考虑专家水平的土木工程质量综合评估模型

应用加权集值统计、属性数学和最小方差等方法 ,建立了考虑专家水平的量化综合评估模型 ,对土木工程质量进行多目标多人的综合评估 ,并给出计算实例 .     

Some Spectral Properties of One Sturm-Liouville Type Problem with Discontinuous Weight

We consider a discontinuous weight Sturm-Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. We extend and generalize some approaches and results of the classic regular Sturm-Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation in such a way that the problem under consideration can be interpreted as an eigenvalue problem for a suitable selfadjoint operator, construct the Green’s function and resolvent operator, and derive asymptotic formulas for eigenvalues and normalized eigenfunctions.Original Russian Text Copyright © 2005 Mukhtarov O. Sh. and Kadakal M.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 860–875, July–August, 2005.     

The homotopy limit problem for two-primary algebraic K-theory

We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen-Lichtenbaum conjecture at the prime 2.     

Mechanical theorem proving in differential geometry

An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chem’s theorems: “The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces.” Some other theorems are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks. Project supported partially by the National Natural Science Foundation of China.     

Protonated Melonate Ca[HC6N7(NCN)3]·7H2O – Synthesis,Crystal Structure,and Thermal Properties

Calcium hydrogenmelonate heptahydrate Ca[HC₆N₇(NCN)₃] · 7H₂O was obtained by metathesis reaction in aqueous solution. The structure of the molecular salt was elucidated by single‐crystal X‐ray diffraction. The crystal structure consists of alternating layers of planar monopronated melonate ions, Ca²⁺ and crystal water molecules. The anions of adjacent layers are staggered so that no π–π stacking occurs. The melonate entities are interconnected by hydrogen bonds within and between the layers. Ca[HC₆N₇(NCN)₃] · 7H₂O was investigated by solid‐state NMR and FTIR spectroscopy, TG and DTA measurements.     

Soft mode dynamics of perovskite type crystals

The soft mode dynamics and related properties of perovskite, ABO₃-type crystals have been studied using the operator form of the model Hamiltonian proposed by Pytte. The correlations have been evaluated using the double time thermal Green’s function technique and Dyson’s equation. Without any decoupling, the higher order correlations, appearing in the dynamical equation, have been evaluated using the renormalized Hamiltonian. The dielectric properties are directly related to the optical soft mode. The phonon width and shift have been calculated for different structural phases. The analysis of the temperature dependence of microwave loss tangent and dielectric constant explains the experimental results.     

The heat kernel and Hardy’s theorem on symmetric spaces of noncompact type

For symmetric spaces of noncompact type we prove an analogue of Hardy’s theorem which characterizes the heat kernel in terms of its order of magnitude and that of its Fourier transform.     

F(p,q,s)空间的嵌入关系

为得到一类广泛的解析函数空间F(p,q,s)之间的嵌入关系,将每个空间F(p,q,s)对应为三维空间R(F)中一点(p,q,s),从而将空间之间的嵌入关系转化为三维空间中直线的单调性进行了研究,完善了已有的结果.     

The minimal excludant and Schmidt's partition theorem

In this work, we study Schmidt's partition theorem in a combinatorial manner, and find a strong refinement which connects the minimal excludant of ordinary partitions to the length of Schmidt's partitions. As a byproduct, we obtain a bivariate form of an identity recorded in Ramanujan's lost notebook.     

Identification of source terms in wave equation with dynamic boundary conditions

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm.