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] .     

闪光照相中源尺寸和散射对成像的影响

 利用Monte Carlo(MC)模拟技术解释实验中心线灰度曲线的各部分波形。结果发现，系统中的散射照射量、光源的尺寸和H-D特征曲线的形状对实验灰度曲线的各部分波形均有影响：散射量越大，中心信号幅度越低;H-D曲线趾部的非线性越严重，中心信号幅度也越低;光源尺寸造成图像越模糊。指出了用实验波形可以半定量确定系统散射程度和光源尺寸。在测量照射量时，应该尽可能避免散射的干扰,用台阶法测量H-D曲线时，应使台阶远离剂量片而前移。     

Establishment of The Power—Time Curve Equation of Bacterial Growth in the Log Phase

The power-time curves of two species of bacteria, Vibro metschnikovii, Vibro bollisae were determined calorimetrically by using a 2277 bioactivity monitor. The power-time curve equation of bacterial growth in the log phase can be expressed as

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.