We consider a directed polymer model in dimension 1 + , where the disorder is given by occupation field of Poisson system independent random walks on Z . In suitable continuum and weak limit, we show that family quenched partition functions converges to Stratonovich solution multiplicative stochastic heat equation (SHE) with Gaussian noise, whose space-time covariance kernel. contrast case whit...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

Let X = G=K be an odd-dimensional semisimple Riemannian symmetric space of the noncompact type, and suppose that all Cartan subgroups of G are conjugate. Let u be a real-valued classical solution of the modiied wave equation u tt = ((+ k)u on R X, the Cauchy data of which are supported in a closed metric ball of radius a at time t = 0. Here t is the coordinate on R, is the (nonpositive deenite)...

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j−k with k > 1. For the Wiener measure occurring in many applications we have k = 2. We want to compute an ε-approximation to path integrals whose integrands are at least Lipschitz. We prove: • Path ...

We study path integration on a quantum computer that performs quantum summa-tion. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j −k with k > 1. For the Wiener measure occurring in many applications we have k = 2. We want to compute an ε-approximation to path integrals whose integrands are at least Lipschitz. We prove: • Pat...

K e y w o r d s M u l t i p l e Wiener integral, Hu-Meyer theorem, Henstock integral. 1. I N T R O D U C T I O N Classically, it is well known that the Riemann approach cannot be used to define stochastic integrals. However, it has been proved that the generalized Riemann approach (with nonuniform meshes), also called the Henstock's approach, can be used to study stochastic integrals. See detai...

whereas there is an exact linear relation between the wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal wiener indices exhibit a completely different behavior: correlation between terminal wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. in this article, we analyze the basic properties of terminal wiener indices...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....