation problem in long waveguides with elliptic cross-section contour. The classical Sturm-Liouville problem for the Mathieu equation is reduced to a spectral problem for a linear self-adjoint operator in the Hilbert space of infinite square summable two-sided sequences. An approach is proposed that permits one to derive rather simple algorithms for computing the characteristic values of the angular Mathieu equation with real parameters and the corresponding eigenfunctions. Priority is given to the application of the most symmetric forms and equations that have not yet been used in the theory of the Mathieu equation. These algorithms amount to constructing a matrix diagonalizing an infinite symmetric pentadiagonal matrix. The problem of generalizing the notion of azimuthal number of a wave propagating in a cylindrical waveguide to the case of elliptic geometry is considered. Two-sided mutually refining estimates are constructed for the spectral values of the Mathieu differential operator with periodic and half-periodic (antiperiodic) boundary conditions.

Comparison of two superconducting elliptical undulators for generating circularly polarized light

Directory of Open Access Journals (Sweden)

C. S. Hwang

2004-09-01

Full Text Available The potential use of two planar superconducting elliptical undulators—a vertically wound racetrack coil structure and a staggered array structure—to generate a circularly polarized hard x-ray source was investigated. The magnetic poles and wires of the up and down magnet arrays were rotated in alternating directions on the horizontal plane, an elliptical field is generated to provide circularly polarized light in the electron-storage ring and the energy-recovery linac accelerator. Rapid switching between right- and left-circularly polarized radiations is performed using two undulators with oppositely rotated wires and poles. Given a periodic length of 15 mm and a gap of 5 mm, the magnetic-flux densities in the elliptical undulator are B_{z}=1.2   T (B_{x}=0.6   T and B_{z}=0.35   T (B_{x}=0.15   T in the planar vertically wound racetrack coil and the staggered structure with poles rotated by 35° and 25°, respectively. In maximizing the merit of the flux and the width of the effective field region in the two superconducting elliptical undulators, the trade-off rotation angles of the coils and poles are 20° and 5°, for vertically wound racetrack coil and staggered undulators, respectively.

Constructive Solution of Ellipticity Problem for the First Order Differential System

Directory of Open Access Journals (Sweden)

Vladimir E. Balabaev

2017-01-01

Full Text Available We built first order elliptic systems with any possible number of unknown functions and the maximum possible number of unknowns, i.e, in general. These systems provide the basis for studying the properties of any first order elliptic systems. The study of the Cauchy-Riemann system and its generalizations led to the identification of a class of elliptic systems of first-order of a special structure. An integral representation of solutions is of great importance in the study of these systems. Only by means of a constructive method of integral representations we can solve a number of problems in the theory of elliptic systems related mainly to the boundary properties of solutions. The obtained integral representation could be applied to solve a number of problems that are hard to solve, if you rely only on the non-constructive methods. Some analogues of the theorems of Liouville, Weierstrass, Cauchy, Gauss, Morera, an analogue of Green’s formula are established, as well as an analogue of the maximum principle. The used matrix operators allow the new structural arrangement of the maximum number of linearly independent vector fields on spheres of any possible dimension. Also the built operators allow to obtain a constructive solution of the extended problem ”of the sum of squares” known in algebra. 

New Rule Use Drives the Relation between Working Memory Capacity and Raven's Advanced Progressive Matrices

Science.gov (United States)

Wiley, Jennifer; Jarosz, Andrew F.; Cushen, Patrick J.; Colflesh, Gregory J. H.

2011-01-01

The correlation between individual differences in working memory capacity and performance on the Raven's Advanced Progressive Matrices (RAPM) is well documented yet poorly understood. The present work proposes a new explanation: that the need to use a new combination of rules on RAPM problems drives the relation between performance and working…

Triangularity effects on the collisional diffusion for elliptic tokamak plasma

International Nuclear Information System (INIS)

Martin, P.; Castro, E.

2007-01-01

In this conference the effect of ellipticity and triangularity will be analyzed for axisymmetric tokamak in the collisional regime. Analytic forms for the magnetic field cross sections are taken from those derived recently by other authors [1,2]. Analytical results can be obtained in elliptic plasmas with triangularity by using an special system of tokamak coordinates recently published [3-5]. Our results show that triangularities smaller than 0.6, increases confinement for ellipticities in the range 1.2 to 2. This behavior happens for negative and positive triangularities; however this effect is stronger for positive than for negative triangularities. The maximum diffusion velocity is not obtained for zero triangularity, but for small negative triangularities. Ellipticity is also very important in confinement, but the effect of triangularity seems to be more important. High electric inductive field increases confinement, though this field is difficult to modify once the tokamak has been built. The analytic form of the current produced by this field is like that of a weak Ware pinch with an additional factor, which weakens the effect by an order of magnitude. The dependence of the triangularity effect with the Shafranov shift is also analyzed. References 1. - L. L. Lao, S. P. Hirshman, and R. M. Wieland, Phys. Fluids 24, 1431 (1981) 2. - G. O. Ludwig, Plasma Physics Controlled Fusion 37, 633 (1995) 3. - P. Martin, Phys. Plasmas 7, 2915 (2000) 4. - P. Martin, M. G. Haines and E. Castro, Phys. Plasmas 12, 082506 (2005) 5. - P. Martin, E. Castro and M. G. Haines, Phys. Plasmas 12, 102505 (2005)

Elliptic Curve Integral Points on y2 = x3 + 3x ‑ 14

Science.gov (United States)

Zhao, Jianhong

2018-03-01

The positive integer points and integral points of elliptic curves are very important in the theory of number and arithmetic algebra, it has a wide range of applications in cryptography and other fields. There are some results of positive integer points of elliptic curve y 2 = x 3 + ax + b, a, b ∈ Z In 1987, D. Zagier submit the question of the integer points on y 2 = x 3 ‑ 27x + 62, it count a great deal to the study of the arithmetic properties of elliptic curves. In 2009, Zhu H L and Chen J H solved the problem of the integer points on y 2 = x 3 ‑ 27x + 62 by using algebraic number theory and P-adic analysis method. In 2010, By using the elementary method, Wu H M obtain all the integral points of elliptic curves y 2 = x 3 ‑ 27x ‑ 62. In 2015, Li Y Z and Cui B J solved the problem of the integer points on y 2 = x 3 ‑ 21x ‑ 90 By using the elementary method. In 2016, Guo J solved the problem of the integer points on y 2 = x 3 + 27x + 62 by using the elementary method. In 2017, Guo J proved that y 2 = x 3 ‑ 21x + 90 has no integer points by using the elementary method. Up to now, there is no relevant conclusions on the integral points of elliptic curves y 2 = x 3 + 3x ‑ 14, which is the subject of this paper. By using congruence and Legendre Symbol, it can be proved that elliptic curve y 2 = x 3 + 3x ‑ 14 has only one integer point: (x, y) = (2, 0).

Malware analysis using visualized image matrices.

Science.gov (United States)

Han, KyoungSoo; Kang, BooJoong; Im, Eul Gyu

2014-01-01

This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API) calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Malware Analysis Using Visualized Image Matrices

Directory of Open Access Journals (Sweden)

KyoungSoo Han

2014-01-01

Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Design and testing of low-divergence elliptical-jet nozzles

Energy Technology Data Exchange (ETDEWEB)

Rouly, Etienne; Warkentin, Andrew; Bauer, Robert [Dalhousie University, Halifax (China)

2015-05-15

A novel approach was developed to design and fabricate nozzles to produce high-pressure low-divergence fluid jets. Rapid-prototype fabrication allowed for myriad experiments investigating effects of different geometric characteristics of nozzle internal geometry on jet divergence angle and fluid distribution. Nozzle apertures were elliptical in shape with aspect ratios between 1.00 and 2.45. The resulting nozzle designs were tested and the lowest elliptical jet divergence angle was 0.4 degrees. Nozzle pressures and flowrates ranged from 0.32 to 4.45 MPa and 13.6 to 37.9 LPM, respectively. CimCool CimTech 310 machining fluid was used in all experiments at a Brix concentration of 6.6 percent.

Electric sail elliptic displaced orbits with advanced thrust model

Science.gov (United States)

Niccolai, Lorenzo; Quarta, Alessandro A.; Mengali, Giovanni

2017-09-01

This paper analyzes the performance of an Electric Solar Wind Sail for generating and maintaining an elliptic, heliocentric, displaced non-Keplerian orbit. In this sense, this paper extends and completes recent studies regarding the performances of an Electric Solar Wind Sail that covers a circular, heliocentric, displaced orbit of given characteristics. The paper presents the general equations that describe the elliptic orbit maintenance in terms of both spacecraft attitude and performance requirements, when a refined thrust model (recently proposed for the preliminary mission design) is taken into account. In particular, the paper also discusses some practical applications on particular mission scenarios in which an analytic solution of the governing equations has been found.

Production and characterization of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices

Energy Technology Data Exchange (ETDEWEB)

Zepon, Karine Modolon [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Petronilho, Fabricia [FICEXP, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Soldi, Valdir [POLIMAT, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Salmoria, Gean Vitor [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Kanis, Luiz Alberto, E-mail: luiz.kanis@unisul.br [TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil)

2014-11-01

The production and evaluation of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices are reported herein. The matrices were melt extruded under nine different conditions, altering the temperature and the screw speed values. The surface morphology of the matrices was examined by scanning electron microscopy. The micrographs revealed the presence of non-melted silver sulfadiazine microparticles in the matrices extruded at lower temperature and screw speed values. The thermal properties were evaluated and the results for both the biopolymer and the drug indicated no thermal degradation during the melt extrusion process. The differential scanning analysis of the extrudate matrices showed a shift to lower temperatures for the silver sulfadiazine melting point compared with the non-extruded drug. The starch/cellulose acetate matrices containing silver sulfadiazine demonstrated significant inhibition of the growth of Pseudomonas aeruginosa and Staphylococcus aureus. In vivo inflammatory response tests showed that the extrudate matrices, with or without silver sulfadiazine, did not trigger chronic inflammatory processes. - Highlights: • Melt extruded bio-based matrices containing silver sulfadiazine was produced. • The silver sulfadiazine is stable during melt-extrusion. • The extrudate matrices shown bacterial growth inhibition. • The matrices obtained have potential to development wound healing membranes.

On the elliptic genus of three E-strings and heterotic strings

International Nuclear Information System (INIS)

Cai, Wenhe; Huang, Min-xin; Sun, Kaiwen

2015-01-01

A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n=3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.

Polynomial sequences generated by infinite Hessenberg matrices

Directory of Open Access Journals (Sweden)

Verde-Star Luis

2017-01-01

Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

Science.gov (United States)

Nigsch, Martin

2007-07-01

A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

Multivariate analysis of nutritional information of foodstuff of plant origin for the selection of representative matrices for the analysis of pesticide residues

International Nuclear Information System (INIS)

Neves Bettencourt da Silva, Ricardo Jorge; Gomes Ferreira Crujo Camoes, Maria Filomena

2010-01-01

Testing safety of foodstuffs of plant origin involves the analysis of hundreds of pesticide residues. This control is only cost-effective through the use of methods validated for the analysis of many thousands of analyte/matrix combinations. Several documents propose representative matrices of groups of matrices from which the validity of the analytical method can be extrapolated to the represented matrices after summarised experimental check of within group method performance homogeneity. Those groups are based on an evolved expert consensus based on the empirical knowledge on the current analytical procedures; they are not exhaustive, they are not objectively defined and they propose a large list of representative matrices which makes their application difficult. This work proposes grouping 240 matrices, based on the nutritional composition pattern equivalence of the analytical portion right after hydration and before solvent extraction, aiming at defining groups that observe method performance homogeneity. This grouping was based on the combined outcome of three multivariate tools, namely: Principal Component Analysis, Hierarchical Cluster Analysis and K-Mean Cluster Analysis. These tools allowed the selection of eight groups for which representative matrices with average characteristics and objective criteria to test inclusion of new matrices were established. The proposed matrices groups are homogeneous to nutritional data not considered in their definition but correlated with the studied multivariate nutritional pattern. The developed grouping that must be checked with experimental test before use was tested against small deviations in food composition and for the integration of new matrices.

S-matrices and integrability

International Nuclear Information System (INIS)

Bombardelli, Diego

2016-01-01

In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross–Neveu models. (topical review)

Matrices Aléatoires Tri-diagonales et Par Blocs.

OpenAIRE

MEKKI, Slimane

2014-01-01

Dans ce mémoire l'étude porte sur la densité de matrice aléatoire, les densités des valeurs propres d'une matrice pour les trois ensembles G.O.E, G.U.E, G.S.E. Après nous avons explicité les formules des densités de valeurs propres des matrices tri-diagonales dans les cas HERMITE et LAGUERRE Des simulations sur les constantes de normalisations pour les densités des matrices aléatoires ou des valeurs propres sont présentées.

CLASSICAL AREAS OF PHENOMENOLOGY: Material parameter equation for rotating elliptical spherical cloaks

Science.gov (United States)

Ma, Hua; Qu, Shao-Bo; Xu, Zhuo; Zhang, Jie-Qiu; Wang, Jia-Fu

2009-01-01

By using the coordinate transformation method, we have deduced the material parameter equation for rotating elliptical spherical cloaks and carried out simulation as well. The results indicate that the rotating elliptical spherical cloaking shell, which is made of meta-materials whose permittivity and permeability are governed by the equation deduced in this paper, can achieve perfect invisibility by excluding electromagnetic fields from the internal region without disturbing any external field.

Impact of elliptical shaped red oak logs on lumber grade and volume recovery

Science.gov (United States)

Patrick M. Rappold; Brian H. Bond; Janice K. Wiedenbeck; Roncs Ese-Etame

2007-01-01

This research examined the grade and volume of lumber recovered from red oak logs with elliptical shaped cross sections. The volume and grade of lumber recovered from red oak logs with low (e ≤ 0.3) and high (e ≥ 0.4) degrees of ellipticity was measured at four hardwood sawmills. There was no significant difference (...

Hierarchical quark mass matrices

International Nuclear Information System (INIS)

Rasin, A.

1998-02-01

I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s 23 ) and the angle in the (1,2) plane (s 12 ) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consist of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s 13 diagonalization angles are sufficiently small compared to the product s 12 s 23 , two special CKM parametrizations emerge: the R 12 R 23 R 12 parametrization follows with s 23 taken before the s 12 rotation, and vice versa for the R 23 R 12 R 23 parametrization. (author)

Laminin active peptide/agarose matrices as multifunctional biomaterials for tissue engineering.

Science.gov (United States)

Yamada, Yuji; Hozumi, Kentaro; Aso, Akihiro; Hotta, Atsushi; Toma, Kazunori; Katagiri, Fumihiko; Kikkawa, Yamato; Nomizu, Motoyoshi

2012-06-01

Cell adhesive peptides derived from extracellular matrix components are potential candidates to afford bio-adhesiveness to cell culture scaffolds for tissue engineering. Previously, we covalently conjugated bioactive laminin peptides to polysaccharides, such as chitosan and alginate, and demonstrated their advantages as biomaterials. Here, we prepared functional polysaccharide matrices by mixing laminin active peptides and agarose gel. Several laminin peptide/agarose matrices showed cell attachment activity. In particular, peptide AG73 (RKRLQVQLSIRT)/agarose matrices promoted strong cell attachment and the cell behavior depended on the stiffness of agarose matrices. Fibroblasts formed spheroid structures on the soft AG73/agarose matrices while the cells formed a monolayer with elongated morphologies on the stiff matrices. On the stiff AG73/agarose matrices, neuronal cells extended neuritic processes and endothelial cells formed capillary-like networks. In addition, salivary gland cells formed acini-like structures on the soft matrices. These results suggest that the peptide/agarose matrices are useful for both two- and three-dimensional cell culture systems as a multifunctional biomaterial for tissue engineering. Copyright © 2012 Elsevier Ltd. All rights reserved.

Hidden neuronal correlations in cultured networks

International Nuclear Information System (INIS)

Segev, Ronen; Baruchi, Itay; Hulata, Eyal; Ben-Jacob, Eshel

2004-01-01

Utilization of a clustering algorithm on neuronal spatiotemporal correlation matrices recorded during a spontaneous activity of in vitro networks revealed the existence of hidden correlations: the sequence of synchronized bursting events (SBEs) is composed of statistically distinguishable subgroups each with its own distinct pattern of interneuron spatiotemporal correlations. These findings hint that each of the SBE subgroups can serve as a template for coding, storage, and retrieval of a specific information

Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

Indian Academy of Sciences (India)

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

Accelerating Matrix-Vector Multiplication on Hierarchical Matrices Using Graphical Processing Units

KAUST Repository

Boukaram, W.

2015-03-25

Large dense matrices arise from the discretization of many physical phenomena in computational sciences. In statistics very large dense covariance matrices are used for describing random fields and processes. One can, for instance, describe distribution of dust particles in the atmosphere, concentration of mineral resources in the earth\\'s crust or uncertain permeability coefficient in reservoir modeling. When the problem size grows, storing and computing with the full dense matrix becomes prohibitively expensive both in terms of computational complexity and physical memory requirements. Fortunately, these matrices can often be approximated by a class of data sparse matrices called hierarchical matrices (H-matrices) where various sub-blocks of the matrix are approximated by low rank matrices. These matrices can be stored in memory that grows linearly with the problem size. In addition, arithmetic operations on these H-matrices, such as matrix-vector multiplication, can be completed in almost linear time. Originally the H-matrix technique was developed for the approximation of stiffness matrices coming from partial differential and integral equations. Parallelizing these arithmetic operations on the GPU has been the focus of this work and we will present work done on the matrix vector operation on the GPU using the KSPARSE library.

Electromagnetically induced transparency in the case of elliptic polarization of interacting fields

Science.gov (United States)

Parshkov, Oleg M.

2018-04-01

The theoretical investigation results of disintegration effect of elliptic polarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed elliptic polarized control field and in weak probe field approximation are presented. It is shown that this disintegration occurs because the probe field in the medium is the sum of two normal modes, which correspond to elliptic polarized pulses with different speeds of propagation. The polarization ellipses of normal modes have equal eccentricities and mutually perpendicular major axes. Major axis of polarization ellipse of one normal mode is parallel to polarization ellipse major axis of control field, and electric vector of this mode rotates in the opposite direction, than electric vector of the control field. The electric vector other normal mode rotates in the same direction that the control field electric vector. The normal mode speed of the first type aforementioned is less than that of the second type. The polarization characteristics of the normal mode depend uniquely on the polarization characteristics of elliptic polarized control field and remain changeless in the propagation process. The theoretical investigation is performed for Λ-scheme of degenerated quantum transitions between 3P0, 3P10 and 3P2 energy levels of 208Pb isotope.

Elliptical and lenticular galaxies evolution

International Nuclear Information System (INIS)

Vigroux, L.

1981-01-01

Different evolutionnary models for elliptical and lenticular galaxies are discussed. In the first part, we show that, at least some peculiar early types galaxies exhibit some activity. Then we describe the observationnal constraints: the color-magnitude diagram, the color gradient and the high metallicity of intraclusters gas. Among the different models, only the dissipation collapse followed by a hot wind driven by supernovae explosion explain in a natural way these constraints. Finally, the origin of SO is briefly discussed [fr

The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces

KAUST Repository

Chen, Yujia

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general curved surfaces. Based on the closest point representation of the underlying surface, we formulate an embedding equation for the surface elliptic problem, then discretize it using standard finite differences and interpolation schemes on banded but uniform Cartesian grids. We prove the convergence of the difference scheme for the Poisson\\'s equation on a smooth closed curve. In order to solve the resulting large sparse linear systems, we propose a specific geometric multigrid method in the setting of the closest point method. Convergence studies in both the accuracy of the difference scheme and the speed of the multigrid algorithm show that our approaches are effective.

Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

Directory of Open Access Journals (Sweden)

Hjalmar Rosengren

2006-12-01

Full Text Available We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux and number theory (representation of integers as sums of squares.

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.

Elliptic Painlevé equations from next-nearest-neighbor translations on the E_8^{(1)} lattice

Science.gov (United States)

Joshi, Nalini; Nakazono, Nobutaka

2017-07-01

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the E_8(1) lattice, given by nearest neighbor vectors. In this paper, we give a new elliptic discrete Painlevé equation obtained by translations along next-nearest-neighbor vectors. This equation is a generic (8-parameter) version of a 2-parameter elliptic difference equation found by reduction from Adler’s partial difference equation, the so-called Q4 equation. We also provide a projective reduction of the well known equation of Sakai.

Anomalous incident-angle and elliptical-polarization rotation of an elastically refracted P-wave

Science.gov (United States)

Fa, Lin; Fa, Yuxiao; Zhang, Yandong; Ding, Pengfei; Gong, Jiamin; Li, Guohui; Li, Lijun; Tang, Shaojie; Zhao, Meishan

2015-08-01

We report a newly discovered anomalous incident-angle of an elastically refracted P-wave, arising from a P-wave impinging on an interface between two VTI media with strong anisotropy. This anomalous incident-angle is found to be located in the post-critical incident-angle region corresponding to a refracted P-wave. Invoking Snell’s law for a refracted P-wave provides two distinctive solutions before and after the anomalous incident-angle. For an inhomogeneously refracted and elliptically polarized P-wave at the anomalous incident-angle, its rotational direction experiences an acute variation, from left-hand elliptical to right-hand elliptical polarization. The new findings provide us an enhanced understanding of acoustical-wave scattering and lead potentially to widespread and novel applications.

Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms

Science.gov (United States)

Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus; von Hippel, Matt; Wilhelm, Matthias

2018-03-01

We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Science.gov (United States)

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2016-05-01

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Boundary-value problems with free boundaries for elliptic systems of equations

CERN Document Server

Monakhov, V N

1983-01-01

This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

TOPICAL REVIEW: The stability for the Cauchy problem for elliptic equations

Science.gov (United States)

Alessandrini, Giovanni; Rondi, Luca; Rosset, Edi; Vessella, Sergio

2009-12-01

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality. Due to the current absence of research funding from the Italian Ministry of University and Research, this work has been completed without any financial support.

A search for HI in elliptical galaxies with nuclear radio sources

International Nuclear Information System (INIS)

Dressel, L.L.; Bania, T.M.; O'Connell, R.W.

1982-01-01

Two of the galaxies with large HI mass, NGC 1052 and 4278, are known to have powerful nuclear continuum radio sources (P 2380 approximately 10 22 WHz -1 ). Since both of these attributes are fairly rare among elliptical galaxies, their coexistence in these galaxies is not likely to have occurred by chance. The authors have therefore observed twelve other elliptical galaxies with nuclear radio power P 2380 > 10 22 WHz -1 at Arecibo Observatory, to determine whether a large mass of HI is a necessary auxillary to nuclear continuum emission. (Auth.)

Mantle cloaks for elliptical cylinders excited by an electric line source

DEFF Research Database (Denmark)

Kaminski, Piotr Marek; Yakovlev, Alexander B.; Arslanagic, Samel

2016-01-01

We investigate the ability of surface impedance mantle cloaks for cloaking of elliptical cylinders excited by an electric line source. The exact analytical solution of the problem utilizing Mathieu functions is obtained and is used to derive optimal surface impedances to cloak a number of configu......We investigate the ability of surface impedance mantle cloaks for cloaking of elliptical cylinders excited by an electric line source. The exact analytical solution of the problem utilizing Mathieu functions is obtained and is used to derive optimal surface impedances to cloak a number...

How Does Abundance Affect the Strength of UV Emission in Elliptical Galaxies?

Science.gov (United States)

Sonneborn, George (Technical Monitor); Brown, Thomas

2005-01-01

This program used the Far Ultraviolet Spectroscopic Explorer (FUSE) to observe elliptical galaxies with the intention of measuring the chemical abundances in their hot stellar populations. It was designed to complement an earlier FUSE program that observed elliptical galaxies with strong UV emission. The current program originally planned observations of two ellipticals with weak UV emission (M32 and M49). Once FUSE encountered pointing control problems in certain regions of the sky (particularly Virgo, which is very unfortunate for the study of ellipticals in general), M49 was replaced with the bulge of M31, which has a similar UV-to-optical flux ratio as the center of M49. As the closest elliptical galaxy and the one with the weakest UV-to-optical flux ratio, M32 was an obvious choice of target, but M49 was the ideal complementary target, because it has a very low reddening (unlike M32). With the inability of FUSE to point at Virgo, nearly all of the best elliptical galaxies (bright galaxies with low foreground extinction) were also lost, and this severely hampered three FUSE programs of the PI, all focused on the hot stellar populations of ellipticals. M31 was the best replacement for M49, but like M32, it suffers from significant foreground reddening. Strong Galactic ISM lines heavily contaminate the FUSE spectra of M31 and M32. These ISM lines are coincident with the photospheric lines from the stellar populations (whereas M49, with little foreground ISM and significant redshift, would not have suffered from this problem). We have reduced the faint (and thus difficult) data for M31 and M32, producing final co-added spectra representing all of the exposures, but we have not yet finished our analysis, due to the complication of the contaminating ISM. The silver lining here is the set of CHI lines at 1175 Angstroms, which are not significantly contaminated by the ISM. A comparison of the M31 spectrum with other galaxies observed by FEE showed a surprising result

Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions

KAUST Repository

Arellano-Valle, Reinaldo B.

2012-02-27

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study in detail the cases of the multivariate skew-normal and skew-t distributions. We implement our findings to the application of the optimal design of an ozone monitoring station network in Santiago de Chile. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

Collage-based approaches for elliptic partial differential equations inverse problems

Science.gov (United States)

Yodzis, Michael; Kunze, Herb

2017-01-01

The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.

Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions

KAUST Repository

Arellano-Valle, Reinaldo B.; Contreras-Reyes, Javier E.; Genton, Marc G.

2012-01-01

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study in detail the cases of the multivariate skew-normal and skew-t distributions. We implement our findings to the application of the optimal design of an ozone monitoring station network in Santiago de Chile. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

IMPROVING CORRELATION FUNCTION FITTING WITH RIDGE REGRESSION: APPLICATION TO CROSS-CORRELATION RECONSTRUCTION

International Nuclear Information System (INIS)

Matthews, Daniel J.; Newman, Jeffrey A.

2012-01-01

Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to obtain secure redshifts for 30%-50% or more of the galaxies targeted). In this paper, we improve on the redshift distribution reconstruction methods from our previous work by incorporating full covariance information into our correlation function fits. Correlation function measurements are strongly covariant between angular or spatial bins, and accounting for this in fitting can yield substantial reduction in errors. However, frequently the covariance matrices used in these calculations are determined from a relatively small set (dozens rather than hundreds) of subsamples or mock catalogs, resulting in noisy covariance matrices whose inversion is ill-conditioned and numerically unstable. We present here a method of conditioning the covariance matrix known as ridge regression which results in a more well behaved inversion than other techniques common in large-scale structure studies. We demonstrate that ridge regression significantly improves the determination of correlation function parameters. We then apply these improved techniques to the problem of reconstructing redshift distributions. By incorporating full covariance information, applying ridge regression, and changing the weighting of fields in obtaining average correlation functions, we obtain reductions in the mean redshift distribution reconstruction error of as much as ∼40% compared to previous methods. We provide a description of POWERFIT, an IDL code for performing power-law fits to correlation functions with ridge regression conditioning that we are making publicly available.

Magnetic properties of elliptical and stadium-shaped nanoparticles: Effect of the shape anisotropy

International Nuclear Information System (INIS)

Corona, R.M.; Altbir, D.; Escrig, J.

2012-01-01

Elliptical and stadium-shaped nanoparticles as a function of their geometry have been investigated using numerical simulations. The effect of the shape anisotropy of the particles on coercivity and remanence together with the angular dependence of the remanence and coercivity are addressed. Our results demonstrate that the stadium-shaped particles have many of the outstanding properties of elliptical particles, but also have unique properties, such that the coercivity and remanence remain stable for a wide range of geometry parameters, and exhibit a peculiar angular dependence in the coercivity. These properties suggest that they can be useful for applications in the area of magnetic recording systems. - Highlights: ► Coercivity and remanence are strongly affected by the shape anisotropy of the particles. ► Coercivities for ellipses are nearly three times the obtained for stadium-shaped particles. ►Elliptical particles with δ≤0.6, the hystereses resemble the square loops of wires. ► An anhisteretic behavior appears for θ=90° for elliptical particles, which do not appear in stadium-shaped particles. ► Stadium-shaped particles have unique properties that allow us to suggest them for applications.

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.

Science.gov (United States)

Oña, Ofelia B; De Clercq, Olivier; Alcoba, Diego R; Torre, Alicia; Lain, Luis; Van Neck, Dimitri; Bultinck, Patrick

2016-09-19

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

Immanant Conversion on Symmetric Matrices

Directory of Open Access Journals (Sweden)

Purificação Coelho M.

2014-01-01

Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.

Multilevel quadrature of elliptic PDEs with log-normal diffusion

KAUST Repository

Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus

2015-01-01

Each function evaluation corresponds to a deterministic elliptic boundary value problem which can be solved by finite elements on an appropriate level of refinement. The complexity is thus given by the number

A Jacobian elliptic single-field inflation

Energy Technology Data Exchange (ETDEWEB)

Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile); Centro de Astrofisica de Valparaiso, Valparaiso (Chile); Gallo, Emanuel [FaMAF, Universidad Nacional de Cordoba, Cordoba (Argentina); Instituto de Fisica Enrique Gaviola (IFEG), CONICET, Cordoba (Argentina)

2015-06-15

In the scenario of single-field inflation, this field is described in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analyzed using the Hamilton-Jacobi approach and then the main results are contrasted with the recent measurements obtained from the Planck 2015 data. (orig.)

Elliptic partial differential equations

CERN Document Server

Han, Qing

2011-01-01

Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

Directed and Elliptic Flow in 158 GeV/Nucleon Pb + Pb Collisions

CERN Document Server

Appelshäuser, H; Bailey, S J; Barnby, L S; Bartke, J; Barton, R A; Bialkowska, H; Blyth, C O; Bock, R; Bormann, C; Brady, F P; Brockmann, R; Buncic, N; Buncic, P; Caines, H L; Cebra, D; Cooper, G E; Cramer, J G; Csató, P; Dunn, J; Eckardt, V; Eckardt, F; Ferguson, M I; Fischer, H G; Flier, D; Fodor, Z; Foka, P; Freund, P; Friese, V; Fuchs, M; Gabler, F; Gál, J; Gazdzicki, M; Gladysz-Dziadus, E; Grebieszkow, J; Günther, J; Harris, J W; Hegyi, S; Henkel, T; Hill, L A; Huang, I; Hümmler, H; Igo, G; Irmscher, D; Jacobs, P; Jones, P G; Kadija, K; Kolesnikov, V I; Kowalski, M; Lasiuk, B; Lévai, Peter; Malakhov, A I; Margetis, S; Markert, C; Melkumov, G L; Mock, A; Molnár, J; Nelson, J M; Odyniec, Grazyna Janina; Pálla, G; Panagiotou, A D; Petridis, A; Piper, A; Porter, R J; Poskanzer, A M; Poziombka, S; Prindle, D J; Pühlhofer, F; Rauch, W; Reid, J G; Rendfort, R; Retyk, W; Ritter, H G; Röhrich, D; Roland, C; Roland, G; Rudolph, H; Rybicki, A; Sandoval, A; Sann, H; Semenov, A Yu; Schäfer, E; Scjmischke, D; Schmitz, N; Schönfelder, S; Seyboth, P; Seyerlein, J; Siklér, F; Skrzypczak, E; Squier, G T A; Stock, R; Ströbele, H; Szentpétery, I; Sziklay, J; Toy, M; Trainor, T A; Trentalage, S; Ullrich, T; Vassiliou, M; Veztergombi, G; Voloshin, S; Vranic, D; Wang, F; Weerasundara, D D; Wenig, S; Whitten, C; Wienold, T; Wood, L; Yates, T A; Zimányi, J; Zybert, R

1998-01-01

The directed and elliptic flow of protons and charged pions has been observed from the semi-central collisions of a 158 GeV/nucleon Pb beam with a Pb target. The rapidity and transverse momentum dependence of the flow has been measured. The directed flow of the pions is opposite to that of the protons but both exhibit negative flow at low pt. The elliptic flow of both is fairly independent of rapidity but rises with pt.

Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak

Energy Technology Data Exchange (ETDEWEB)

Lee, Y. Y.; Ahn, D. [University of Seoul, Seoul (Korea, Republic of)

2012-05-15

A dispersive full-wave finite-difference time-domain (FDTD) model is used to calculate the performance of elliptic cylindrical cloaking devices. The permittivity and the permeability tensors for the cloaking structure are derived by using an effective medium approach in general relativity. The elliptic cylindrical invisibility devices are found to show imperfect cloaking, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of the propagation of those waves, the semi-focal distances and the loss tangents of the meta-material. When the semifocal distance of the elliptic cylinder decreases, the performance of the cloaking becomes very good, with neither noticeable scatterings nor field penetrations. For a larger semi-focal distance, only the TM wave with a specific propagation direction shows good cloaking performance. Realistic cloaking materials with loss still show a cloak that is working, but attenuated back-scattering waves exist.

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields.

Science.gov (United States)

Gu, Bing; Xu, Danfeng; Rui, Guanghao; Lian, Meng; Cui, Yiping; Zhan, Qiwen

2015-09-20

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

The 'golden' matrices and a new kind of cryptography

International Nuclear Information System (INIS)

Stakhov, A.P.

2007-01-01

We consider a new class of square matrices called the 'golden' matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The 'golden' matrices can be used for creation of a new kind of cryptography called the 'golden' cryptography. The method is very fast and simple for technical realization and can be used for cryptographic protection of digital signals (telecommunication and measurement systems)

On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

KAUST Repository

Pestana, Jennifer

2014-01-01

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.

On Investigating GMRES Convergence using Unitary Matrices

Czech Academy of Sciences Publication Activity Database

Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.

2014-01-01

Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

"G.P.S Matrices" programme: A method to improve the mastery level of social science students in matrices operations

Science.gov (United States)

Lee, Ken Voon

2013-04-01

The purpose of this action research was to increase the mastery level of Form Five Social Science students in Tawau II National Secondary School in the operations of addition, subtraction and multiplication of matrices in Mathematics. A total of 30 students were involved. Preliminary findings through the analysis of pre-test results and questionnaire had identified the main problem faced in which the students felt confused with the application of principles of the operations of matrices when performing these operations. Therefore, an action research was conducted using an intervention programme called "G.P.S Matrices" to overcome the problem. This programme was divided into three phases. 'Gift of Matrices' phase aimed at forming matrix teaching aids. The second and third phases were 'Positioning the Elements of Matrices' and 'Strenghtening the Concept of Matrices'. These two phases were aimed at increasing the level of understanding and memory of the students towards the principles of matrix operations. Besides, this third phase was also aimed at creating an interesting learning environment. A comparison between the results of pre-test and post-test had shown a remarkable improvement in students' performances after implementing the programme. In addition, the analysis of interview findings also indicated a positive feedback on the changes in students' attitude, particularly in the aspect of students' understanding level. Moreover, the level of students' memory also increased following the use of the concrete matrix teaching aids created in phase one. Besides, teachers felt encouraging when conducive learning environment was created through students' presentation activity held in third phase. Furthermore, students were voluntarily involved in these student-centred activities. In conclusion, this research findings showed an increase in the mastery level of students in these three matrix operations and thus the objective of the research had been achieved.

An Interoperability Consideration in Selecting Domain Parameters for Elliptic Curve Cryptography

Science.gov (United States)

Ivancic, Will (Technical Monitor); Eddy, Wesley M.

2005-01-01

Elliptic curve cryptography (ECC) will be an important technology for electronic privacy and authentication in the near future. There are many published specifications for elliptic curve cryptosystems, most of which contain detailed descriptions of the process for the selection of domain parameters. Selecting strong domain parameters ensures that the cryptosystem is robust to attacks. Due to a limitation in several published algorithms for doubling points on elliptic curves, some ECC implementations may produce incorrect, inconsistent, and incompatible results if domain parameters are not carefully chosen under a criterion that we describe. Few documents specify the addition or doubling of points in such a manner as to avoid this problematic situation. The safety criterion we present is not listed in any ECC specification we are aware of, although several other guidelines for domain selection are discussed in the literature. We provide a simple example of how a set of domain parameters not meeting this criterion can produce catastrophic results, and outline a simple means of testing curve parameters for interoperable safety over doubling.

Global weighted estimates for second-order nondivergence elliptic ...

Indian Academy of Sciences (India)

Fengping Yao

2018-03-21

Mar 21, 2018 ... One of the key a priori estimates in the theory of second-order elliptic .... It is well known that the maximal functions satisfy strong p–p .... Here we prove the following auxiliary result, which will be a crucial ingredient in the proof.

Recombination plus fragmentation model at RHIC: elliptic flow

Energy Technology Data Exchange (ETDEWEB)

Nonaka, C [Department of Physics, Duke University, Durham, NC 27708 (United States); Fries, R J [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Mueller, B [Department of Physics, Duke University, Durham, NC 27708 (United States); Bass, S A [Department of Physics, Duke University, Durham, NC 27708 (United States); RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 (United States); Asakawa, M [Department of Physics, Osaka University, Toyonaka 560-0043 (Japan)

2005-04-01

We discuss hadron production in relativistic heavy-ion collisions in the framework of the recombination and fragmentation model. We propose elliptic flow as a useful tool for exploring final interactions of resonances, the hadron structure of exotic particles and the phase structure of the reaction.

Hidden Correlations in Indivisible Qudits as a Resource for Quantum Technologies on Examples of Superconducting Circuits

International Nuclear Information System (INIS)

Man'ko, M A; Man'ko, V I

2016-01-01

We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki-Lieb inequality, which characterize hidden quantum correlations of observables associated with these indivisible systems. We derive these relations employing a specific map of the entropic inequalities known for density matrices of multiqudit systems to the inequalities for density matrices of single-qudit systems. We present the obtained relations in the form of mathematical inequalities for arbitrary Hermitian N × N-matrices. We consider examples of superconducting qubits and qudits. We discuss the hidden correlations in single- qudit states as a new resource for quantum technologies analogous to the known resource in correlations associated with the entanglement in multiqudit systems. (paper)

Studying the collision energy dependence of elliptic and triangular flow with a hybrid model

Energy Technology Data Exchange (ETDEWEB)

Auvinen, Jussi [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Petersen, Hannah [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany)

2014-07-01

Elliptic flow has been one of the key observables for establishing the finding of the quark-gluon plasma (QGP) at the highest energies of Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). As a sign of collectively behaving matter, the elliptic flow is expected to decrease at lower beam energies, where the QGP is not produced. However, in the recent RHIC beam energy scan, it has been found that the inclusive charged hadron elliptic flow changes relatively little in magnitude within the energy range 7.7-39 GeV per nucleon-nucleon collision. We study the collision energy dependence of the elliptic and triangular flow utilizing a Boltzmann+hydrodynamics hybrid model. Such a hybrid model provides a natural framework for the transition from high collision energies, where the hydrodynamical description is essential, to smaller energies, where the hadron transport dominates. This approach is thus suitable for investigating the relative importance of these two mechanisms for the production of the collective flow at different beam energies.

Topology of the elliptical billiard with the Hooke's potential

Directory of Open Access Journals (Sweden)

Radnović Milena

2015-01-01

Full Text Available Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential. [Projekat Ministarstva nauke Republike Srbije, br. 174020: Geometry and Topology of Manifolds and Integrable Dynamical Systems

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

Science.gov (United States)

Owens, A. R.; Kópházi, J.; Eaton, M. D.

2017-12-01

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature.

A study of Ni-based WC composite coatings by laser induction hybrid rapid cladding with elliptical spot

International Nuclear Information System (INIS)

Zhou Shengfeng; Huang Yongjun; Zeng Xiaoyan

2008-01-01

Ni-based WC composite coatings by laser induction hybrid rapid cladding (LIHRC) with elliptical spot were investigated. Results indicate that the efficiency using the elliptical spot of 6 mm x 4 mm (the major and minor axis of laser beam are 6 mm and 4 mm, respectively, the major axis is parallel to the direction of laser scanning) is higher than that using the elliptical spot of 4 mm x 6 mm (the major axis is perpendicular to the direction of laser scanning). The precipitated carbides with the blocky and bar-like shape indicate that WC particles suffer from the heat damage of 'the disintegration pattern + the growth pattern', whichever elliptical spot is used at low laser scanning speed. However, at high laser scanning speed, the blocky carbides are only formed if the elliptical spot of 6 mm x 4 mm is adopted, showing that WC particles present the heat damage of 'the disintegration pattern', whereas the fine carbides are precipitated when the elliptical spot of 4 mm x 6 mm is used, showing that WC particles take on the heat damage of 'the radiation pattern'. Especially, the efficiency of LIHRC is increased much four times higher than that of the general laser cladding and crack-free ceramic-metal coatings can be obtained

NMR studies of metallic tin confined within porous matrices

International Nuclear Information System (INIS)

Charnaya, E. V.; Tien, Cheng; Lee, M. K.; Kumzerov, Yu. A.

2007-01-01

119 Sn NMR studies were carried out for metallic tin confined within synthetic opal and porous glass. Tin was embedded into nanoporous matrices in the melted state under pressure. The Knight shift for liquid confined tin was found to decrease with decreasing pore size. Correlations between NMR line shapes, Knight shift, and pore filling were observed. The melting and freezing phase transitions of tin under confinement were studied through temperature dependences of NMR signals upon warming and cooling. Melting of tin within the opal matrix agreed well with the liquid skin model suggested for small isolated particles. The influence of the pore filling on the melting process was shown

Statistical analysis of the Einstein normal galaxy sample. III. Radio and X-ray properties of elliptical and S0 galaxies

International Nuclear Information System (INIS)

Fabbiano, G.; Klein, U.; Trinchieri, G.; Wielebinski, R.; Bonn Universitaet, West Germany; Arcetri, Osservatorio Astrofisico, Florence, Italy; Max-Planck-Institut fuer Radioastronomie, Bonn, West Germany)

1987-01-01

Radioastronomy, optical and X-ray data were used to probe the cause of high X-ray luminosities of 28 radio-quiet elliptical galaxies (RQE) and S0 galaxies previously scanned by the Einstein Observatory. Comparisons were made with similar data on double-lobed 3CR galaxies. Radio luminosities were highly correlated with the X-ray luminosities, agreeing with models of radio nuclear sources in early-type galaxies as accreting compact objects. Additionally, 3CR galaxies seemed to be large-scale versions of normal RQE. The significance of interstellar medium/intracluster medium interactions for high correlations between the core and total radio power from X-ray emitting galaxies is discussed. 54 references

Co-evolution of elliptical galaxies and their central black holes

International Nuclear Information System (INIS)

Ciotti, I.

2009-01-01

After the discovery that supermassive black holes (SMBHs) are ubiquitous at the center of stellar spheroids and that their mass M BH , in the range 10 6 M-10 9 M, is tightly related to global properties of the host stellar system, the idea of the co-evolution of elliptical galaxies and of their SMBHs has become a central topic of modern astrophysics. Here, I summarize some consequences that can be derived from the galaxy Scaling Laws (SLs) and present a coherent scenario for the formation and evolution of elliptical galaxies and their central SMBHs, focusing in particular on the establishment and maintenance of their SLs. In particular, after a first observationally based part, the discussion focuses on the physical interpretation of the Fundamental Plane. Then, two important processes in principle able to destroy the galaxy and SMBH SLs, namely galaxy merging and cooling flows, are analyzed. Arguments supporting the necessity to clearly distinguish between the origin and maintenance of the different SLs, and the unavoidable occurrence of SMBH feedback on the galaxy ISM in the late stages of galaxy evolution (when elliptical galaxies are sometimes considered as dead, red objects), are then presented. At the end of the paper I will discuss some implications of the recent discovery of super-dense ellipticals in the distant Universe. In particular, I will argue that, if confirmed, these new observations would lead to the conclusion that at early epochs a relation between the stellar mass of the galaxy and the mass of the central SMBH should hold, consistent with the present day Magorrian relation, while the proportionality coefficient between M BH and the scale of velocity dispersion of the hosting spheroids should be significantly smaller than that at the present epoch

Elliptical optical solitary waves in a finite nematic liquid crystal cell

Science.gov (United States)

Minzoni, Antonmaria A.; Sciberras, Luke W.; Smyth, Noel F.; Worthy, Annette L.

2015-05-01

The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the "chirp" variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.

From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curves

Directory of Open Access Journals (Sweden)

Salah Boukraa

2007-10-01

Full Text Available We recall the form factors $f^(j_{N,N}$ corresponding to the $lambda$-extension $C(N,N; lambda$ of the two-point diagonal correlation function of the Ising model on the square lattice and their associated linear differential equations which exhibit both a "Russian-doll" nesting, and a decomposition of the linear differential operators as a direct sum of operators (equivalent to symmetric powers of the differential operator of the complete elliptic integral $E$. The scaling limit of these differential operators breaks the direct sum structure but not the "Russian doll" structure, the "scaled" linear differential operators being no longer Fuchsian. We then introduce some multiple integrals of the Ising class expected to have the same singularities as the singularities of the $n$-particle contributions $chi^{(n}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equations satisfied by these multiple integrals for $n = 1, 2, 3, 4$ and, only modulo a prime, for $n = 5$ and 6, thus providing a large set of (possible new singularities of the $chi^{(n}$. We get the location of these singularities by solving the Landau conditions. We discuss the mathematical, as well as physical, interpretation of these new singularities. 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 $chi^{(3}$, actually corresponds to the occurrence of complex multiplication for elliptic curves. The interpretation of complex multiplication for elliptic curves as complex fixed points of generators of the exact renormalization group is sketched. The other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting a geometric interpretation in terms of more general (motivic mathematical structures beyond the theory of elliptic curves. The scaling limit of the (lattice

CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES

OpenAIRE

Riyaz Ahmad Padder; P. Murugadas

2016-01-01

Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.

Unified approach to probing Coulomb effects in tunnel ionization for any ellipticity of laser light.

Science.gov (United States)

Landsman, A S; Hofmann, C; Pfeiffer, A N; Cirelli, C; Keller, U

2013-12-27

We present experimental data that show significant deviations from theoretical predictions for the location of the center of the electron momenta distribution at low values of ellipticity ε of laser light. We show that these deviations are caused by significant Coulomb focusing along the minor axis of polarization, something that is normally neglected in the analysis of electron dynamics, even in cases where the Coulomb correction is otherwise taken into account. By investigating ellipticity-resolved electron momenta distributions in the plane of polarization, we show that Coulomb focusing predominates at lower values of ellipticity of laser light, while Coulomb asymmetry becomes important at higher values, showing that these two complementary phenomena can be used to probe long-range Coulomb interaction at all polarizations of laser light. Our results suggest that both the breakdown of Coulomb focusing and the onset of Coulomb asymmetry are linked to the disappearance of Rydberg states with increasing ellipticity.

Negative elliptic flow of J/ψ's: A qualitative signature for charm collectivity at RHIC

International Nuclear Information System (INIS)

Krieg, D.; Bleicher, M.

2009-01-01

We discuss one of the most prominent features of the very recent preliminary elliptic flow data of J/ψ-mesons from the PHENIX Collaboration (PHENIX Collaboration (C. Silvestre), arXiv:0806.0475 [nucl-ex]). Even within the rather large error bars of the measured data a negative elliptic flow parameter (v 2 ) for J/ψ in the range of p T =0.5-2.5 GeV/c is visible. We argue that this negative elliptic flow at intermediate p T is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity β T for charm quarks that is necessary to reproduce the data is β T (charm) ∝0.55-0.6c and therefore compatible with the flow of light quarks. (orig.) 3

Negative elliptic flow of J/ψ's: A qualitative signature for charm collectivity at RHIC

Science.gov (United States)

Krieg, D.; Bleicher, M.

2009-01-01

We discuss one of the most prominent features of the very recent preliminary elliptic flow data of J/ψ-mesons from the PHENIX Collaboration (PHENIX Collaboration (C. Silvestre), arXiv:0806.0475 [nucl-ex]). Even within the rather large error bars of the measured data a negative elliptic flow parameter (v2) for J/ψ in the range of p T = 0.5-2.5 GeV/ c is visible. We argue that this negative elliptic flow at intermediate pT is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity βT^{} for charm quarks that is necessary to reproduce the data is βT^{}( charm) ˜ 0.55-0.6 c and therefore compatible with the flow of light quarks.

Aerodynamic Comparison of Hyper-Elliptic Cambered Span (HECS) Wings with Conventional Configurations

Science.gov (United States)

Lazos, Barry S.; Visser, Kenneth D.

2006-01-01

An experimental study was conducted to examine the aerodynamic and flow field characteristics of hyper-elliptic cambered span (HECS) wings and compare results with more conventional configurations used for induced drag reduction. Previous preliminary studies, indicating improved L/D characteristics when compared to an elliptical planform prompted this more detailed experimental investigation. Balance data were acquired on a series of swept and un-swept HECS wings, a baseline elliptic planform, two winglet designs and a raked tip configuration. Seven-hole probe wake surveys were also conducted downstream of a number of the configurations. Wind tunnel results indicated aerodynamic performance levels of all but one of the HECS wings exceeded that of the other configurations. The flow field data surveys indicate the HECS configurations displaced the tip vortex farther outboard of the wing than the Baseline configuration. Minimum drag was observed on the raked tip configuration and it was noted that the winglet wake lacked the cohesive vortex structure present in the wakes of the other configurations.

Scattering by a conducting elliptic cylinder with a multilayer dielectric coating

Science.gov (United States)

Caorsi, Salvatore; Pastorino, Matteo; Raffetto, Mirco

1997-11-01

A solution to the electromagnetic scattering of a transverse magnetic plane wave due to a perfectly conducting elliptic cylinder coated by a lossless, nonmagnetic, and elliptic multilayer dielectric is proposed. Despite the lack of orthogonality of the eigenfunctions of the field inside different layers, an efficient recursive procedure for the computation of the solution is devised. It is based on series expansions of the fields in terms of Mathieu functions and on a Galerkin approach. An outline of the procedure is given, and some numerical results, concerning both the field quantities and the radar cross section per unit length, are provided.

Domain decomposition based iterative methods for nonlinear elliptic finite element problems

Energy Technology Data Exchange (ETDEWEB)

Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

1994-12-31

The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

Loop diagrams without γ matrices

International Nuclear Information System (INIS)

McKeon, D.G.C.; Rebhan, A.

1993-01-01

By using a quantum-mechanical path integral to compute matrix elements of the form left-angle x|exp(-iHt)|y right-angle, radiative corrections in quantum-field theory can be evaluated without encountering loop-momentum integrals. In this paper we demonstrate how Dirac γ matrices that occur in the proper-time ''Hamiltonian'' H lead to the introduction of a quantum-mechanical path integral corresponding to a superparticle analogous to one proposed recently by Fradkin and Gitman. Direct evaluation of this path integral circumvents many of the usual algebraic manipulations of γ matrices in the computation of quantum-field-theoretical Green's functions involving fermions

Analytical model of impedance in elliptical beam pipes

CERN Document Server

Pesah, Arthur Chalom

2017-01-01

Beam instabilities are among the main limitations in building higher intensity accelerators. Having a good impedance model for every accelerators is necessary in order to build components that minimize the probability of instabilities caused by the interaction beam-environment and to understand what piece to change in case of intensity increasing. Most of accelerator components have their impedance simulated with finite elements method (using softwares like CST Studio), but simple components such as circular or flat pipes are modeled analytically, with a decreasing computation time and an increasing precision compared to their simulated model. Elliptical beam pipes, while being a simple component present in some accelerators, still misses a good analytical model working for the hole range of velocities and frequencies. In this report, we present a general framework to study the impedance of elliptical pipes analytically. We developed a model for both longitudinal and transverse impedance, first in the case of...

Traffic Efficiency Evaluation of Elliptical Roundabout Compared with Modern and Turbo Roundabouts Considering Traffic Signal Control

Directory of Open Access Journals (Sweden)

Hadi Hatami

2017-02-01

Full Text Available This paper compared the performance of elliptical roundabout with turbo and modern roundabouts. It considers the effects of increasing the central island radius and speed limit on delay and capacity. Three types of roundabouts (modern, turbo and elliptical roundabouts with different numbers of lanes (single lane, two-lane and three-lane were designed. Unsignalized and signalized controls were applied for these roundabouts. The robustness of the designed roundabouts was investigated for saturated and unsaturated flow conditions. Based on the obtained results, increasing the central island radius had both positive and negative effects on delay and capacity. However, a positive effect on these variables was observed in all roundabouts when increasing the speed limit. In unsignalized and signalized control under unsaturated flow conditions, a modern roundabout had lower delay time than an elliptical roundabout. Moreover, in saturated flow, the elliptical roundabout had the best performance in terms of delay. Overall, in comparison with the turbo roundabouts, modern and elliptical roundabouts had the highest capacities in unsignalized and signalized controls. This study can provide useful information for engineers who decide to design a roundabout.

Classification en référence à une matrice stochastique

OpenAIRE

Verdun , Stéphane; Cariou , Véronique; Qannari , El Mostafa

2009-01-01

International audience; Etant donné un tableau de données X portant sur un ensemble de n objets, et une matrice stochastique S qui peut être assimilée à une matrice de transition d'une chaîne de Markov, nous proposons une méthode de partitionnement consistant à appliquer la matrice S sur X de manière itérative jusqu'à convergence. Les classes formant la partition sont déterminées à partir des états stationnaires de la matrice stochastique. Cette matrice stochastique peut être issue d'une matr...

TUNNEL POINT CLOUD FILTERING METHOD BASED ON ELLIPTIC CYLINDRICAL MODEL

Directory of Open Access Journals (Sweden)

N. Zhu

2016-06-01

Full Text Available The large number of bolts and screws that attached to the subway shield ring plates, along with the great amount of accessories of metal stents and electrical equipments mounted on the tunnel walls, make the laser point cloud data include lots of non-tunnel section points (hereinafter referred to as non-points, therefore affecting the accuracy for modeling and deformation monitoring. This paper proposed a filtering method for the point cloud based on the elliptic cylindrical model. The original laser point cloud data was firstly projected onto a horizontal plane, and a searching algorithm was given to extract the edging points of both sides, which were used further to fit the tunnel central axis. Along the axis the point cloud was segmented regionally, and then fitted as smooth elliptic cylindrical surface by means of iteration. This processing enabled the automatic filtering of those inner wall non-points. Experiments of two groups showed coincident results, that the elliptic cylindrical model based method could effectively filter out the non-points, and meet the accuracy requirements for subway deformation monitoring. The method provides a new mode for the periodic monitoring of tunnel sections all-around deformation in subways routine operation and maintenance.

Capture Matrices Handbook

Science.gov (United States)

2014-04-01

materials, the affinity ligand would need identification , as well as chemistries that graft the affinity ligand onto the surface of magnetic...ACTIVE CAPTURE MATRICES FOR THE DETECTION/ IDENTIFICATION OF PHARMACEUTICALS...6 As shown in Figure 2.3-1a, the spectra exhibit similar baselines and the spectral peaks lineup . Under these circumstances, the spectral

Binary Positive Semidefinite Matrices and Associated Integer Polytopes

DEFF Research Database (Denmark)

Letchford, Adam N.; Sørensen, Michael Malmros

2012-01-01

We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature-the cut, boolean qua...

Magnetic properties of elliptical and stadium-shaped nanoparticles: Effect of the shape anisotropy

Energy Technology Data Exchange (ETDEWEB)

Corona, R.M. [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Altbir, D. [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Escrig, J., E-mail: jescrigm@gmail.com [Departamento de Fisica, Universidad de Santiago de Chile (USACH), Avda. Ecuador 3493, 917-0124 Santiago (Chile); Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Avda. Ecuador 3493, 917-0124 Santiago (Chile)

2012-11-15

Elliptical and stadium-shaped nanoparticles as a function of their geometry have been investigated using numerical simulations. The effect of the shape anisotropy of the particles on coercivity and remanence together with the angular dependence of the remanence and coercivity are addressed. Our results demonstrate that the stadium-shaped particles have many of the outstanding properties of elliptical particles, but also have unique properties, such that the coercivity and remanence remain stable for a wide range of geometry parameters, and exhibit a peculiar angular dependence in the coercivity. These properties suggest that they can be useful for applications in the area of magnetic recording systems. - Highlights: Black-Right-Pointing-Pointer Coercivity and remanence are strongly affected by the shape anisotropy of the particles. Black-Right-Pointing-Pointer Coercivities for ellipses are nearly three times the obtained for stadium-shaped particles. Black-Right-Pointing-Pointer Elliptical particles with {delta}{<=}0.6, the hystereses resemble the square loops of wires. Black-Right-Pointing-Pointer An anhisteretic behavior appears for {theta}=90 Degree-Sign for elliptical particles, which do not appear in stadium-shaped particles. Black-Right-Pointing-Pointer Stadium-shaped particles have unique properties that allow us to suggest them for applications.