In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometri...
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting or reject...
A loop $(X,\circ)$ is said to be a Bruck loop if it satisfies the (right) Bol identity $((z\circ x)\circ y)\circ x = z\circ ((x\circ y)\circ x)$ and the automorphic inverse property $(x\circ y)^{-1}=x^{-1}\circ y^{-1}$. If $X$ is a finite Bruck loo...
For a certain finite graph E, we consider the corresponding finite dimensional algebra A with radical square zero. An explicit compact generator for the homotopy category of acyclic complexes of injective (resp. projective) modules over A, called the...
Let $K$ be a field. We characterise the row-finite weighted graphs $(E,w)$ such that the weighted Leavitt path algebra $L_K(E,w)$ is isomorphic to an unweighted Leavitt path algebra. Moreover, we prove that if $L_K(E,w)$ is locally finite, or Noether...
This paper proposes a different interpretation on the renormalization program of an interacting Klein-Gordon field in curved space-times. Rather than being just another renormalization program we argue that it that it makes the QFT ultraviolet-finite...
We present a finite size spin wave calculation on the Heisenberg antiferromagnet on the triangular lattice focusing in particular on the low-energy part of the excitation spectrum. For s=1/2 the good agreement with the exact diagonalization and qua...
In this paper, we apply a method of reducing the dynamics of FRW cosmological models with the barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time s...
We consider natural polynomial truncations of hypergeometric power series defined over finite fields. For these truncations, we establish asymptotic upper bounds of order $O(p^{11/12})$ on the number of roots in the prime field $\mathbb{F}_p$. We dis...
A comparative study between the Lüscher's finite volume method and the time-dependent HAL QCD method is given for the $ΞΞ$($^1\mathrm{S}_0$) interaction as an illustrative example. By employing the smeared source and the wall source for the interp...
We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods w...
This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds $M$ that fiber over a non-orientable base space. An orientable base space dou...
We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture....
Enflo and Rosenthal proved that $\ell_p(\aleph_1)$, $1 < p < 2$, does not (isomorphically) embed into $L_p(μ)$ with $μ$ a finite measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p < 2$, and $\ell_p(\aleph_1)$ does not embed into $...
A dictionary is a set of finite words over some finite alphabet X. The omega-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [Omega-powers and descriptive set theory, JSL 200...
We use the path integral approach to a two-dimensional noncommutative harmonic oscillator to derive the partition function of the system at finite temperature. It is shown that the result based on the Lagrangian formulation of the problem, coincides...
Simulations of vehicle/track interaction (VTI) in switches and crossings (S\&C) require taking into account the complexity of their geometry. The VTI can be handled via a co-simulation process between a finite element (FE) model of the track and a mu...
We give an expression for number of points for the family of Dwork K3 surfaces $$X_λ^4: \hspace{.1in} x_1^4+x_2^4+x_3^4+x_4^4=4λx_1x_2x_3x_4$$ over finite fields of order $q\equiv 1\pmod 4$ in terms of Greene's finite field hypergeometric functions...
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS is written...
We show that a heavy glueball (much heavier than that studied by others which is in the range of 1-2 GeV) is generated in a pure gluon plasma when color-singletness condition is imposed on the partition function at finite temperature. This confirms...
The structure and dynamics of a harmonically confined three dimensional finite dust cluster are investigated via both Langevin Dynamics (LD) and frictionless Molecular Dynamics (fMD) simulation. The static structure of the system is analyzed through...
We study the recombination process of three atoms scattering into an atom and diatomic molecule in heteronuclear mixtures of ultracold atomic gases with large and positive interspecies scattering length at finite temperature. We calculate the tempera...
Given a finite point set $P \subset \mathbb{R}^d$, a $k$-ary semi-algebraic relation $E$ on $P$ is the set of $k$-tuples of points in $P$, which is determined by a finite number of polynomial equations and inequalities in $kd$ real variables. The des...
Linearized polynomials over finite fields have been much studied over the last several decades. Recently there has been a renewed interest in linearized polynomials because of new connections to coding theory and finite geometry. We consider the pr...
We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use o...
In this paper, we study properties of the Diophantine exponents $w_n$ and $w_n^{*}$ for Laurent series over a finite field. We prove that for an integer $n\geq 1$ and a rational number $w>2n-1$, there exist a strictly increasing sequence of positive...
This paper has two parts. First, we recall and detail the definition of the Grothendieck topos of a connectivity space, that is the topos of sheaves on such a space. In the second part, we prove that every finite connectivity space is Morita-equivale...
Let for a prime $p$, $\mathfrak{X}$ (respectively $\mathfrak{Y}$) be the class of all $p$-biprimitively finite (respectively periodic $p$-conjugatively biprimitively finite) groups and $G\in \mathfrak{X}$ (respectively $G\in \mathfrak{Y}$), $V$ be a...
We show that all finite lattices, including non-distributive lattices, arise as stable matching lattices under standard assumptions on choice functions. In the process, we introduce new tools to reason on general lattices for optimization purposes: t...
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the ele...
We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex Ginzburg-L...
We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded into the finite-dimensional inertial manifold if the so-called spectral...
We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $n$-component $|\varphi|^4$ model for all integers $n \ge 1$ in all dimensions $d\ge 4$, for both free and periodic boundary conditions. For $d>4$, we prove that for a...
In this paper, we are interested in the numerical analysis of blow up for the Chipot-Weissler equation with Dirichlet boundary conditions in bounded domain. To approximate the blow up solution, we construct a finite difference scheme and we prove tha...
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit ourselves...
We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompre...
We explicitly construct a finite set of separating invariants for the basic $\Ga$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $\Ga$ of a field of characteristic zero, and their invari...
A two-dimensional, transient, multi-scale modeling approach is presented for predicting the magnitude and rate of percolation segregation for binary mixtures of granular material in a rotating drum and conical hopper. The model utilizes finite elemen...
Consider a finite irreducible Markov chain with invariant probability $π$. Define its inverse communication speed as the expectation to go from x to y, when x, y are sampled independently according to $π$. In the discrete time setting and when $π$...
We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups....