相关论文: An elliptic determinant transformation

In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…

We define and study "hyperbolic forcing".

We compute stationary gravitational descendants in symplectic ellipsoids of any dimension, and use these to derive a number of new recursive formula for punctured curve counts in symplectic manifolds with ellipsoidal ends. Along the way we…

We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated…

The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.

In this paper, in continuation of our work, on the determinants of cubic -matrix of order 2 and order 3, we have analyzed the possibilities of developing the concept of determinant of cubic-matrix with three indexes, studying the…

The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…

We prove the determinant connectivity matrix formula. Mathematically, the proof introduces novel techniques based on an algebraic approach and connectivity properties. Although this is the second part of a previous paper and has its…

We investigate the elliptic umbilic canonical integral with an approach based on a series expansion of its initial distribution shifted to the caustic points. An absolutely convergent integral representation for the elliptic umbilic is…

We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BC_n and A_n; as a special case, we recover some integral identities conjectured by van Diejen and…

We discuss elliptic Pl\"ucker transformations of three-dimensional elliptic spaces. These are permutations on the set of lines such that any two related (orthogonally intersecting or identical) lines go over to related lines in both…

We give a formula for matrix exponentials and partial fraction decompositions.

We review recent progress in potential theory of second-order elliptic operators and on the metastable behavior of Markov processes.

In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be…

We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's…

We derive expressions for the partition function p(n), with n in the form 7k+a, as (k+1)-dimensional determinants.

The manuscript establishes a series expansion of the core integral that relates changes in longitude and latitude along the geodetic line in oblate elliptical coordinates, and of a companion integral which is the path length along this line…

Exton [Ganita 54(2003)13-15] obtained numerous new quadratic transformations involving hypergeometric functions of order two and of higher order by applying various known classical summation theorems to a general transformation formula…

We consider second-order partial differential operators $H$ in divergence form on $\Ri^d$ with a positive-semidefinite, symmetric, matrix $C$ of real $L_\infty$-coefficients and establish that $H$ is strongly elliptic if and only if the…

The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a…