相关论文: A two-parameter generalization of the complete ell…
Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe…
One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter $\alpha$. For the regularized model it was shown that all static correlation…
We apply an integral formula obtained by the author for a general $G$--structure to the case of $G=G_2$. We derive an integral formula relating curvatures and some quadratic invariants of the endomorphism induced by the intrinsic torsion.…
We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and…
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised $\sin_{p,q}$ in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
First some definite integrals of W. H. L. Russell, almost all with trigonometric function integrands, are derived, and many generalized. Then a list is given in Russell-style of generalizations of integral identities of Amdeberhan and Moll.…
We study some Diophantine problems related to triangles with two given integral sides. We solve two problems posed by Zolt\'an Bertalan and we also provide some generalization.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
We discuss the basic properties of various versions of two variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the…
We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a…
We classify two dimensional integrable mappings by investigating the actions on the fiber space of rational elliptic surfaces. While the QRT mappings can be restricted on each fiber, there exist several classes of integrable mappings which…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
We show that all Eichler integrals, and more generally all "generalized second order modular forms" can be expressed as linear combinations of corresponding generalized second order Eisenstein series with coefficients in classical modular…
We investigate the analytic classification of two dimensional neighborhoods of an elliptic curve with torsion normal bundle. We provide the complete analytic classification for those neighborhoods in the simplest formal class and we…
The table of Gradshteyn and Ryzhik contains many entries that are related to elliptic integrals. We present a systematic derivation of some of them.
We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…