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A simple formal recasting of well known arguments concerning the ordering problems of General Relativity allows to obtain in such a context a Gr\"{o}enewald Van Hove like theorem.
In this paper, we prove new upper bounds for sums of reciprocals of fractional parts over general aligned boxes, thus extending a previous result of the author concerning bounds for sums of reciprocals over symmetric boxes. These new upper…
We conjecture an explicit formula for the higher dimensional Dirichlet character; the formula is based on the K-theory of the so-called noncommutative tori. It is proved, that our conjecture is true for the two-dimensional and…
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.
Composite theories are the algebraic equivalent of distributive laws. In this paper, we delve into the details of this correspondence and concretely show how to construct a composite theory from a distributive law and vice versa. Using term…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…
We give a geometric interpretation of the reciprocal complement of an integral domain $D$ in the case $D$ is a one-dimensional finitely generated algebra over an algebraically closed field.
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the…
An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.
The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
It is noted that quantum theory includes the correspondence principle which is independent of the value of quantum corrections. Some consequences of this generalized correspondence principle are considered. For example, it is discussed how…
In this article we study the 2-Selmer groups of number fields $F$ as well as some related groups, and present connections to the quadratic reciprocity law in $F$.
Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented.
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.
A general or truss distributive laws between two associative operations on the same set are studied for cancellative and inverse semigroups.
This is part one of a series of papers. In this series of papers, we consider problems analogous to the Oppenheim conjecture from the viewpoint of prehomogeneous vector spaces.