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

A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded rectangular table in multiple dimensions. To derive a second-order scheme, we combine a MUSCL type spatial reconstruction with strong stability preserving Runge-Kutta time stepping method. The resulting scheme is ensured to be well-balanced through a modified limiting approach that allows the scheme to reduce to well-balanced first-order scheme near the steady state while maintaining the second-order accuracy away from it. The well-balanced property of the scheme is proven analytically in one dimension and demonstrated numerically in two dimensions. Additionally, numerical experiments reveal that the second-order scheme reduces finite time oscillations, takes fewer time iterations for achieving the steady state and gives sharper resolutions of the physical structure of the sandpile, as compared to the existing first-order schemes of the literature.

We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the geometry of the domain.

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In this article, we derive two novel mixture representations for the $\mathrm{GIG}(p, a, b)$: one that expresses the distribution as a continuous mixture of inverse Gaussians and another one that expresses it as a continuous mixture of truncated exponentials. Beyond their conceptual interest, these representations are useful for random number generation. We use the first representation to derive a geometrically ergodic Gibbs sampler whose stationary distribution is $\mathrm{GIG}(p, a, b)$, and the second one to define a recursive algorithm to generate exact independent draws from the distribution for half-integer $p$. Additionally, the second representation gives rise to a recursive algorithm for evaluating the cumulative distribution function of the $\mathrm{GIG}(p, a, b)$ for half-integer $p$. The algorithms are simple and can be easily implemented in standard programming languages.

We explore new interactions between finite model theory and a number of classical streams of universal algebra and semigroup theory. A key result is an example of a finite algebra whose variety is not finitely axiomatisable in first order logic, but which has first order definable finite membership problem. This algebra witnesses the simultaneous failure of the {\L}os-Tarski Theorem, the SP-preservation theorem and Birkhoff's HSP-preservation theorem at the finite level as well as providing a negative solution to a first order formulation of the long-standing Eilenberg Sch\"utzenberger problem. The example also shows that a pseudovariety without any finite pseudo-identity basis may be finitely axiomatisable in first order logic. Other results include the undecidability of deciding first order definability of the pseudovariety of a finite algebra and a mapping from any fixed template constraint satisfaction problem to a first order equivalent variety membership problem, thereby providing examples of variety membership problems complete in each of the classes $\texttt{L}$, $\texttt{NL}$, $\texttt{Mod}_p(\texttt{L})$, $\texttt{P}$, and infinitely many others (depending on complexity-theoretic assumptions).

Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.

Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. In this paper we study some geometric properties of the spaces of group equivariant operators and show how a space $\mathcal{F}$ of group equivariant non-expansive operators can be endowed with the structure of a Riemannian manifold, so making available the use of gradient descent methods for the minimization of cost functions on $\mathcal{F}$. As an application of this approach, we also describe a procedure to select a finite set of representative group equivariant non-expansive operators in the considered manifold.

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a $\Theta$-convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.

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.

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 construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of recovering the solution operator of hyperbolic PDEs is the presence of characteristics, along which the associated Green's function is discontinuous. Therefore, a central component of our algorithm is a rank detection scheme that identifies the approximate location of the characteristics. By combining the randomized singular value decomposition with an adaptive hierarchical partition of the domain, we construct an approximant to the solution operator using $O(\Psi_\epsilon^{-1}\epsilon^{-7}\log(\Xi_\epsilon^{-1}\epsilon^{-1}))$ input-output pairs with relative error $O(\Xi_\epsilon^{-1}\epsilon)$ in the operator norm as $\epsilon\to0$, with high probability. Here, $\Psi_\epsilon$ represents the existence of degenerate singular values of the solution operator, and $\Xi_\epsilon$ measures the quality of the training data. Our assumptions on the regularity of the coefficients of the hyperbolic PDE are relatively weak given that hyperbolic PDEs do not have the ``instantaneous smoothing effect'' of elliptic and parabolic PDEs, and our recovery rate improves as the regularity of the coefficients increases.