Related papers: A Note on Matching Variables to Equations

We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some…

This note explains how to prove that for any simply-connected reductive group G and any infinite field k, the inclusion of k in k[t] induces an isomorphism on homology. This generalizes results of Soule and Knudson.

A polynomial P in n complex variables is said to have the "half-plane property" (or Hurwitz property) if it is nonvanishing whenever all the variables lie in the open right half-plane. Such polynomials arise in combinatorics, reliability…

This is the English translation of the short note where the first nontrivial tetrahedron relation (solution of the Zamolodchikov tetrahedron equation) with variables on the edges was presented.

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

This paper develops the fundamentals of modular representation theory for finite monoids, introducing the decomposition matrix and exploring its connection to Brauer characters. We define modular characteristic and explain how the…

The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let $n\in \mathbb{N}$ be arbitrary, $\mathbb{K}$ a field and $f_{1}, \ldots,…

We prove a Liv\v{s}ic-type theorem for H\"older continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever $(f,\mu)$ is a non-uniformly hyperbolic system and $A:M \to GL(d,\mathbb{R})…

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within the category of Lie algebras. We first show that no Lie…

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a…

Fillmore Theorem says that if A is an nxn complex non-scalar matrix and {\gamma}_1,...,{\gamma}_{n} are complex numbers with {\gamma}_1+...+{\gamma}_{n}=trA, then there exists a matrix B similar to A with diagonal entries…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

We generalize two embedding theorems and investigate the existence and multiplicity of nontrivial solutions for a $(p,q)$-Laplacian coupled system with perturbations and two parameters $\lambda_1$ and $\lambda_2$ on locally finite graph. By…

Let $F(\boldsymbol x)$ be a homogeneous polynomial in $n \ge 1$ variables of degree $1 \leq d \leq n$ with integer coefficients so that its degree in every variable is equal to $1$. We give some sufficient conditions on $F$ to ensure that…

A system of linear equations $L$ is common over $\mathbb{F}_p$ if, as $n\to\infty$, any 2-coloring of $\mathbb{F}_p^n$ gives asymptotically at least as many monochromatic solutions to $L$ as a random 2-coloring. The notion of common linear…

In this article, we investigate homogeneous versions of certain nonlinear Ramsey-theoretic results, with three significant applications. As the first application, we prove that for every finite coloring of $\mathbb{Z}^+$, there exist an…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

We show that the homotopy category of injective $A$-modules is generically trivial if and only if the derived category of all modules is generically trivial for an algebra $A$. Moreover we show some connections between the generic objects,…