Search results for "COMPUTATION"
showing 10 items of 7362 documents
Cardinal estimates involving the weak Lindelöf game
2021
AbstractWe show that if X is a first-countable Urysohn space where player II has a winning strategy in the game $$G^{\omega _1}_1({\mathcal {O}}, {\mathcal {O}}_D)$$ G 1 ω 1 ( O , O D ) (the weak Lindelöf game of length $$\omega _1$$ ω 1 ) then X has cardinality at most continuum. This may be considered a partial answer to an old question of Bell, Ginsburg and Woods. It is also the best result of this kind since there are Hausdorff first-countable spaces of arbitrarily large cardinality where player II has a winning strategy even in the weak Lindelöf game of countable length. We also tackle the problem of finding a bound on the cardinality of a first-countable space where player II has a wi…
Finitary shadows of compact subgroups of $$S(\omega )$$
2020
AbstractLet LF be the lattice of all subgroups of the group $$SF(\omega )$$SF(ω) of all finitary permutations of the set of natural numbers. We consider subgroups of $$SF(\omega )$$SF(ω) of the form $$C\cap SF(\omega )$$C∩SF(ω), where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost containedness. We also study complexity of the corresponding families of compact subgroups of $$S(\omega )$$S(ω).
Arithmetical Analysis of Biomolecular Finite Automaton
2013
In the paper we present a theoretical analysis of extension of the finite automaton built on DNA (introduced by the Shapiro team) to an arbitrary number of states and symbols. In the implementation we use a new idea of several restriction enzymes instead of one. We give arithmetical conditions for the existence of such extensions in terms of ingredients used in the implementation.
On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms
2011
The application of a Method of Lines to a hyperbolic PDE with source terms gives rise to a system of ODEs containing terms that may have very different stiffness properties. In this case, Implicit-Explicit Runge-Kutta (IMEX-RK) schemes are particularly useful as high order time integrators because they allow an explicit handling of the convective terms, which can be discretized using the highly developed shock capturing technology, together with an implicit treatment of the source terms, necessary for stability reasons. Motivated by the structure of the source term in a model problem introduced by LeVeque and Yee in [J. Comput. Phys. 86 (1990)], in this paper we study the preservation of ce…
Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma
2017
The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L . Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L .
Rationalizability of square roots
2021
Abstract Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots i…
A note on cocharacter sequence of Jordan upper triangular matrix algebra
2016
Let UJn(F) be the Jordan algebra of n × n upper triangular matrices over a field F of characteristic zero. This paper is devoted to the study of polynomial identities satisfied by UJ2(F) and UJ3(F). In particular, the goal is twofold. On one hand, we complete the description of G-graded polynomial identities of UJ2(F), where G is a finite abelian group. On the other hand, we compute the Gelfand–Kirillov dimension of the relatively free algebra of UJ2(F) and we give a bound for the Gelfand–Kirillov dimension of the relatively free algebra of UJ3(F).
The diamond partial order for strong Rickart rings
2016
The diamond partial order has been first introduced for matrices, and then discussed also in the general context of *-regular rings. We extend this notion to Rickart rings, and state various properties of the diamond order living on the so-called strong Rickart rings. In particular, it is compared with the weak space preorder and the star order; also existence of certain meets and joins under diamond order is discussed.
Existence of dynamical low-rank approximations to parabolic problems
2021
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.
Rejoinder on: Natural Induction: An Objective Bayesian Approach
2009
Giron and Moreno. We certainly agree with Professors Giron and Moreno on the interest in sensitivity of any Bayesian result to changes in the prior. That said, we also consider of considerable pragmatic importance to be able to single out a unique, particular prior which may reasonably be proposed as the reference prior for the problem under study, in the sense that the corresponding posterior of the quantity of interest could be routinely used in practice when no useful prior information is available or acceptable. This is precisely what we have tried to do for the twin problems of the rule of succession and the law of natural induction. The discussants consider the limiting binomial versi…