Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota     

The study of the influence of uniaxial stress on impurity complexes in silicon

The influence of external uniaxial stress on the different indium-donor complexes in silicon has been studied using the perturbed γ –γ angular correlation (PAC) method. Such effect of an applied stress is detected by means of the probe atoms situated at different complexes in the sample. The current results showed that the responses of the probes in an extrinsic silicon samples are found to be dissimilar for the same value of stress. Such change in the local environments of the probe atoms could be associated with the various strain field created by the implantations of varied size of impurities. The phosphorous implantation in silicon has even lead to the complete absence of observable effect of the applied stress suggesting significant lose of the elasticity of the sample.     

A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesoscopic details of crack tip deformation field by application of differential interference contrast method

An experimental method is developed to examine the near tip deformation at the mesoscopic scale level. The differential interference contrast (DIC) method is used by application of the Nomarski prism in polarized microscope for measuring the out of surface deformation. The method is very sensitive to small height changes detected by different interference color. Discussed are results for the crack tip deformation field.     

Physical Interpretation of the Motion of a Laser Pulse within the Framework of the Four-Oscillator Model

A physical multidimensional local model of the propagation process of a laser pulse in air having no analogy to famous models in laser physics is constructed. It is based on the representations of classical wave mechanics characteristic of the theory of scalar wave fields.     

Synthesis and characterization of soluble polyimides containing trifluoromethyl groups in their backbone

A series of polyimides were synthesized from 2,2‐Bis(3,4‐dicarboxyphenyl)hexafluoropropane, 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane, and 4,4′‐oxydianiline by chemical imidization. The effects of the diamine ratios on the properties of the films were evaluated through the study of their thermal, electrical, and morphological properties. All the polymers exhibited better solubility in most of the organic solvents and hence were easily processable. Polyimides with more 2,2‐bis(3‐amino‐4‐hydroxyphenyl)‐hexafluoropropane exhibited better solubility and a low refractive index, which is highly desired for microelectronic applications. The dielectric constant and birefringence were strongly dependent on the fluorine content. With an increase in the fluorine substitution, both the dielectric constant and birefringence decreased. All the polymers exhibited high thermal stability (>400 °C). The absence of crystalline melting in differential scanning calorimetry and broad wide‐angle X‐ray diffraction patterns revealed the amorphous nature of the polymers, which was due to the presence of bulky CF₃ groups and hinged ether linkages of the diamine component. The residual stress values decreased with an increase in the 4,4′‐oxydianiline content, and the results were in agreement with the dielectric constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4303–4312, 2004     

Multiphysical modeling and meshless simulation of electric‐sensitive hydrogels

According to a multiphase mixture theory, we have mathematically developed a multiphysical model with chemoelectromechanical coupling considerations, termed the multieffect‐coupling electric‐stimulus (MECe) model, to simulate the responsive behavior of electric‐sensitive hydrogels immersed in a bath solution under an externally applied electric field. For solutions of the MECe model consisting of coupled nonlinear partial differential governing equations, a meshless Hermite–Cloud method with a hierarchical iteration technique has been used for a one‐dimensional steady‐state analysis of a hydrogel strip. The computed results are compared with the experimental data, and there is very good agreement. Simulations within the domains of both hydrogels and surrounding solutions also present distributions of the ionic concentrations and electric potential as well as the hydrogel displacement. The effects of various physical parameters on the response behavior of electric‐stimulus responsive hydrogels are discussed in detail. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1514–1531, 2004     

级联三能级原子与单模场相互作用下的腔场谱

研究了高Q腔内级联三能级原子与单模光场相互作用模型的腔场谱.结果表明,原子初态处于上能级时，随R=g2/g1的增大,真空场的拉比峰个数按2→6→4→2→4的规律变化，在R1时，所有的拉比峰都消失.在初始场较弱时,腔场谱可出现3峰、5峰或7峰.在初始场很强时,腔场谱中只有单一的经典共振峰.如果原子初态处在中能级且R=1,腔场谱为简单的对称双峰结构，与标准J-C模型的谱相似. 关键词： 级联三能级原子 单模光场 腔场谱     

多壁碳纳米管膜湿敏特性的研究

研究了多壁碳纳米管(MWNTs)薄膜的湿敏特性，实验所用的多壁碳纳米管是用热灯丝化学气相沉积法(CVD)合成的.分别对未修饰和修饰的多壁碳纳米管膜温度和湿度特性进行研究后发现，修饰的多壁碳纳米管对温度和湿度非常敏感，且对湿度的响应时间和恢复时间短，重复性好.而未修饰的多壁碳纳米管对温度和湿度不太敏感.对修饰多壁碳纳米管的湿敏特性进行了理论分析，给出了其理论表示式. 关键词： 多壁碳纳米管 化学修饰 湿敏特性 物理吸附     

半自由声场的全息重建和预测实验研究

半自由声场环境下的声源重建和声场预测研究对声全息技术走向实际应用具有非常重要的意义.在提出基于分布源边界点法的半自由声场全息重建和预测方法的基础上，对此展开了实验研究.并将重建和预测的结果与常规方法重建和预测的结果进行了比较和讨论，说明了重建预测过程中反射声压的影响和考虑反射声压的必要性，证明了所提出方法在解决半自由声场环境下存在地面反射时的声源重建和声场预测时的有效性和准确性.还提出了采用奇异值截断滤波和Tikhonov正则化方法来削弱测量误差的影响，从而进一步优化了重建结果，提高了全息成像的可信度. 关键词： 声全息 半自由场 边界点 声辐射 反射声