The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

光学薄膜在现代汽车工业中的应用

本文论述应用光学薄膜技术对汽车窗口玻璃和塑料的若干性能进行改进的技术发展水平，这些性能包括塑料表面的硬化，红外区的反射，紫外区的吸收，偏振化作用，双折射，憎水性以及光学角度选择性等，评论等离子体处理和物理蒸汽淀积薄膜工艺近来应用的一些例子。对于物理蒸汽淀积薄膜所提供的异常功能连同实际使用中它们的耐久性作了特殊的强调。     

Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

α-Al2O3纳米粒子对Co-Ni合金异常共沉积电化学行为的影响

为了研究在电化学复合共沉积过程中,惰性纳米粒子和金属离子、电极表面的相互作用,以及由此产生的对合金电化学共沉积行为的影响.本文从两个吸附过程出发: 电解液中的金属离子和H＋在纳米粒子表面的吸附；纳米粒子迁移到阴极表面,在电极表面的吸附.采用Zeta电势和稳态极化以及电化学交流阻抗（EIS）研究了纳米Al2O3粒子和电解液中的金属离子，和电极表面的相互作用,进而分析了纳米粒子对Co2＋和Ni2＋还原沉积的影响规律.通过对阻抗数据的拟合,讨论了Al2O3纳米粒子对等效电路中各物理参数的影响.在H＋和不同金属离子在纳米粒子上发生竞争吸附的基础上,提出了纳米粒子和合金共沉积的可能反应历程.     

Novel zigzag-shaped compounds exhibiting apolar columnar mesophases with oblique and rectangular lattices

The design, synthesis and characterisation of some compounds whose constituent molecules have a completely new shape have been carried out. A total of eight different series/part of series of these zigzag-shaped compounds that are either symmetrical or unsymmetrical were synthesised. Only two mesophases were observed, and on the basis of polarising optical microscopy, differential scanning calorimetry, X-ray diffraction and electro-optical studies, these have been characterised as columnar phases with a rectangular or an oblique lattice. Perhaps, these represent the first examples of a rigid zigzag-shaped compound exhibiting a mesophase.     

Comparisons of the vector method and tensor method for simulating liquid crystal devices

In calculating the director configuration in a liquid crystal device, two methods are commonly employed: a vector model and a tensor model. In this paper, we compare and contrast these methods for liquid crystal devices consisting of a layer of liquid crystal sandwiched between two plates. We compare the reliability and accuracy of the results, the speed of computation and the complexity of implementations of each method.     

Invariance for stochastic differential systems with time-dependent constraining sets

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.     

钨球对高硬度钢斜侵彻效应

为研究高硬度钢板抗不同着角钨球的侵彻性能及破坏模式,通过弹道枪进行了?8 mm、?11 mm钨合金球形破片以0°、20°、40°着角撞击厚度为6 mm、8 mm的高硬度钢板试验,得到了极限贯穿速度v₅₀;分析了钨球轴向径向变形及靶板失效模式与撞击速度的关系,发现高硬度钢板失效模式主要为压缩开坑破坏和沿厚度方向剪切破坏。采用有限元方法对试验进行了模拟,验证了数值模型及参数的合理性,并运用数值模拟方法研究了撞击着角对靶板吸能模式影响,结合试验数据,修正已有极限贯穿速度计算公式。结果表明:随侵彻着角增大,极限贯穿速度提高,且着角越大,极限贯穿速度增长越快;随着角增大,靶板吸能模式逐渐由压缩开坑向剪切冲塞过渡,且着角大于50°时,剪切冲塞耗能将超过压缩开坑耗能;修正后极限贯穿速度计算公式适用范围更广、精度更高,具有较好工程应用价值。     

基于斜向背散射偏振拉曼光谱的{100}c-Si面内应力分析

复杂应力状态下应力分量的解耦分析对半导体的设计和制造具有重要意义。本文开展了方法学研究,首先建立了{100}晶面族单晶硅面内应力分量解耦分析模型,基于该模型,通过改变入射光和散射光的几何构型和偏振构型,可得到单晶硅拉曼频移与应力分量的解析关系。在此基础上,提出了一种利用斜向背散射偏振拉曼光谱在不同倾角、偏振方向和样品旋转角度下开展原位拉曼探测实现应力分量解耦分析的实用技术。本文通过实验验证了该方法的可靠性和适用性。