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We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it a priori} unknown interior region. We prove that positive solutions have a…

We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of the unknowns in different directions, and the sources.…

We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper…

We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third…

The theory of subfactors of groups, together with the associated notions of subindices and index stability for groupsandtheirsubsets, hasrecentlybeenintroducedandsystematicallydeveloped. Theseconceptsexhibitdeepconnections with additive…

The present article is focused on the study of a special class of systems of nonlinear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of the study of such systems, we develop a…

We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.

We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

The concept of additive basis has been investigated in the literature for several mathematicians which works with number theorem. Recently, the concept of finitely stable additive basis was introduced. In this note we provide a…

We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.

The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

We lift the classical theorem of Arnol'd on homological stability for configurations spaces of the plane to the motivic world. More precisely, we prove that the schemes of unordered configurations of points in the affine line satisfy…

In this paper, we consider radial symmetry property of positive solutions of an integral equation arising from some higher order semi-linear elliptic equations on the whole space $\mathbf{R}^n$. We do not use the usual way to get symmetric…

Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G has no subgroups isomorphic to the additive or the commutative…

This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…

Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for…