环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.     

The regularizing properties of anisotropic radial basis functions

In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples.     

Constraint incorporation in optimization

Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations) cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods, barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework relies on addition and chain rules for constraint incorporation which we develop here.     

A system-theoretic framework for a wide class of systems I: Applications to numerical analysis

A system-theoretic framework is proposed, which allows the study of hybrid uncertain systems, which do not satisfy the so-called “semigroup property.” Characterizations of the notion of robust global asymptotic output stability (RGAOS) are given. Based on the provided characterizations, the qualitative behavior of hybrid systems obtained by time-discretization of systems of ordinary differential equations with a globally asymptotically stable equilibrium point, is studied.     

基于演化博弈的武器装备研制合同定价模型研究

针对合同的动态性，提出利用基于演化博弈建立定价模型。考虑到决策群体中个体的认识误差，对所建立的定价模型进行修正，建立带偏离的定价模型并分析了偏离对均衡解的影响。最后将以上模型应用实例进行比较分析。     

Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

Separable anisotropic differential operators and applications

The nonlocal boundary value problems for anisotropic partial differential-operator equations with a dependent coefficients are studied. The principal parts of the appropriate generated differential operators are nonself-adjoint. Several conditions for the maximal regularity and the fredholmness in Banach-valued Lp-spaces of these problems are given. These results permit us to establish that the inverse of corresponding differential operators belongs to Schatten q-class. Some spectral properties of the operators are investigated. In applications, the nonlocal BVP's for quasielliptic partial differential equations and for systems of quasielliptic equations on cylindrical domain are studied.     

First-principle studies on the electronic structure of Fe3O4(110) surface

The first-principle was employed to study the six possible models for the Fe₃O₄(110) surface, namely the AB-terminated surface (AB model), the AB-terminated with Fe_A vacancy (AB-Fe_A vac model), the AB-terminated with Fe_B vacancy (AB-Fe_B vac model), the B-terminated surface (B model), the B-terminated surface with Fe_B vacancy (B-Fe_B vac model) and the B-terminated surface with O vacancy (B-O vac model). The stability, the electronic structure and the magnetic properties of the six surface models were also calculated. The results predict that the B-O vac model is more stable than other types of surface models. The half-metallic property remain in the AB and B models, while the other four surface models exhibit metallic properties. At the same time, the AB, AB-Fe_A vac, AB-Fe_B vac, B and the B-Fe_B vac models have ferrimagnetic properties, while the B-O vac model has antiferromagnetic property.      

粒子鉴别中dE/dx和TOF的权重

在北京谱仪数据分析中,粒子鉴别使用了dE/dx和TOF的信息.在利用dE/dx和TOF联合鉴别粒子时,通常的做法是把两者的χ²值等权重相加(χ²方法).在不同的动量区间,dE/dx和TOF对粒子的鉴别能力不同.本文给出两者联合鉴别时不同动量区间的权重,并构造一个新的线性变量来进行粒子鉴别     

Operator–valued Fourier multiplier theorems on Besov spaces

We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative w.r.t. two atomless finite Borel measures μ and ν with compact supports supp μ ? supp ν on the real line. This class of operators includes a generalization of the well‐known Sturm‐Liouville operator as well as of the measure geometric Laplacian given by . We obtain for this differential operator under both Dirichlet and Neumann boundary conditions similar properties as known in the classical Lebesgue case for the euclidean Laplacian like Gauß‐Green‐formula, inversion formula, compactness of the resolvent and its kernel representation w.r.t. the corresponding Green function. Finally we prove nuclearity of the resolvent and give two representations of its trace.