Let $0<\sigma<n/2$ and $H=(-\Delta)^\sigma +V(x)$ be Schr\"odinger type operators on $\mathbb R^n$ with a class of scaling-critical potentials $V(x)$, which include the Hardy potential $a|x|^{-2\sigma}$ sharp coupling constant $a\ge -C_{\sigma,n}$ ($C_{\sigma,n}$ is best Hardy's inequality order $\sigma$). In present paper we consider several global estimates for resolvent solution to time-depe...

In this paper we consider the nonautonomous semilinear parabolic problems with time-dependent linear operatorsut+A(t)u=f(t,u),t>τ;u(τ)=u0, in a Banach space X. Under suitable conditions, obtain regularity results for ut(t,x) respect to its spatial variable x and estimates ut stronger spaces (Xα). We then apply those reaction-diffusion equationut−div(a(t,x)∇u)+u=f(t,u) Neumann boundary condition...

We study semigroups generated by general fractional Ornstein–Uhlenbeck operators acting on $$L^2({\mathbb {R}}^n)$$ . characterize geometrically the partial Gevrey-type smoothing properties of these semigroups, and we sharply describe blow-up associated seminorms for short times, generalizing hypoelliptic quadratic cases. As a byproduct this study, establish subelliptic estimates enjoyed whole ...

This article presents algorithms for temporal parallelization of Bayesian smoothers. We define the elements and operators to pose these problems as solutions all-prefix-sums operations which efficient parallel scan-algorithms are available. present general filtering smoothing equations, specialize them linear/Gaussian models. The advantage proposed is that they reduce linear complexity standard...

In many applications in finance, insurance, and reinsurance, one seeks a solution of finding a covariance matrix satisfying a large number of given linear equality and inequality constraints in a way that it deviates the least from a given symmetric matrix. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper,...

In this article we study global-in-time Strichartz estimates for the Schrödinger evolution corresponding to long-range perturbations of the Euclidean Laplacian. This is a natural continuation of a recent article [28] of the third author, where it is proved that local smoothing estimates imply Strichartz estimates. By [28] the local smoothing estimates are known to hold for small perturbations o...

Quadratic and even higher order finite elements are interesting candidates for the numerical solution of partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. The systems of equations that arise from the discretisation of the underlying (elliptic) PDEs are often solved by iterative solvers like preconditioned Krylow-space method...

This paper provides a comparison study among a set of robust diffusion algorithms for processing optical flows. The proposed algorithms combine the smoothing ability of the heat kernel, modelled by the local Hessian, and the outlier rejection mechanisms of robust statistics algorithms. Smooth optical flow variation can be modelled very well using heat kernels. The diffusion kernel is considered...

In this paper we study theoretical properties of multigrid algorithms and multilevel preconditioners for discretizations of second-order elliptic problems using nonconforming rotated Q1 finite elements in two space dimensions. In particular, for the case of square partitions and the Laplacian we derive properties of the associated intergrid transfer operators which allow us to prove convergence...