Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.     

Optimal control of parabolic variational inequalities with delays and state constraint

In this paper, an optimal control problem for parabolic variational inequalities with delays and state constraint is investigated and the necessary conditions for optimal controls are derived.     

Total minus domination in k-partite graphs

A function f defined on the vertices of a graph G=(V,E),f:V→{-1,0,1} is a total minus dominating function (TMDF) if the sum of its values over any open neighborhood is at least one. The weight of a TMDF is the sum of its function values over all vertices. The total minus domination number, denoted by , of G is the minimum weight of a TMDF on G. In this paper, a sharp lower bound on of k-partite graphs is given.     

Condition numbers with their condition numbers for the weighted moore-penrose inverse and the weighted least squares solution

In this paper, the authors investigate the condition number with their condition numbers for weighted Moore-Penrose inverse and weighted least squares solution of $\mathop {\min }\limits_x ||Ax - b||_M $ , whereA is a rank-deficient complex matrix in ?^{m × n} andb a vector of lengthm in ?^m,x a vector of length n in ?ⁿ. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.     

Sphere and Dot Product Representations of Graphs

A graph G is a k-sphere graph if there are k-dimensional real vectors v ₁,…,v _n such that ij∈E(G) if and only if the distance between v _i and v _j is at most 1. A graph G is a k-dot product graph if there are k-dimensional real vectors v ₁,…,v _n such that ij∈E(G) if and only if the dot product of v _i and v _j is at least 1.     

Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions

In this work, a projection algorithm is considered for treating strongly continuous semigroups of demicontinuous pseudocontractions. Theorems of strong convergence of fixed points are established in the framework of real Hilbert spaces.     

A variant of the Reynolds operator

Let be a linearly reductive group over a field , and let be a -algebra with a rational action of . Given rational --modules and , we define for the induced -action on Hom a generalized Reynolds operator, which exists even if the action on Hom is not rational. Given an -module homomorphism , it produces, in a natural way, an -module homomorphism which is -equivariant. We use this generalized Reynolds operator to study properties of rational - modules. In particular, we prove that if is invariantly generated (i.e. ), then is a projective (resp. flat) -module provided that is a projective (resp. flat) -module. We also give a criterion whether an -projective (or -flat) rational --module is extended from an -module.

     

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.     

固体发动机保险机构在高温高压下的实验研究

针对固体发动机部件保险机构所出现破现象,对其进行了激光散斑和电阻应变法联合测试。由于保险机构在高温和高压环境下工作,材料有蠕变现象,出现较大的热变形,传统的光我法实施,发展了一种叠合散斑技术,使之能够对大变形进行非接触式测量,在实验室测试的基础上,对保险机构进行了热容器试验,测量了点火后应变随时间的变化规律。实验结构发现,在保险机构机体上存在着一个接近破环应力的高危应力区,这是保险机破坏的主要因素