Eigenvalue distributions for some correlated complex sample covariance matrices

The distributions of the smallest and largest eigenvalues for the matrix product $Z^\dagger Z$, where $Z$ is an $n \times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m \times m$ determinants. In the case of correlation along rows, these expressions are computationally more efficient than those involving sums over partitions and Schur polynomials reported recently for the same distributions.Comment: 11 page

AUTO-IMMUNITY IN CHRONIC ADRENAL INSUFFICIENCY

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CLINICO-LABORATORY CHARACTERISTICS AND PATHOGENETIC FEATURES OF THE MORGAGNI-STEWART-MOREL SYNDROME

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CHANGES IN THE FUNCTIONAL STATE OF THE LIVER IN THYROTOXICOSIS PATIENTS

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Isolation and primary identification of shiga toxin producing Escherichia coli O157 in dairy cattle

During the last years, the significance of diseases associated etiologically to Shiga-toxin producing Escherichia coli (STEC) is continuously increasing at a global scale, while the O157 serotype is con-sidered as one of the most important pathogens of animal origin. Large ruminants play a key role in the epidemiology of E. coli diseases among men. Bovine faeces are a primary source of contamina-tion of the environment and foods with this agent. The purpose of this study was to test a specific, microbiological algorithm for primary identification of STEC isolates from bovine faeces using sorbi-tol McConkey agar supplemented with cefixime and tellurite. The attempts were focused not only on increasing the sensitivity and specificity of serotype identification, but also on optimisation of labour and analysis costs. From May 2013 to October 2014, a total number of 1104 faecal swab samples from calves 3 to 6 months of age were collected from 19 farms in different administrative and geo-graphical regions of Bulgaria. Thirty six sorbitol-negative E. coli isolates (3.26%) were detected as belonging to the O157 serotype after slide agglutination test

Noncentral bimatrix variate generalised beta distributions

In this paper, we determine the density functions of nonsymmetrised doubly noncentral matrix variate beta type I and II distributions. The nonsymetrised density functions of doubly noncentral and noncentral bimatrix variate generalised beta type I and II distributions are also obtained.Comment: 14 page

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

Genesis of the Entrepreneurial Idea in the Economic Theory: Review and Interpretation

The paper, using the historical approach, reveals the sources and the basis of formation of the present-day knowledge on the essence of entrepreneurship prior to the middle of the 20 century. The views of representatives of the main economic schools are being analyzed. The specific national features and conditions having given birth to the idea of entrepreneurship are being stressed. Four major directions in the history and development of the theory of entrepreneurship are being outlined and examined: the limited entrepreneurial knowledge; the innovation approach of J. Schumpeter; the cultural-organizational direction of M. Weber and the Austrian approach of “entrepreneurial discovery”. The basic idea, defended in the paper, is that the development of the theory of entrepreneurship is dependent on two fundamental factors: economic freedom and knowledge.