亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Laguerre spectral approximations play an important role in the development of efficient algorithms for problems in unbounded domains. In this paper, we present a comprehensive convergence rate analysis of Laguerre spectral approximations for analytic functions. By exploiting contour integral techniques from complex analysis, we prove that Laguerre projection and interpolation methods of degree $n$ converge at the root-exponential rate $O(\exp(-2\rho\sqrt{n}))$ with $\rho>0$ when the underlying function is analytic inside and on a parabola with focus at the origin and vertex at $z=-\rho^2$. As far as we know, this is the first rigorous proof of root-exponential convergence of Laguerre approximations for analytic functions. Several important applications of our analysis are also discussed, including Laguerre spectral differentiations, Gauss-Laguerre quadrature rules, the scaling factor and the Weeks method for the inversion of Laplace transform, and some sharp convergence rate estimates are derived. Numerical experiments are presented to verify the theoretical results.

For a matrix $A$ which satisfies Crouzeix's conjecture, we construct several classes of matrices from $A$ for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that Crouzeix's Conjecture holds in full generality if and only if it holds for the differentiation operator on a class of analytic functions. We pose several open questions, which if proved, will prove Crouzeix's conjecture. We also begin an investigation into Crouzeix's conjecture for symmetric matrices and in the case of $3 \times 3$ matrices, we show Crouzeix's conjecture holds for symmetric matrices if and only if it holds for analytic truncated Toeplitz operators.

We propose a method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type) and of coupled systems of renewal and delay differential equations. The method consists in the reformulation of the delay equation as an abstract differential equation, the reduction of the latter to a system of ordinary differential equations via pseudospectral collocation, and the application of the standard discrete QR method. The effectiveness of the method is shown experimentally and a MATLAB implementation is provided.

We prove the convergence of meshfree method for solving the elliptic Monge-Ampere equation with Dirichlet boundary on the bounded domain. L2 error is obtained based on the kernel-based trial spaces generated by the compactly supported radial basis functions. We obtain the convergence result when the testing discretization is finer than the trial discretization. The convergence rate depend on the regularity of the solution, the smoothness of the computing domain, and the approximation of scaled kernel-based spaces. The presented convergence theory covers a wide range of kernel-based trial spaces including stationary approximation and non-stationary approximation. An extension to non-Dirichlet boundary condition is in a forthcoming paper.

Resonance based numerical schemes are those in which cancellations in the oscillatory components of the equation are taken advantage of in order to reduce the regularity required of the initial data to achieve a particular order of error and convergence. We investigate the potential for the derivation of resonance based schemes in the context of nonlinear stochastic PDEs. By comparing the regularity conditions required for error analysis to traditional exponential schemes we demonstrate that at orders less than $ \mathcal{O}(t^2) $, the techniques are successful and provide a significant gain on the regularity of the initial data, while at orders greater than $ \mathcal{O}(t^2) $, that the resonance based techniques does not achieve any gain. This is due to limitations in the explicit path-wise analysis of stochastic integrals. As examples of applications of the method, we present schemes for the Sch\"odinger equation and Manakov system accompanied by local error and stability analysis as well as proof of global convergence in both the strong and path-wise sense.

This paper presents an asymptotic preserving (AP) implicit-explicit (IMEX) scheme for solving the quantum BGK equation using the Hermite spectral method. The distribution function is expanded in a series of Hermite polynomials, with the Gaussian function serving as the weight function. The main challenge in this numerical scheme lies in efficiently expanding the quantum Maxwellian with the Hermite basis functions. To overcome this, we simplify the problem to the calculation of polylogarithms and propose an efficient algorithm to handle it, utilizing the Gauss-Hermite quadrature. Several numerical simulations, including a spatially 2D lid-driven cavity flow, demonstrate the AP property and remarkable efficiency of this method.

We define a model of predicate logic in which every term and predicate, open or closed, has an absolute denotation independently of a valuation of the variables. For each variable a, the domain of the model contains an element [[a]] which is the denotation of the term a (which is also a variable symbol). Similarly, the algebra interpreting predicates in the model directly interprets open predicates. Because of this models must also incorporate notions of substitution and quantification. These notions are axiomatic, and need not be applied only to sets of syntax. We prove soundness and show how every 'ordinary' model (i.e. model based on sets and valuations) can be translated to one of our nominal models, and thus also prove completeness.

In recent literature, for modeling reasons, fractional differential problems have been considered equipped with anti-symmetric boundary conditions. Twenty years ago the anti-reflective boundary conditions were introduced in a context of signal processing and imaging for increasing the quality of the reconstruction of a blurred signal/image contaminated by noise and for reducing the overall complexity to that of few fast sine transforms i.e. to $O(N\log N)$ real arithmetic operations, where $N$ is the number of pixels. Here we consider the anti-symmetric boundary conditions and we introduce the anti-reflective boundary conditions in the context of nonlocal problems of fractional differential type. In the latter context, we study both types of boundary conditions, which in reality are similar in the essentials, from the perspective of computational efficiency, by considering nontruncated and truncated versions. Several numerical tests, tables, and visualizations are provided and critically discussed.

There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along the gradient flow of the Kullback-Leibler divergence towards the asymptotic state corresponding to the desired distribution. Mathematically, the method can be formulated as a joint limit of time $t$ and number of particles $N$ going to infinity. We first observe that the recent work of Lu, Lu and Nolen (2019) implies that if $t \approx \log \log N$, then the joint limit can be rigorously justified in the Wasserstein distance. Not satisfied with this time scale, we explore what happens for larger times by investigating the stability of the method: if the particles are initially close to the asymptotic state (with distance $\approx 1/N$), how long will they remain close? We prove that this happens in algebraic time scales $t \approx \sqrt{N}$ which is significantly better. The exploited method, developed by Caglioti and Rousset for the Vlasov equation, is based on finding a functional invariant for the linearized equation. This allows to eliminate linear terms and arrive at an improved Gronwall-type estimate.

Fitting's Heyting-valued modal logic and Heyting-valued logic have previously been examined from an algebraic perspective. Topological duality theorems have been developed in addition to algebraic axiomatizations with the completeness of Fitting's logic and modal logic. Recently, bitopological techniques have been used to study duality for Heyting-valued logic. But the development of duality for Heyting-valued modal logic noticeably lacks bitopology and biVietoris-coalgebra techniques. We are trying to bridge this gap in this paper. We establish a bitopological duality for algebras of Fitting's Heyting-valued modal logic. We build a bi-Vietoris functor on the category of Heyting-valued pairwise Boolean spaces, denoted by $PBS_{\mathcal{L}}$. In the end, we derive a dual equivalence between algebras of Fitting's Heyting-valued modal logic and categories of bi-Vietoris coalgebras. We thus conclude that, with respect to the coalgebras of a bi-Vietoris functor, Fitting's many-valued modal logic is sound and complete.