Mutual neutralization in low-energy collisions of Na^(+)+H^(-)ions

The low-energy mutual neutralization(MN)reactions Na^(+)+H^(-)→Na(nl)+H have been studied by employing the full quantum-mechanical molecular-orbital close-coupling(QMOCC)method over a wide energy range of 10^(-3)-10^(3) e V/u.Total and state-selective cross sections have been investigated and compared with the available theoretical and experimental data,and the state-selective rate coefficients for the temperature range of 100-10000 K have been obtained.In the present work,all the necessary highly excited states are included,and the influences of rotational couplings and 10 active electrons are considered.It is found that in the energy below 10 e V/u,the Na(4s)state is the most dominant exit state with a contribution of approximately 78%to the branch fraction,which is in best agreement with the experimental data.For energies above 10 e V/u,the MN total cross section is larger than those obtained in other theoretical calculations and shows a slow decreasing trend because the main exit states change,when the energy is above 100 e V/u,the dominant exit state becomes the Na(3p)state,while the Na(4s)state becomes the third most important exit state.The datasets presented in this paper,including the potential energy curve,the radial and rotational couplings,the total and state-selective cross sections,are openly available at https://doi.org/10.57760/sciencedb.j00113.00112.

有向图是极大连通的和超连通的充分条件（英文）

设D是顶点集为V(D)的有限简单有向图.V(D)中的顶点v的度d(v)被定义为v的出度d+(v)和入度d-(v)中的最小值.如果有向图D的最小度为δ,连通度为κ,则κ≤δ.如果κ=δ,则称有向图是极大连通的.对极大连通的有向图D的每个最小点割S,如果D-S要么是非强连通的且至少有一个平凡的强连通分支,要么是平凡的,则称D是超连通的.通过弧数给出有向图或二部有向图在最小度给定时是极大连通的或超连通的充分条件,并举例说明这些条件中的下界是紧的.

半导体与超晶格的数学模型及其分析Ⅱ:分析<英>

本文先介绍等熵可压缩Euler方程的相关补偿列紧框架.然后,我们综述基于补偿列紧方法的关于半导体流体动力模型的诸如整体弱解,松弛极限和拟中性.松弛极限的一些新近数学结果.

半导体与超晶格的数学模型及其分析Ⅰ:模型(英文)

本文论及半导体与超晶格的数学模型方法的一些新近发展动态.介绍了半导体与超 晶格的一些背景材料并给出了半导体宏观模型间的层次框架.超晶格中载流子传输的SHE扩散 模型也被观察.

抛物型方程的近似解及其计算机图形显示

In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably combining the difference and the basic recursion of elements in the bivariate spline space S21(Δmn(2)) to construct the approximate solutions. We have proved their convengence. And we will give a flow diagraph to display curved surface on a computer, and give an example.

DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.

Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.

Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem

A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.

Self-diffusion coefficients of organic solvents in linear and branched high density polyethylene particles measured by PFG NMR

Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.

Teleportation with an Arbitrary Mixed Resource as a Trace-Preserving Quantum Channel

General conditions are given in order to perform a perfect teleportation process in the case where theHilbert spaces involved have different dimensions. An explicit expression is obtained for the quantum channel associatedwith the standard teleportation protocol To with an arbitrary mixed state resource. The transmission fidelity of thecorresponding quantum channel is given.

A LIOUVILLE THEOREM FOR STATIONARY INCOMPRESSIBLE FLUIDS OF VON MISES TYPE

We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p > 1(including the classical Navier-Stokes system for the choice p = 2), and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p = 1. It turns out that, for dissipative potentials of linear growth, the condition of μ-ellipticity with exponent μ < 2 is sufficient for proving the Liouville theorem.

Absorbing Boundary Conditions for Hyperbolic Systems

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS

We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.

Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices.It is shown that the correlation matrix(CM)separability criterion can be improved from the normal form we obtained under filtering transformations.Based on CMcriterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite andmultipartite systems.

Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.

Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations

混合的多国参加的量的等价在本地人下面声明单一的转变被学习。为在本地单一的转变下面的非退化的混合的多国参加的量状态的等价的一个标准被介绍。

Higher Genus Characters for Vertex Operator Superalgebras on Sewn Riemann Surfaces

We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.

Improved Nearness Research

In the realm of Bounded Topology we now consider supernearness spaces as a common generalization of various kinds of topological structures. Among them the so-called Lodato spaces are of significant interest. In one direction they are standing in one-to-one correspondence to some kind of topological extensions. This last statement also holds for contiguity spaces in the sense of Ivanova and Ivanov, respectively and moreover for bunch-determined nearness spaces as Bentley has shown in the past. Further, Do?tch?nov proved that the compactly determined Hausdorff extensions of a given topological space are closely connected with a class of supertopologies which he called b-supertopologies. Now, the new class of supernearness spaces—called paranearness spaces—generalize all of them, and moreover its subclass of clan spaces is in one-to-one correspondence to a certain kind of symmetric strict topological extension. This is leading us to one theorem which generalize all former mentioned.

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.