Related papers: On Non-Standard Models of B\"uchi Arithmetics

We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…

The logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound

The perturbation technique within the framework of the asymptotic iteration method is used to obtain large-order shifted 1/N expansions, where N is the number of spatial dimensions. This method is contrary to the usual…

Let \(C(x)\), \(A(x)\), and \(N(x)\) denote the counting functions of cyclic, abelian, and nilpotent numbers not exceeding \(x\), respectively. Their asymptotic formulas have been established in recent work by Pollack and Just. In this…

The purpose of this paper is to show that Non-Archimedean Mathematics (NAM), namely mathematics which uses infinite and infinitesimal numbers, is useful to model some Physical problems which cannot be described by the usual mathematics. The…

Classicality associated with joint measurability of operators manifests through a valid classical joint probability distribution on measurement outcomes. For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method…

Let $n \ge 2$ be an integer and $\alpha_1, \ldots, \alpha_n$ be non-zero algebraic numbers. Let $b_1, \ldots , b_n$ be integers with $b_n \not= 0$, and set $B = \max\{3, |b_1|, \ldots , |b_n|\}$. For $j =1, \ldots, n$, set $h^* (\alpha_j) =…

We give a new characterization of generalized B\"uchi sequences (sequences whose sequence of squares has constant second difference $(a)$, for some fixed integer $a$) of length 3 over the integers and a strategy for attacking B\"uchi's n…

A critical literature review and comprehensive simulation study is used to show that (a) non-parametric bootstrap is a viable alternative to commonly taught and used methods in basic estimation tasks (mean, variance, quartiles, correlation)…

There are nonstandard models of normal open induction ($NOI$) for which $\mathbb{Z}$ is a direct summand of their additive group. We show that this is impossible for nonstandard models of $IE_2$.

In this article, we give an abstract characterization of the ``identity'' of an operator space $V$ by looking at a quantity $n_{cb}(V,u)$ which is defined in analogue to a well-known quantity in Banach space theory. More precisely, we show…

A non-perturbative effective model is derived for the Higgs sector of the standard model, described by a simple scalar theory. The renormalized couplings are determined by the derivatives of the Gaussian Effective Potential that are known…

Symbol-pair codes, introduced by Cassuto and Blaum [1], have been raised for symbol-pair read channels. This new idea is motivated by the limitation of the reading process in high-density data storage technologies. Yaakobi et al. [8]…

We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…

We introduce a new type of nonuniform two--way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we…

The method of Tur\'an in establishing the normal order for the number of prime divisors of a number is used to show that a certain class of arithmetic functions do not have a normal order.

We propose symbolic regression as a powerful tool for studying Beyond the Standard Model physics. As a benchmark model, we consider the so-called Constrained Minimal Supersymmetric Standard Model, which has a four-dimensional parameter…

In this paper, we study Lusztig's $a$-function for a Coxeter group with unequal parameters. We determine that function explicitly in the ``asymptotic case'' in type $B_n$, where the left cells have been determined in terms of a generalized…

We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, $r$-convexity, among others, in a nonparametric framework using…

We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…