Multi-reference calculations of the photodissociation of HSCH3 molecule

This paper performs multi-reference second-order perturbation theory calculations on the ground state and a number of low-lying excited states of HSCH3 molecule, and calculates the vertical excitation energies and low-energy potential-energy curves, based on which the photodissociation channels of HSCH3 at 193,222,248 nm are clarified.     

Studies of synthesizing behaviors and superconductivity of sol-gel YBa2Cu3O7-x samples in flowing oxygen atmosphere

Systematic studies of synthesizing behaviors of sol-gel YBa₂Cu₃O_7−x samples in flowing oxygen atmosphere and their superconductivity have been performed. A set of high temperature ρ-T curves has been obtained for the whole synthesizing process. After four rounds of synthesizing, the resistivity of the sample was around ρ=1.00×10⁻³Ω · cm at room temperature. The ρ-T curve of the fourth round shows that the orthorhombic to tetragonal phase transformation of the sample occurs around 600 °C, which is lower than that of the YBa₂Cu₃O_7−x sample prepared by conventional solid-state reaction method. Other measurements, such as X-ray diffraction, SEM measurement and low temperature R-T and M-T measurement, were also performed. And the R-T and M-T measurement results suggest that during the synthesizing process, there exist some state at which the sample has better superconductivity than the other states. Moreover, we found screw dislocations presenting on the sample broken surface from the SEM images. This will change the concept that the screw dislocations can only grow on the surface of the YBCO thin films and single crystals.      

Laser frequency stabilization based on Sagnac interferometric spectroscopy

A simple method based on Sagnac interferometric spectroscopy (SIS) is applied for frequency stabilization of diode lasers. Sagnac interferometric spectra of rubidium vapor are investigated both theoretically and experimentally. The interference signal at the output of the Sagnac interferometer displays a sharp dispersion feature near the atomic resonance. This dispersion curve is used as the feedback error signal to stabilize the laser frequency. Linewidth of a diode laser is stabilized down to 1 MHz by this modulation-free method.     

On systems of binomials in the ideal of a toric variety

Let be a toric set in the affine space . Given a set of binomials in the toric ideal of , we give a criterion for deciding the equality rad( ) = . This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.

     

Arithmetic on superelliptic curves

This paper is concerned with algorithms for computing in the divisor class group of a nonsingular plane curve of the form which has only one point at infinity. Divisors are represented as ideals, and an ideal reduction algorithm based on lattice reduction is given. We obtain a unique representative for each divisor class and the algorithms for addition and reduction of divisors run in polynomial time. An algorithm is also given for solving the discrete logarithm problem when the curve is defined over a finite field.

     

The Sigmoidal Transfer Function and the Gain-Threshold Exponential Dependence for Neurons from Statistical Mechanics Treatment

Analogy is used to treat the system of non-interacting integrate-and-fire neurons as an ideal Fermi gas. It allows to obtain the nonlinear gain curve in the form of sigmoid in agreement with biological findings. As the by-product the gain-threshold mechanism in neurons is presented. Surprisingly enough, this is in agreement with new biological findings, too. Besides, the application of this mechanism to the dynamics of neurons leads to the non-monotone transfer function.     

On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Nef Divisors in Codimension One on the Moduli Space of Stable Curves

Let M _g be the moduli space of smooth curves of genus g 3, and M¯ _g the Deligne-Mumford compactification in terms of stable curves. Let M¯ _g ^[1] be an open set of M¯ _g consisting of stable curves of genus g with one node at most. In this paper, we determine the necessary and sufficient condition to guarantee that a -divisor D on M¯ _g is nef over M¯ _g ^[1], that is, (D · C) 0 for all irreducible curves C on M¯ _g with C M¯ _g ^[1] .     

一种改进的ECC数字签名方案

利用组合公钥体制（CPK）的基本思想，结合椭圆曲线加密（ECC）算法，提出了一种改进的数字签名方案。该方案中，签名者使用双私钥对消息进行签名，并通过结合运用CPK和ECC的特点，实现了高效的密钥管理以及高可靠性，较传统数字签名方法有更高的安全性和方便性。最后，对该签名方案进行了安全性分析。