相关论文: Popular difference sets

Let $\mathbb{F}_q$ be a finite field of order $q$. Iosevich and Rudnev (2005) proved that for any set $A\subset \mathbb{F}_q^d$, if $|A|\gg q^{\frac{d+1}{2}}$, then the distance set $\Delta(A)$ contains a positive proportion of all…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…

The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…

The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…

In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…

In this work we describe an explicit, simple, construction of large subsets of F^n, where F is a finite field, that have small intersection with every k-dimensional affine subspace. Interest in the explicit construction of such sets, termed…

This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…

We compare the size of the difference set $A-A$ to that of the set $kA$ of $k$-fold sums. We show the existence of sets such that $|kA| < |A-A|^{a_k}$ with $a_k<1$.

Let $A$ be a finite multiset of powers of a positive integer $d>1$. We describe the structure of the set $\mathrm{span}(A)$ of all sums of submultisets of $A$, and in particular give a criterion of $\mathrm{span}(A)=\mathrm{span}(B)$ for…

This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.

In this article we survey some of the recent developments in the structure theory of set addition.

There have been major developments in the theory of moduli of varieties in the past decade, essentially settling the construction of moduli spaces of log canonically polarized slc pairs and moduli spaces of K-polystable log Fano pairs.…

We give a modern account of the construction and structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.

We give an explicit construction of a large subset of F^n, where F is a finite field, that has small intersection with any affine variety of fixed dimension and bounded degree. Our construction generalizes a recent result of Dvir and Lovett…

Certain new inequalities for the sums of factorials are presented.

The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…

New lower bounds involving sum, difference, product, and ratio sets for a set $A\subset \C$ are given. The estimates involving the sum set match, up to constants, the one obtained by Solymosi for the reals and are obtained by generalising…

We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…