Related papers: (1 + d/dz)^(-1)
We list all connected components of sets of non-discriminant functions near all {\em parabolic} function singularities (which are the second most important family of singularity classes of smooth functions after {\em simple} singularities).…
In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous…
The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method for nonlinear PDEs. In this regard, we consider an appropriate space ML(X) of normal lower…
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
The Musielak--Orlicz setting unifies the variable exponent, Orlicz, weighted Sobolev, and double-phase spaces. They inherit technical difficulties resulting from general growth and inhomogeneity. In this survey we present an overview of…
We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and…
We consider the nonlinear equation $-\frac{1}{m}=z+Sm$ with a parameter $z$ in the complex upper half plane $\mathbb{H} $, where $S$ is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values…
We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on $\mathbb{Z}^d$. We prove that the vector space of harmonic functions growing at most linearly is…
In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
We develop a numerical solver, that extends the computational framework considered in [Phys. Rev. D 65, 084016 (2002)], to include scalar perturbations of nonrotating black holes. The nonlinear Einstein-Klein-Gordon equations for a massless…
We give some classes of power maps with low $c$-differential uniformity over finite fields of odd characteristic, {for $c=-1$}. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect $c$-nonlinear…
We examine codimension--1 topological defects whose associated worldline is geodesically embedded in $\AdS_{2}$. This discussion extends a previous study of exact analytical solutions to the equations of motion of topological defects in…
Let M be a singular irreducible complex manifold of dimension n. There are Q divisors D[-1], D[0], D[1],...,D[n+1] on Nash's manifold U -> M such that D[n+1] is relatively ample on bounded sets, D[n] is relatively eventually basepoint free…
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We…
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases…
It is shown that perturbations around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, can be canonically simplified, a property that is shown to hold to any order in perturbation theory. Recalling that the…
We study higher-derivative gravity theories in arbitrary space-time dimension d with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to…
We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only…
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.