72 research outputs found
Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, 28 April 2015
No full textA.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada. He is currently the Director of the Centre for Mathematical and Statistical Sciences India. His research contributions cover a wide spectrum of topics in mathematics, statistics, physics, astronomy, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, and a member of the International Statistical Institute. He is a founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He was instrumental in the implementation of the United Nations Basic Space Science Initiative (1991–2012). This paper highlights research results of A.M. Mathai in the period of time from 1962 to 2015. He published over 300 research papers and over 25 books
Linear Algebra: a Course for Physicists and Engineers/ Arak M. Mathai, Hans J. Haubold.
No full textEbpS Open AccessIn English.Includes bibliographical references and index.In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements suc.Frontmatter -- Preface -- Acknowledgement -- Contents -- List of Symbols -- 1. Vectors -- 2. Matrices -- 3. Determinants -- 4. Eigenvalues and eigenvectors -- 5. Some applications of matrices and determinants -- 6. Matrix series and additional properties of matrices -- References -- Index.1 online resource (467 pages
On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data
No full textAn entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided
Some Matrix-Variate Models Applicable in Different Areas
No full textMatrix-variate Gaussian-type or Wishart-type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when the factors involving a determinant and a trace enter into the model or a matrix-variate gamma-type or Wishart-type model with an exponential trace having an arbitrary power, they are extremely difficult to handle. One such model with factors involving a trace and a determinant and the exponential trace having an arbitrary power, in the real domain, is known in the literature as the Kotz model. No explicit evaluation of the normalizing constant in the Kotz model seems to be available. The normalizing constant that is widely used in the literature, is interpreted as the normalizing constant in the general model, and that is referred to as a Kotz model does not seem to be correct. One of the main contributions in this paper is the introduction of matrix-variate distributions in the real and complex domains belonging to the Gaussian-type, gamma-type, and type 1 and type 2 beta-types, or Mathai’s pathway family, when the exponential trace has an arbitrary power and explicit evaluations of the normalizing constants therein. All of these models are believed to be new. Another new contribution is the logistic-based extensions of the models in the real and complex domains, with the exponential trace having an arbitrary exponent and connecting to extended zeta functions introduced by this author recently. The techniques and steps used at various stages in this paper will be highly useful for people working in multivariate statistical analysis, as well as for people applying such models in engineering problems, communication theory, quantum physics, and related areas, apart from statistical applications
On Extended d-D Kappa Distribution
No full textThermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields are described by kappa distributions. The kappa distribution provides a replacement for the Maxwell-Boltzmann distribution which can be considered as a generalization for describing systems characterized by local correlations among their particles as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai.10 page
A Versatile Integral in Physics and Astronomy and Fox’s H-Function
No full textThis paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck–Cohen superstatistics in statistical mechanics, and Mathai’s pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox’s H-function are pointed out
On Extended d-D Kappa Distribution
No full textThe thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields can be described by kappa distributions. The kappa distribution provides a replacement for the Maxwell–Boltzmann distribution, which can be considered as a generalization for describing systems characterized by local correlations among their particles, as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai. The aim of the present paper is to bring to attention the application of various forms of the kappa distribution, its various special cases and its generalizations, which, in scalar-variable and multivariate situations, belong to a general family of distributions known as Mathai’s pathway models, comprising three different families of functions, namely the generalized type-1 beta, type-2 beta and gamma families. Through one parameter, known as the pathway parameter, one will be able to reach all the three families of functions and the stages of transitioning from one family to another. After pointing out the connection of multivariate (vector-variate) kappa distributions to the multivariate pathway model, the multivariate kappa distribution is extended to the real matrix-variate case by working out the various forms and by evaluating the normalizing constants of the various forms of the matrix-variate case explicitly. It is also pointed out that the pathway models are available for the scalar, vector and rectangular matrix-variate cases in the real domain as well as in the complex domain
Mathai-Quillen forms and Lefschetz theory
No full textMathai-Quillen forms are used to give an integral formula for the Lefschetz number of a smooth map of a closed manifold. Applied to the identity map, this formula reduces to the Chern-Gauss-Bonnet theorem. The formula is computed explicitly for constant curvature metrics. There is in fact a one-parameter family of integral expressions. As the parameter goes to infinity, a topological version of the heat equation proof of the Lefschetz fixed submanifold formula is obtained. As the parameter goes to zero and under a transversality assumption, a lower bound for the number of points mapped into their cut locus is obtained. For diffeomorphisms with Lefschetz number unequal to the Euler characteristic, this number is infinite for most metrics, in particular for metrics of non-positive curvature.First author draf
Evolution and future trends in battle injuries to the CNS
No full textDespite advances in personal protection, brain and spinal injuries amongst combatants pose significant management challenges. Battle field medical care has evolved over the year. In this article we discuss evolutions of military medicine, study current protocols and outcomes and discuss future perspectives. Mention is also made of some original work by the author
Dynamics of finite-sized light spheres in turbulence
No full textWe report experimental results on the Lagrangian dynamics of finite-size light particles in turbulence. Using an orthogonal camera setup and 3D particle tracking, we study the velocity and acceleration statistics of rigid light spheres in a water tunnel with nearly homogeneous and isotropic turbulence. The Reynolds number (ReY) is varied from 180 to 300, and the study covers a range of size ratios (4 < D/η < 16) for marginally light spheres. We find that the normalised acceleration PDF decreases in intermittency with increasing size ratio - in qualitative agreement with the predictions of the Faxén corrected model. We also present preliminary results on the rotational dynamics of large light spheres in turbulence
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