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...

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 , ...

We consider the problem of characterizing nonnegativity of the Moore-Penrose inverse for matrix perturbations of the type A − XGY, when the Moore-Penrose inverse of A is nonnegative. Here, we say that a matrix B = (b ij ) is nonnegative and denote it by B ≥ 0 if b ij ≥ 0, ∀i, j. This problemwasmotivated by the results in [1], where the authors consider an M-matrix A and find sufficient conditio...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...