Abstract. Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σij(n) √ n X ij , the X n ij being independent and identically distributed, centered with unit variance and satisfying some mild moment assumption. Consider now a deterministic N×n matrix An whose columns and rows are uniformly bounded for the Euclidean norm. Let Σn = Yn + An. We prove in this articl...

Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is p...

Let ??RN be a smooth bounded domain. In this paper we investigate the existence of least energy positive solutions to following Schrödinger system with d?2 equations??ui+?iui=|ui|p?2ui?j=1d?ij|uj|p in ?,ui=0 on ??,i=1,...,d, case critical exponent 2p=2?=2NN?2 high dimensions N?5. We treat focusing (?ii>0 for every i) variational setting ?ij=?ji i?j, dealing Brézis-Nirenberg type problem: ??1(?)...

We provide a new characterization of the Dirichlet distribution. Let ij , 1 i k; 1 j n, be positive random variables that sum to unity. Deene i = P n j=1 ij , I = f i g k?1 i=1 , jji = ij = P j ij , and Jji = f jji g n?1 j=1. We prove that if f I ; Jj1 ; : : :; Jjk g are mutually independent and f J ; Ij1 ; : : :; Ijn g are mutually independent (where J and Ijj are deened analogously), and assu...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...

The weighted kappa statistic provides a measure of agreement κ w (scorer1, scorer2) between two scorers (scorer1 and scorer2) who classify observations into one of several groups or categories. The following description is adapted from reference (E1). Two scorers (scorer1 and scorer2) analyze a set of N observations by classifying each observation into one of g groups. This leads to a g × g-mat...

The theoretical background of spatial interaction models is reviewed and used as a basis for the derivation of a novel approach for directly calibrating spatial interaction models concurrently with the main solution procedure. The analysis was prompted by a link with Fisher Information. The new approach is compared with a number of earlier approaches, particularly that of Sen and Smith. 1. Thre...

Using resonance ultrasound spectroscopy, we measured the monocrystal elastic-stiffness coefficients, the Voigt C ij, of TiB2. With hexagonal symmetry, TiB2 exhibits five independent C ij: C 11, C 33, C 44, C 12, C 13. Using Voigt-Reuss-Hill averaging, we converted these monocrystal values to quasiisotropic (polycrystal) elastic stiffnesses. Briefly, we comment on effects of voids. From the C ij...

A matrix $A$ is totally positive (or non-negative) of order $k$, denoted $TP_k$ $TN_k$), if all minors size $\leq k$ are non-negative). It well-known that such matrices characterized by the variation diminishing property together with sign non-reversal property. We do away former, and show only every submatrix formed from at most $k$ consecutive rows columns has In fact this can be strengthened...

For n 2, the boolean quadric polytope P n is the convex hull in d := ? n+1 2 dimensions of the binary solutions of x i x j = y ij , for all i < j in N := f1; 2; :::; ng. The polytope is naturally modeled by a somewhat larger polytope; namely, Q n the solution set of y ij x i , y ij x j , x i + x j 1 + y ij , y ij 0, for all i; j in N. In a rst step toward seeing how well Q n approximates P n , ...