The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Degradation of ZnS:Cu,Al,Au phosphor powder in different gas mixtures

The ZnS:Cu,Al,Au (P22G) phosphor powder was bombarded by an electron beam in an O₂ ambient, Ar ambient and other mixture of gases. These gases consisted of mixtures of O₂ and CO_x, and O₂, CO_x and Ar gas. Auger electron spectroscopy (AES) was used to monitor changes in the surface composition of the P22G phosphor during electron bombardment. When the P22G phosphor powder was exposed to the electron beam in a water-rich O₂ ambient, a chemically limited ZnO layer was formed on the surface. The electron beam degradation of the P22G phosphor powder was also performed in a dry O₂ ambient and a layer of ZnSO₄ was formed on the surface. The ZnSO₄ formation decayed exponentially with time and it is postulated that this was due to the diffusion of the charge reactants through the ZnSO₄ film to the reaction interfaces. The P22G phosphor exposed to the electron beam in an Ar ambient and to the other gas mixtures degraded at a lower rate than in the case of the O₂ ambient. This suggests that Ar and CO_x may suppress the degradation of the P22G phosphor powder.     

Molecular dynamics simulation of thermodynamic properties of NaCl at high pressures and temperatures

The expansivity, constant-pressure heat capacity, and isothermal bulk modulus of sodium chloride (NaCl) have been obtained by using molecular dynamics method. The calculated thermodynamic parameters are found to be in agreement with the available experimental data. At an extended temperature and pressure ranges, these parameters have also been predicted. The thermodynamic properties of NaCl are summarized in the pressure 0-500 kbar ranges and the temperature up to 1000 K.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

Diphenylmethane transformations over boron trifluoride modified alumina and silica-alumina

Transformations of diphenylmethane were investigated in a flow system in the presence of alumina and silica-alumina modified with boron trifluoride at atmospheric pressure and elevated temperatures. Hydrogen transfer reaction was observed on addition of tetralin to the substrate stream. This revised version was published online in August 2006 with corrections to the Cover Date.     

神光Ⅱ上柱形黑腔辐射驱动冲击波

利用神光Ⅱ的八路三倍频激光装置，驱动柱形黑腔产生的x 射线作辐射源驱动台阶铝样品产生冲击波，获得了清晰的冲击波图像，通过冲击波过台阶样 品的时间差获得冲击波速度和压力分别为31.2km/s和17.5×10⁵MPa.采用软x射线能谱 仪通过激光注入孔测量的辐射温度与采用冲击波法测量辐射温度的结果一致. 关键词： 冲击波 辐射驱动 辐射温度     

单圈图的最大特征值序

主要讨论了单圈图按其最大特征值进行排序的问题，确定了该序的前六个图。     

The Characterisitic of Proton-Exchanged LiNbO3 Waveguide Formed by Different Proton Source

Benzoic acid as a source of proton is widely used in the technology of manufacture of proton exchanged ( PE) waveguide .But the diffusing speed of proton is too fast to make the waveguide stable in the pure benzoic acid. The characteristic of waveguide is improved with mixture of benzoic acid and lithium benzoate .     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“

Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528.