Vector bundles with a fixed determinant on an irreducible nodal curve

LetM be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curveX. LetM _−L be the closure of its subset consisting of GPBs with fixed determinant− L. We define a moduli functor for whichM _−L is the coarse moduli scheme. Using the correspondence between GPBs onX and torsion-free sheaves on a nodal curveY of whichX is a desingularization, we show thatM _−L can be regarded as the compactified moduli scheme of vector bundles onY with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves onY. The relation to Seshadri-Nagaraj conjecture is studied.     

Newton’s method as a tool for finding the eigenvalues of certain two-parameter (multiparameter) spectral problems

An iterative algorithm is examined for finding the eigenvalues of the two-parameter (multiparameter) algebraic eigenvalue problem. This algorithm uses Newton’s method and an efficient numerical procedure for differentiating determinants. Some numerical examples are given.     

Influence of processing variables on the formation of La2Zr2O7 in transferred arc plasma torch processing

The transferred arc plasma (TAP) torch process has various noteworthy features such as extremely high temperatures, low environmental impact and short processing time which makes it the most suitable technique for synthesizing ceramic composite materials. Furthermore, it is a direct two-step technique which by its virtue of high temperature and power density paves way for high production rate. Hence in this study, an effort has been made to utilize the TAP torch processing technique for the bulk production of La₂Zr₂O₇ with time effectiveness from the mixture of La₂O₃ and ZrO₂ powders (1:2 mol ratios) which were ball milled for 4 h. For this purpose, transferred arc plasma torch was specially designed in laboratory scale level and the operating parameters were optimized in order to achieve maximum La₂Zr₂O₇ formation efficiency. In this study, the phase and microstructure formation of the processed samples was analyzed via X-ray diffraction (XRD) and scanning electron microscope (SEM) images respectively. Moreover, EDX analysis was incorporated to highlight the superior influence of the longer processing time on the stoichiometric ratio of ZrO₂/La₂O₃ in the processed sample as against input power and the gas flow rate.     

一种可调制的连续光谱点光源

短弧氙灯是一种发光强度高,具有从紫外到红外的连续光谱的点光源。本文介绍交流供电的短弧氙灯光源,用两电极短弧氙灯实现三电极短弧氙灯性能的方法。给出了用一个系统满足各种不同发光强度、不同调制波形、不同调制频率的要求,以及在制造和使用过程中应注意的事项。     

二类广义Vandermonde行列式的计算

给出了二类广义Vandermonde行列式计算的显式表示式.     

STABILITY OF A KIND OF COMPOUND BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE

In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the perturbation of boundary curve.     

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.     

求条件极值的一种新方法

利用线性代数的理论方法，对多元函数求条件极值的拉格朗日乘数法加以改进，建立了求条件极值的一种新方法     

复函数Cauchy微分中值定理的推广

以分割区域D为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式.     

ARC INTERFACE CRACK IN A THREEPHASE PIEZOELECTRIC COMPOSITE CONSTITUTIVE MODEL

An in-depth investigation is made on the problem of an arc-shaped interface insulating crack in a three-phase concentric circular cylindrical piezoelectric composite constitutive model. An exact solution in series form is derived by employing the complex variable method. In addition, the distribution of physical quantities such as stresses, strains, electric displacements and electric fields in the whole field and along the interface is also presented. Explicit expressions for crack opening displacement, jump in electric potential on the crack surface and the electro-elastic field intensity factors at the crack tips are obtained. Specific calculations demonstrate that the convergence of the series form solution is satisfactory and that the outer phase (composite phase) will exert a significant effect on the electro-mechanical coupling response of the composite system. Owing to the fact that stresses and electric displacements still possess conventional inverse square root singularities, the oscillating singularities near the crack tip under plane strain conditions will be absent and, as a result, no unphysical interpenetration phenomenon of the two crack surfaces will occur. In conclusion, the elastic solution obtained is also based on a solid physical foundation. Project supported by the National Natural Science Foundation of China (No.59635140), and the Doctorate Foundation of Xi'an Jiaotong University.