The local zeta functions (also called Igusa’s zeta functions) over p-adic fields are connected with the number of solutions of congruences and exponential sums mod pm. These zeta functions are defined as integrals over open and compact subsets with respect to the Haar measure. In this paper, we introduce new integrals defined over submanifolds, or more generally, over non-degenerate complete in...

— In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of skew symmetric matrices. In particular, we relate the multiple integrals of a determinant, which arises while finding the eigenvalue distributions, in terms ...

Higher order variational functionals, emerging in the study of problems from materials science and engineering, have attracted a great deal of attention in last few years (e.g. [4], see [5]). In particular, the regularity of minimizers of such functionals has been studied very recently. In [15] and [16] the partial Ck,α regularity has been established for quasiconvex integrals with a p-power gr...

An integral equations method for a three-dimensional crack in a finite or infinite body is achieved by means of Kupradze potentials. Surface and through cracks can be studied according to this approach with only the assumption that the body has a linear, elastic, homogeneous and isotropic behavior. Both singular surface integrals and line integrals appear in the derived equations. For surface a...

We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic generation and photon cascades. For each model, we construct a complete set of commuting integrals of motion of the Hamiltonian, fully characterize the common eigen...

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order and this order is at most 4, we prove that ...

The paper deals with the aggregation of classification rules by means of fuzzy integrals, in particular with the fuzzy measures employed in that aggregation. It points out that the kinds of fuzzy measures commonly encountered in this context do not take into account the diversity of classification rules. As a remedy, a new kind of fuzzy measures is proposed, called similarity-aware measures, an...

In Burrage and Burrage (1996) it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In ...

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known f...

We find new representations for Itzykson-Zuber like angular integrals for arbitrary β, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat Lebesge measure integral, and we deduce some recursion formula on n. The same methods gives also the Shatashvili’s type moments. Finally we prove that, in agreem...