相关论文: The Whitham equations revisited

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a non-archimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph, and show that in type A,…

We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…

The work studies some Difference equations, which are connected with Mejer's function.

We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet $L$-functions over function fields. In some situations, we are actually able to establish finer…

New results on the convexity of geodesic-length functions on Teichm\"{u}ller space are presented. A formula for the Hessian of geodesic-length is presented. New bounds for the gradient and Hessian of geodesic-length are described. A…

We review some of the uses of Whitham hierarchies in the context of the theory of the prepotential in N=2 supersymmetric gauge theories. We focus on the structure of the contact terms in the twisted topological theory, and on the connection…

This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein…

We revisit the classic Wigner semi-circle from two different angles. One consists in studying the Stieltjes transform directly on the real axis, which does not converge to a fixed value but follows a Cauchy distribution that depends on the…

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…

We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of…

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…

The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the…