A holomorphic and background independent partition function for matrix models and topological strings

We study various properties of a nonperturbative partition function which can be associated with any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N$1/N$ expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi–Yau 3-folds.     

土壤重金属铬元素的激光诱导击穿光谱定量分析研究

利用Nd ∶YAG脉冲激光器(波长:1064 nm)作为光源,在实验室自然大气环境下诱导产生土壤激光等离子体,通过等离子体原子发射光谱法定量分析了国家标准土壤样品中元素Cr的含量.实验上研究了在最佳实验条件下土壤中Cr的LIBS分析谱线,测定了Cr元素的定标曲线.实验结果表明,Cr元素浓度在(60—400)×10^-6范围内,元素含量与光谱线强度之间有较好的线性关系;元素Cr浓度分析测量的相对标准偏差(RSD)为7.89%,定量分析结果与标准值的相对偏差为5.3%,Cr元素的检测限为1 关键词： 土壤污染 定量分析 激光诱导击穿光谱 定标曲线     

高功率激光整形脉冲波形控制技术

 针对神光-Ⅲ原型装置物理实验要求的三台阶整形脉冲（三个台阶的脉冲宽度比为1.5∶1.0∶0.5,强度比为1∶4∶16,脉冲总能量为500 J）,并根据该装置的系统构成和具备任意脉冲整形技术,开展了高功率激光整形脉冲波形控制技术研究,通过对基频光段的增益饱和效应和三倍频光的频率转换过程的分析,获得了脉冲时间波形在传输、放大及频率转换过程中的一些变化特点,在此基础上建立了一套简单的预测模型。经过反复迭代计算和多次全系统联机实验获得了实验结果,并在物理实验中得到了应用,初步形成了高功率激光整形脉冲波形的控制方法。     

Developing a sampling plan by variables inspection for controlling lot fraction of defectives

Acceptance sampling has been widely used tool for determining whether the submitted lot should be accepted or rejected. However, it cannot avoid two kinds of risks, accepting undesired poor product lots and rejecting good product lots. Such risks are even more significant as the rapid advancement of the manufacturing technology and stringent customers demand is enforced. A yield index S_pk has been developed to provide an exact measure on process yield or fraction nonconforming for normally distributed processes with two-sided specification limits. Therefore, the aim of this paper is to develop a variables sampling plan for evaluating the lot or process fraction nonconforming based on the yield index. The probability of lot acceptance is derived based on the sampling distribution and two-point condition on OC curve is used to determine the plan parameters. Tables of the plan parameters and step-by-step procedure are provided for the practitioner to make decision on lot sentencing especially for situations of products with very low fraction of nonconformities.     

Circle approximation using LN Bézier curves of even degree and its application

We present an approximation method of circular arcs using linear-normal (LN) Bézier curves of even degree, four and higher. Our method achieves G^m$G^m$ continuity for endpoint interpolation of a circular arc by a LN Bézier curve of degree 2m  , for m=2,3$m=2,3$. We also present the exact Hausdorff distance between the circular arc and the approximating LN Bézier curve. We show that the LN curve has an approximation order of 2m+2$2m+2$, for m=2,3$m=2,3$. Our approximation method can be applied to offset approximation, so obtaining a rational Bézier curve as an offset approximant. We derive an algorithm for offset approximation based on the LN circle approximation and illustrate our method with some numerical examples.     

Approximating Pareto curves using semidefinite relaxations

We approximate as closely as desired the Pareto curve associated with bicriteria polynomial optimization problems. We use three formulations (including the weighted sum approach and the Chebyshev approximation) and each of them is viewed as a parametric polynomial optimization problem. For each case is associated a hierarchy of semidefinite relaxations and from an optimal solution of each relaxation one approximates the Pareto curve by solving an inverse problem (first two cases) or by building a polynomial underestimator (third case).     

六次PH曲线C~1 Hermite插值

本文讨论六次PH(pythagorean hodograph)曲线的Hermite插值问题.六次PH曲线可以分为两种类型,本文使用参数曲线的复数表示形式,分别给出这两类曲线的构造方法.在给定C1连续的Hermite条件下,需要指定一个自由参数以确定插值曲线,本文进一步阐述这个自由参数的几何意义.由于六次PH曲线是非正则曲线,对于第一类曲线,不易控制奇异点在曲线中的位置;而对于第二类曲线,奇异点可以在构造过程中显式地被指定,因此可以有效地避免其在特定曲线段上的出现.     

Connectedness of curve complex of surface

For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.     

Asymptotics of Christoffel functions on arcs and curves

For a system of smooth Jordan curves and arcs asymptotics for Christoffel functions is established. A separate new method is developed to handle the upper and lower estimates. In the course to the upper bound a theorem of Widom on the norm of Chebyshev polynomials is generalized.     

Arc Length Estimation and the Convergence of Polynomial Curve Interpolation

When fitting parametric polynomial curves to sequences of points or derivatives we have to choose suitable parameter values at the interpolation points. This paper investigates the effect of the parameterization on the approximation order of the interpolation. We show that chord length parameter values yield full approximation order when the polynomial degree is at most three. We obtain full approximation order for arbitrary degree by developing an algorithm which generates more and more accurate approximations to arc length: the lengths of the segments of an interpolant of one degree provide parameter intervals for interpolants of degree two higher. The algorithm can also be used to estimate the length of a curve and its arc-length derivatives. AMS subject classification (2000) 65D05, 65D10