Related papers: On multiplicative properties of combinatorial cube…
Following the sum-product paradigm, we prove that for a set $B$ with polynomial growth, the product set $B.B$ cannot contain large subsets with size of order $|B|^2$ with small doubling. It follows that the additive energy of $B.B$ is…
In this paper, we derive an explicit combinatorial formula for the number of $k$-subset sums of quadratic residues over finite fields.
This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is…
The least upper bounds of the powers extracted and scattered by bi-anisotropic particles are investigated analytically. A rigorous derivation for particles having invertible polarizability tensors is presented, and the particles with…
We study solutions to the equation $a+b=c$, where $a,b,c$ form a triple of coprime natural numbers. The $abc$ conjecture asserts that, for any $\epsilon>0$, such triples satisfy $\mathrm{rad}(abc) \ge c^{1-\epsilon}$ with finitely many…
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
We discuss combinatorial conditions for the existence of various types of reductions between equivalence relations, and in particular identify necessary and sufficient conditions for the existence of injective reductions.
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we…
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
We say that a set $S$ is additively decomposed into two sets $A$ and $B$ if $S = \{a+b : a\in A, \ b \in B\}$. A. S\'ark\"ozy has recently conjectured that the set $Q$ of quadratic residues modulo a prime $p$ does not have nontrivial…
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…
We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples…
From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the integrals of functions associated with Legendre…
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.
A recent paper of A. Sofo proves some results about sums of products of quadratic alternating harmonic numbers and reciprocal binomial coefficients. In this paper, we extend his result to cubic alternating harmonic number sums and develop…
The twin prime conjecture asserts that there are infinitely many pairs of primes that differ by two. While recent advances have improved our understanding of bounded prime gaps, the conjecture remains unresolved. This paper refines the…