On steady state Euler-Poisson models for semiconductors

This paper is concerned with an analysis of the Euler-Poisson model for unipolar semiconductor devices in the steady state isentropic case. In the two-dimensional case we prove the existence of smooth solutions under a smallness assumption on the prescribed outflow velocity (small boundary current) and, additionally, under a smallness assumption on the gradient of the velocity relaxation time. The latter assumption allows a control of the vorticity of the flow and the former guarantees subsonic flow. The main ingredient of the proof is a regularization of the equation for the vorticity.Also, in the irrotational two- and three-dimensional cases we show that the smallness assumption on the outflow velocity can be replaced by a smallness assumption on the (physical) parameter multiplying the drift-term in the velocity equation. Moreover, we show that solutions of the Euler-Poisson system converge to a solution of the drift-diffusion model as this parameter tends to zero.     

Infinite divisibility and a non-commutative Boolean-to-free Bercovici–Pata bijection

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue for the Bercovici–Pata bijection. An important tool is Voiculescu?s subordination property for operator-valued free convolution.     

Pullback attractors for closed cocycles

In this article, using a result of Pata and Zelik (2007) [45], we derive a general result on the existence of pullback attractors for closed cocycles acting on a Banach space, where the strong continuity is replaced by a much weaker requirement that the cocycle be a closed map. As application, we prove the existence of the pullback attractor of a cocycle associated with the z-weak solutions of a non-autonomous two-dimensional primitive equations of the ocean.     

Explosive solution of the nonlinear equation of a parabolic type

In this paper the unbounded increasing solution of the scalar nonlinear partial equation of the parabolic type for finite time is investigated. The sufficient condition for nonlinearity is established. Under this condition every solution of the investigated problem is exploded by the absence of restriction to smallness on the initial function. The existence of the solution is proved by smallness of the initial function.     

Local limit theorems for multiplicative free convolutions

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random variables implies superconvergence of their probability densities to the density of the limit law. Superconvergence to the marginal law of free multiplicative Brownian motion at a specified time is also studied. In the unitary case, the superconvergence to free Brownian motion and that to the Haar measure are shown to be uniform over the entire unit circle, implying further a free entropic limit theorem and a universality result for unitary free Lévy processes. Finally, the method of proofs on the positive half-line gives rise to a new multiplicative Boolean to free Bercovici–Pata bijection.     

On the eigenproblem for displacement integral equations

Summary This paper is concerned with the eigenproblem for displacement integral equations which have kernels that are finite cosine transforms. Previous work is extended to a broader class of kernels and the eigenfunctions are treated for the first time.This work was supported by the United States Atomic Energy Commission.     

On the global wellposedness of the 3-D Navier-Stokes equations with large initial data

We give a condition for the periodic, three-dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the scale invariant space , which contains all the known spaces in which there is a global solution for small data. The smallness condition is rather a nonlinear type condition on the initial data; an explicit example of such initial data is constructed, which is arbitrarily large and yet gives rise to a global, smooth solution.     

Resolvent kernels of Green's function kernels and other finite-rank modifications of Fredholm and Volterra kernels

Many important Fredholm integral equations have separable kernels which are finite-rank modifications of Volterra kernels. This class includes Green's functions for Sturm-Liouville and other two-point boundary-value problems for linear ordinary differential operators. It is shown how to construct the Fredholm determinant, resolvent kernel, and eigenfunctions of kernels of this class by solving related Volterra integral equations and finite, linear algebraic systems. Applications to boundary-value problems are discussed, and explicit formulas are given for a simple example. Analytic and numerical approximation procedures for more general problems are indicated.This research was sponsored by the United States Army under Contract No. DAA29-75-C-0024.     

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process.The uniqueness of the periodic solution is also given.     

The approximate decomposition of exponential order of slow-fast motions in multifrequency systems

This paper deals with multifrequency slow-fast systems. It is shown that, under a suitable change of coordinates, the system can be reduced to a simple form such that slow motions are described by autonomous equations except for exponential error of perturbations. Hence, the fast and slow motions are decoupled. The Newton rapid iteration is used. In addition, for a perturbation, only the smallness condition is needed.     

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system of second-order inclusion for displacement and a parabolic equation for temperature. We provide a fully discrete approximation of the problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated by numerical simulations.     

空巢老人手机用户的精准识别

以神经网络为计算模型,在合理处理已知数据的异常情况后,依据给定指标制定出(非)空巢老人的标准,以此建立(非)空巢老人集合的核作为学习样本,从而获得初步的识别结果,同时从输入和输出2个方面对其进行了多种检验。这套完整流程,也可用于解决类似的精准识别和其他数据挖掘问题。     

Two-sided deconvolution for bandlimited kernels

The two-sided deconvolution problem, for a certain class of a bandlimited kernels, is reduced to a discrete deconvolution problem by the sampling theorem, yielding a bandlimited solution. For this solution, in addition, a Galerkin type approximation is given. In general, the solution of the convolutioon equation for bandlimited kernels is not bandlimited. This follows from a characterization of the general solution     

pth-order approximation of the solution set of nonlinear equations

Given a system of nonlinear equations, a formula is derived for the family of its approximate solutions of up to the pth order of smallness. A formula approximating an implicit function up to the third order of smallness is presented. Iterative methods converging with the pth order are constructed for solving systems of nonlinear equations. These results are extended to the degenerate case. Examples of applying the results are given.     

Recursive Kernels

This paper is an extension of earlier papers [8, 9] on the “native” Hilbert spaces of functions on some domain Ω ⊂ R ^d in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recursively defined reproducing kernels. As an application, we get a recursive Neville-Aitken-type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.     

Regular and singular periodic perturbations of an oscillator with cubic restoring force

The paper considers small periodic regular and singular perturbations of a system, whose conservative part is an oscillator with cubic restoring force. The smallness of perturbations is due to both the smallness of the neighborhood of equilibrium and the presence of a small parameter. In the absence of a small parameter, we obtain conditions for Lyapunov stability of the equilibrium position. If a small parameter is present, we derive (both for regular and singular perturbations) an equation whose positive roots are in correspondence with invariant two-dimensional tori of the perturbed system.     

A steady state potential flow model for semiconductors

Summary We present a three-dimensional steady state irrotational flow model for semiconductors which is based on the hydrodynamic equations. We prove existence and local uniqueness of smooth solutions under a smallness assumptions on the data. This assumption implies subsonic flow of electrons in the semiconductors device.     

EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION

This paper is concerned with the initial boundary value problem for a vis-coelastic model with relaxation. Under the only assumption that the C^0-norm of theinitial data is small, without smallness hypothesis for the C^1-norm, the existence of theglobal smooth solution to the corresponding initial boundary value problem is proved.The analysis is based on some a priori estimates obtained by the “maximum principle” offirst-order quasilinear hyperbolic system.     

On the global and periodic regular flows of viscoelastic fluids with a differential constitutive law

This paper is concerned with the existence and uniqueness of global, periodic and stationary solutions for flows of incompressible viscoelastic fluids for which the extra-stress tensor satisfies a differential constitutive law. More precisely, we prove that the results obtained by C Guillopé and J.C. Saut [5] remain true without any restriction on the smallness of the retardation parameter.     

Smallness of fundamental groups for arithmetic schemes

The smallness is proved of étale fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the Hermite-Minkowski theorem. We also refer to the case of varieties over finite fields. As an application, we prove certain finiteness results of representations of the fundamental groups over algebraically closed fields.