Related papers: Dynamic Structures of Monomials on $p$-adic Intege…
In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at…
Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any…
Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates…
Nanomagnets form the building blocks for a gamut of miniaturized energy-efficient devices including data storage, memory, wave-based computing, sensors and biomedical devices. They also offer a span of exotic phenomena and stern challenges.…
We consider a family of $(2,2)$-rational functions given on the set of complex $p$-adic field $\mathcal{C}_p$. Each such function $f$ has the two distinct fixed points $x_1=x_1(f)$, $x_2=x_2(f)$. We study $p$-adic dynamical systems…
The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In…
We adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…
Let \psi(x) be a polynomial with rational coefficients. Suppose that \psi has the positive leading coefficient and zero constant term. Let A be a set of positive integers with the positive upper density. Then there exist x,y\in A and a…
Let $I$ be a monomial ideal in a polynomial ring $A=K[x_1,...,x_n]$. We call a monomial ideal $J$ to be a minimal monomial reduction ideal of $I$ if there exists no proper monomial ideal $L \subset J$ such that $L$ is a reduction ideal of…
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in particular used in a…
We study the existence of unitriangular basic sets for the symmetric group which behave nicely with respect to the Mullineux involution. Such sets give a natural labelling for the modular irreducible representations. We show that, for any…
In this talk, we review some recent advances in the theory of dynamic tides in close binaries. We particularly focus on the effects of resonances of dynamic tides with free oscillation modes and on the role of dynamic tides in the…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
We study the structural and dynamical mechanisms of reinforcement of a polymer nanocomposite (PNC) via coarse-grained molecular dynamics simulations. In a regime of strong polymer-filler interactions, the stress at failure of the PNC is…
We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation…
Observational evidence for dynamo action in spiral galaxies is reviewed, and the capabilities of various theories in explaining the basic features of galactic magnetic fields are discussed. Mean-field dynamo models appear to be unique in…
We determine fundamental systems of invariants for complex solvable rigid Lie algebras having nonsplit nilradicals of characteristic sequence $(3,1,..,1)$, these algebras being the natural followers of solvable algebras having Heisenberg…
The spin dynamics of a hydrogen atom during the passage of a periodic magnetic structure is discussed. The occupation numbers of the components of the hyperfine structure are considered as a function of time. The characteristic…