Related papers: Concerning problems about cardinal invariants on B…
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
The paper deals with locally bounded solutions of a Schilling's problem.
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
In classical invariant theory, the Gr\"obner base of the ideal of syzygies and the normal forms of polynomials of invariants are two core contents. To improve the performance of invariant theory in symbolic computing of classical geometry,…
This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
We consider a conformally invariant version of the Calder\'on problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main…
In work the numerical solutions of Kundu-Eckhaus equation are presented. The conditions of dominate nonlinearity or disperse are cleared up.
A general discussion of equations with universal invariance for a scalar field is provided in the framework of Lagrangian theory of first-order systems.
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and…
Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial…
In this note I make some comments on the review MR2723767 (2011m:03064) appeared in Mathematical Reviews
We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights.
We directly apply the theory of viscosity solutions to partial differential equations of order greater than two. We prove that there exists a solution in $C^{2,\alpha}(B_R)\cap C(\overline{B_R})$ for the inhomogeneous $\infty$-Bilaplacian…
Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.
Boggio's formula in balls is known for integer-polyharmonic Dirichlet problems and for fractional Dirichlet problems with fractional parameter less than 1. We give here a consistent formulation for fractional polyharmonic Dirichlet problems…
We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…