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Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
We construct normalized differentials on families of curves of infinite genus. Such curves are used to investigate integrable PDE's such as the focusing Nonlinear Schr{\"o}dinger equation.
Possibilities for defining the radial derivative of the delta distribution $\delta(\underline{x})$ in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Sch\"odinger equation (DNLS). These transformations are shown to lead to two solution formulas for DNLS in…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
Starting from the standard form of the five discrete Painlev\'e equations we show how one can obtain (through appropriate limits) a host of new equations which are also the discrete analogues of the continuous Painlev\'e equations. A…
Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…
The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its…
We discuss some variants of cone theorem for movable curves in any codimensions.
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…
Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representation for various objects using a well-structured family of…
We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.
In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…
This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and…
In this paper, we derive global bounds for the H\"older norm of the gradient of solutions of graphic mean curvature flow with boundary of arbitrary codimension.
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.