Related papers: Localized versions of extremal problems

We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…

For rational functions, we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erd\"os-Lax and Tur\'an to rational functions R. In return these…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…

Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.

The extension of an $r$-uniform hypergraph $G$ is obtained from it by adding for every pair of vertices of $G$, which is not covered by an edge in $G$, an extra edge containing this pair and $(r-2)$ new vertices. In this paper we determine…

We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing…

We use actions by finite cyclic groups to derive generalizations of three classical theorems from elementary number theory.

We unify the recently developed abstract theories of universal series and extended universal series to include sums of the form $\sum_{k=0}^n a_k x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\geq k\geq 0}$ in a topological vector…

Recently, Grynkiewicz et al. [{\it Israel J. Math.} {\bf 193} (2013), 359--398], using tools from additive combinatorics and group theory, proved necessary and sufficient conditions under which the linear congruence $a_1x_1+\cdots…

We investigate natural Tur\'an problems for mixed graphs, generalizations of graphs where edges can be either directed or undirected. We study a natural \textit{Tur\'an density coefficient} that measures how large a fraction of directed…

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

We investigate a generalization of the {\L}o\'s-Tarski preservation theorem via the semantic notion of \emph{preservation under substructures modulo $k$-sized cores}. It was shown earlier that over arbitrary structures, this semantic notion…

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…

The Tur\'an problem asks for the largest number of edges in an $n$-vertex graph not containing a fixed forbidden subgraph $F$. We construct a new family of graphs not containing $K_{s,t}$, for $t= C^s$, with $\Omega(n^{2-1/s})$ edges…

We generalise Livens theorem, showing that Hamiltonian equation on the vector bundle $E^\ast\rightarrow M$, dual to a general algebroid $E\rightarrow M$, can be derived by means of a variational principle. The framework can be used to…

In this paper we show that it is possible to project onto the solutions of the $\mathfrak{grt}$ hexagon equation. We also consider in some sense generalized hexagon equations and other symmetry equations for multiple argument maps between…

We investigate solvability of a continuous Dirichlet boundary value problem together with its classical discretization using a gobal diffeomorphism theorem.

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…