On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

The consensus string problem for a metric is NP-complete

Given a set S of strings, a consensus string of S based on consensus error is a string w that minimizes the sum of the distances between w and all the strings in S. In this paper, we show that the problem of finding a consensus string based on consensus error is NP-complete when the penalty matrix is a metric.     

Elements of the Lagrangian Whitney trick

We investigate the possibility of a Lagrangian Whitney trick, a process to remove a pair of intersection points of a self-transverse Lagrangian immersion by a homotopy through Lagrangian immersions. There is a model for which a Lagrangian Whitney trick with compact support works assuming the model satisfies an area-capacity condition. Reduction of more general cases to the model, not necessarily fulfilling the area-capacity requirement, is possible if the given pair of double points admits a suitable symplectic disc and a certain Maslov-Viterbo index is 1. We look into an example to see the actualities of the Maslov-Viterbo index and the area-capacity conditions. The authors would like to thank the anonymous referee whose suggestions improved remarkably the exposition of the paper. This work was supported by the grant no.R01-2000-000-00004-0 from Korea Science & Engineering Foundation.     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

Drift transforms and Green function estimates for discontinuous processes

In this paper, we consider Girsanov transforms of pure jump type for discontinuous Markov processes. We show that, under some quite natural conditions, the Green functions of the Girsanov transformed process are comparable to those of the original process. As an application of the general results, the drift transform of symmetric stable processes is studied in detail. In particular, we show that the relativistic α-stable process in a bounded C^1,1-smooth open set D can be obtained from symmetric α-stable process in D through a combination of a pure jump Girsanov transform and a Feynman-Kac transform. From this, we deduce that the Green functions for these two processes in D are comparable.     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

自适应光学中的非等晕性

本文讨论了自适应光学中非等晕域对补偿效果的影响,提出了一种减小非等晕性误差的新方法—位相梯度法。分析结果表明,该方法可显著增大有效校正的角范围,使非等晕性误差的影响大大减小。我们预期位相梯度法有望解决自适应光学中信标的非等晕性问题。     

Coupling Constant in High Temperature QCD and Deconfinement Phase Transition

Finite temperature renormalization group equation is employed to investigate the effective coupling constant of QCD with respect to temperature.At high temperature,it is very small over the entire region of momentum,this leads to the property of deconfinement of QCD.     

光子扫描隧道显微镜的光电成像系统研究

本文论述了光子扫描隧道显微镜（ＰＳＴＭ）的显微成像机理、成像规律，针对具体的物理模型进行数值模拟计算，并得到了与实际探测相一致的场分布规律。采用自行研制的光子扫描隧道显微镜（ＰＳＴＭ）的显微实验系统对多种样品进行了表面显微成像研究，获得了关于样品表面三维立体图像信息，通过多种图像处理手段对原始图像进行后期处理，得到了更具视觉效果、更为逼真的样品表面图像。     

横向位移双曝光散斑图维纳谱的信息分布

讨论了横向位移双曝光散斑图维纳谱的信息分布，并由此导出杨氏纹图的一般表达式。讨论了条纹可见度与应变，面内转动，照明光束直径与条纹图图空间坐标的关系，指出了在条纹可见度影响下最大可见条纹数目。还讨论了散斑衬比与衍射晕的关系。