Related papers: On additive decompositions of primitive elements i…

We investigate the construction of circulant matrices derived from primitive roots over finite fields. Our approach reduces exponential sums to Jacobi sums, thereby establishing explicit connections between character theory and matrix…

We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…

We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…

This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…

The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…

We discuss the implications of causality on a primordial magnetic field. We show that the residual field on large scales is much more suppressed than usually assumed and that a helical component is even more reduced. Due to this strong…

This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz…

In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary…

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…

We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like…

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…

These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular,…

We consider the problem of enumeration of primitive TSRs of order n over any finite field. Here we prove the existence of primitive TSRs of order two over binary field extensions. Moreover we give a general search algorithm for primitive…

We investigate the discrete Painleve II equation over finite fields. We treat it over local fields and observe that it has a property that is similar to the good reduction over finite fields. We can use this property, which seems to be an…

Let $p$ be a odd prime such that 2 is a primitive element of finite field $F_p*$. In this short note we propose a new algorithm for the computation of discrete logarithm in $F_p*$. This algorithm is based on elementary properties of finite…

Given a generalization of Lebesgue decomposition we obtain an extension to the finitely additive setting of the theorems of Halmos and Savage and of Yan.

We explain how to deduce the degenerate analogue of Ariki's categorification theorem over the ground field C as an application of Schur-Weyl duality for higher levels and the Kazhdan-Lusztig conjecture in finite type A. We also discuss some…

The structure of infinite nuclear matter is studied with two of the Zimanyi - Moszkowski (ZM) models in the framework of a relativistic approximation which takes into account Hartree terms and beyond and is compared with the results which…

This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…

We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.