相关论文: The Generating Formula for The Solutions to The As…

This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…

This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.

Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…

The WDVV equation is satisfied by the genus 0 correlation functions of any topological field theory in two dimensions coupled to topological gravity, and may be used to determine the genus 0 (rational) Gromov-Witten invariants of many…

We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and…

The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \[d_{k}(xy)=\sum_{i=0}^{k}\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \qquad (x,y\in \R,\,k\in\{0,\ldots,n\}) \] is studied, where…

We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…

We consider exact solutions to the problem of ballistic aggregation in a flow of adhesive particles, providing a model for large-scale structure formation in cosmology within the framework of the Zel'dovich approximation. Two different…

Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…

Exact solutions of the Wheeler-DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schr\"odinger wavefunctionals having support on 3-metrics of constant spatial…

A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.

We establish long time soliton asymptotics for the nonlinear system of Maxwell equations coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the long time approximation, any…

We give a family of solutions of Witten-Dijkgraaf-Verlinde-Verlinde equations in $n$-dimensional space. It is defined in terms of $BC_{n}$ root system and $n+2$ independent multiplicity parameters. We also apply these solutions to define…

A formula to construct classic exact solutions to Tricomi partial differential equation. The steps to obtain this formula require only elementary resolution of a simple system of first order PDEs.

We explicitly obtain the $m$-soliton solutions of the (1+2)-dimensional matrix Davey-Stewartson equation from the known general solution of the matrix Toda chain with fixed ends. We write these solutions in terms of $m+m$ independent…

A well known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper we present a generalization of this construction for the…

Analytical solution of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of…

A string-inspired duality symmetry of the spatially flat Friedmann equations of general-relativistic cosmology is discussed and generalized, providing a map between exact solutions corresponding to different values of the barotropic index.

This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs.