Related papers: A General Reciprocity Law for Symbols on Arbitrary…
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…
Use is made of the theory of elliptic equations with measures data to prove the Maxwell-Volterra reciprocity law. A simple one-dimensional example is also given.
Recently, Brailovskaya & van Handel (GAFA, 2024) established a suite of nonasymptotic universality laws which demonstrate that the spectral statistics of an independent sum of random matrices mirror the spectral statistics of a Gaussian…
To apply the abstract quantum formalism to a particular physical system, one must specify the precise form of the relevant measurement and symmetry transformation operators. These operators are determined by a set of rules, the…
We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of…
In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of excluded middle, the law of non-contradiction, the…
In this paper, a sum rule means a relationship between a functional defined on a subset of all probability measures on $\mathbb{R}$ involving the reverse Kullback-Leibler divergence with respect to a particular distribution and recursion…
Ponderable objects moving in free space according to Newton's First Law constitute both rulers and clocks when one such object is viewed from the rest frame of another. Together with the Reciprocity Principle this is used to demonstrate, in…
We give explicit, polynomial-time computable formulas for the number of integer points in any two-dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of…
We study an apparently new question about the behaviour of Weyl sums on a subset $\mathcal{X}\subseteq [0,1)^d$ with a natural measure $\mu$ on $\mathcal{X}$. For certain measure spaces $(\mathcal{X}, \mu)$ we obtain non-trivial bounds for…
The Grothendieck and Artin-Mumford exact sequences for the Brauer group of a function field in 1 or 2 variables are applied to derive reciprocity laws for $q$th power residues.
In 1991, Beardon and Stephenson [2] generalized the classical Schwarz-Pick lemma in hyperbolic geometry to the discrete Schwarz-Pick lemma for Andreev circle packings. This paper continues to investigate the discrete Schwarz-Pick lemma for…
The purpose of this paper is to establish a general strong law of large numbers (SLLN) for arbitrary sequences of random variables (rv's) based on the squared indice method and to provide applications to SLLN of associated sequences. This…
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
Fourier-Dedekind sums are a generalization of Dedekind sums - important number-theoretical objects that arise in many areas of mathematics, including lattice point enumeration, signature defects of manifolds and pseudo random number…
For a reciprocity functor $\mathcal{M}$ we consider the local symbol complex $\mathcal{M}\otimes^{M}\mathbb{G}_{m}(\eta_{C})\to\oplus_{P\in C}\mathcal{M}(k)\to\mathcal{M}(k)$, where $C$ is a smooth complete curve over an algebraically…
We prove cancellation theorems for reciprocity sheaves and cube-invariant modulus sheaves with transfers of Kahn--Saito--Yamazaki, generalizing Voevodsky's cancellation theorem for $\mathbf{A}^1$-invariant sheaves with transfers. As an…
Using Serre's adelic interpretation of cohomology, we develop a `differential and integral calculus' on an algebraic curve X over an algebraically closed filed k of constants of characteristic zero, define algebraic analogs of additive…
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.