The non-linear relation between electric polarization and electric field strength is achieved through introducing the retarded electromagnetic interactions between classical charge particles. The result agrees with the phenomenological theory in current non-linear optics, means that the non-linear phenomena in optics come from the retarded electromagnetic interaction between charged particles. ...

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...

El artículo tiene como propósito establecer un diálogo entre Watchmen, el cómic de Alan Moore y Dave Gibbons, su continuación televisiva, realizada bajo la dirección creativa Damon Lindelof. Este se establece sobre contenido político ambas obras, puntualmente en crítica al neoliberalismo régimen económico. Argumentamos que espacio temático narrativo tanto del serie es similar porque ambos const...

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...