The Δ- Method for the Boltzmann Equation

A new numerical method is proposed to solve the Boltzmann equation. A frame is set up by using a discrete velocity approximation in the infinite velocity space, but by considering only those distribution function points which are not too small. The distribution function points may occur anywhere in the infinite discrete velocity space and are not constrained to a pre-specified region. A fourth-order finite difference is used for the convection terms. A Monte Carlo-like method is applied to the discrete velocity model of the collision integral. The effort of the method is proportional to the number of discrete points. Numerical examples are given for the full Boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions.     

热象无损检测技术应用

本文将热象无损检测技术应用于鉴定受测物结构和性质,并测出受测物中的缺陷,实验结果取得了较为满意的进展。     

利用莫尔条纹的准正弦特性的三维轮廓术

分析了两个矩形光栅迭合产生的莫尔条纹的光强分布特性，通过选择适当的光栅参数，可得到一个近似的正弦分划板，并把它用于三维面形测量中，实验结果表明，这种方法简单，易于自动处理，有广泛的实用价值。     

On Solvability of a Boundary Value Problem for Singular Integral Equations

This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05     

Self-Assembled Multistable Scattering Mode for Versatile Energy-Saving Smart Windows

Smart windows are crucial to dynamic control over light transmission to fulfill various demands in energy saving, privacy, and information display; however, most present technologies still perform a single function (often tint or haze adjustment) and require continuous electricity for operation. In this study, novel self-assembled ionic liquid crystals (ILCs) doped with negative cholesteric liquid crystals (CLCs) to offer electrically switchable and stable scattering-mode light modulators are presented. The novel smectic A phase based on the ILCs exhibits high solubility in the adopted nematics, enhancing the LC device's performance in several ways, including improved homogeneity, stable alignment quality, prolonged stability, and simplified fabrication. The LC device can potentially offer a dynamically rapid switching function between stable transparent (imperfect fingerprint textures) states and stable scattering (focal conic textures with small domains) states by using external stimuli and highly maintained multistable states for prolonged periods, even when the external stimuli are removed. The LC device also offers polarization-independent scattering and transparent-mode LC light modulators, low operating voltage, excellent contrast, and broad viewing angles. Its versatility and outstanding field-off stability make it ideal for various applications such as smart lighting, building climate control, energy-saving displays, and augmented reality (AR) glasses.     

EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

The classical risk process that is perturbed by diffusion is studied .The explicit expressions for the runi probability and the surplus distribution of the risk process at the time of runi are obtained when the claim amount distribution is a finite mixture of exponential distributions of a Gamma (2,α） distribution.     

New minimax inequality with applications to existence theorems of equilibrium points

A new minimax inequality is proved on a set which is the union of an increasing sequence of compact convex sets in a topological vector space. As applications, several existence theorems of equilibrium points for different games are obtained.The authors would like to thank the referees for their helpful suggestions.     

一类非线性方程存在多个极限环的一个充分条件

关于方程(1)的极限环唯多性问题,不少人作了研究,[1]引进“n重互相包含”曲线类,,经[2]的改进获得较好的结果,但这类曲线要求的条件较多。本文不从[1]的观点出发,不包含[1]的全部条件,独立地用①11。’,LtnnoB变换折叠相平面,据轨线与折叠线交点的位置,对(1)的等价方程按线性方程积分,将积分的正负项作成比值进行比较,得出一组充分条件。