We identify a new sufficient condition for the finite convergence of moment relaxations of polynomial optimization problems with correlative sparsity. This condition, which follows from a solution to a correlatively sparse version of the classical tr...
The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowin...
Here we examine some Erdos-Falconer-type problems in vector spaces over finite fields involving right angles. Our main goals are to show that a) a subset A of F_q^d of size >> q^[(d+2)/3] contains three points which generate a right angle, and b) a s...
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical technique...
In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for the density...
The phase diagram of QCD at finite temperature and density and the existence of a critical point are currently very actively researched topics. Although tremendous progress has been made, in the case of two light quark flavors even the order of the...
Let $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$. Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal representation, $\barπ$, of $G$ over a sufficiently large finite field, $k$, of characteristic $\ell$ suc...
This thesis takes Brady's construction of $K(π,1)$s for the braid groups as a starting point. It is widely known that this construction can - with the right ingredients - be generalized to Artin groups of finite type. Results of Bessis as well as Br...
The finite reorient-time of swimmers leads to a finite run length $\ell$ and the kinetic accumulation boundary layer on the microscopic length scale $δ$ on a non-penetrating wall. That boundary layer is the microscopic origin of the swim pressure, a...
In this paper, a comparative study between the Coco-Russo scheme (based on finite-difference scheme) and the $\mathghost$-FEM (based on finite-element method) is presented when solving the Poisson equation in arbitrary domains. The comparison between...
We analyze the requirements for fault-tolerant quantum computation with atom-atom gates based on cavity quantum electrodynamics (cQED) mediated by a photon with a finite pulse length. For short photon pulses, the distorted shape of the reflected puls...
Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great solution. Howev...
We propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speedup of the decoding process of Bose-Chaudhuri-Hocquenghem, Reed-Solomon, and some other error-correcting codes....
We study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some integer d \geq 0, there is a finite morphism from X to P^d_S over S s...
The classical result of Landau on the existence of kings in finite tournaments (=finite directed complete graphs) is extended to continuous tournaments for which the set X of players is a compact Hausdorff space. The following partial converse is pro...
In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize this noti...
We study the reverse mathematics of the principle stating that, for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, this variant of Tukey's lemma is equivalent to the axiom of...
We determine, up to isomorphism, the indecomposable maximal Cohen-Macaulay modules over certain complete one-dimensional local rings of finite Cohen-Macaulay type. We then investigate the direct sum relations of maximal Cohen-Macaulay modules over...
The effect of the finite ion Larmor radius on the dynamics of two counterstreaming weakly collisional plasma flows in a magnetic field of an arch configuration is considered. Hybrid numerical simulations show that in a system whose dimensions are clo...
Call a reduced word $w$ multiplicity-bounding if and only if a finite group on which the word map of $w$ has a fiber of positive proportion $ρ$ can only contain each nonabelian finite simple group $S$ as a composition factor with multiplicity bounde...