Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.     

Existence and uniqueness of solutions of reaction–convection equations with non-Lipschitz nonlinearity

In this work we study single balance law _ut+∇⋅Φ(u)=f(u)$u_t+\mathrm{\nabla }\cdot \Phi (u)=f(u)$ with bounded initial value, and find that there may exist maximal and minimal solutions, if f(u)$f(u)$ is not Lipschitz continuous at u=0$u=0$. We also show that comparison principle is valid for such solutions, and the solutions may blow up or not under certain conditions. It is determined by the strength of source supply, as well as the competition between the source and flux.     

Removable singularities of plurisubharmonic functions of restricted growth

LetG be a domain in ⁿ ,n2, letA be a connected complex (n–1)-dimensional submanifold ofG, and let be a plurisubharmonic function inGA. We obtain conditions on the growth of that guarantee the local boundedness of at a point a A G and the existence of a plurisubharmonic extension of toG.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 64–72, July, 1998.The author wishes to express her gratitude to Professor E. M. Chirka for numerous useful discussions and for his assistance in writing the present text.     

Practical use of variational principles for modeling water waves

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving a variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact traveling wave solutions are constructed when possible.     

正交各向异性摩擦接触分析的一个二阶锥线性互补法

建立了用于各向异性摩擦接触分析的一个新型互补模型:二阶锥线性互补模型.通过与弹翅性力学的类比,并引入线性二阶锥互补的概念,将正交各向异性摩擦接触定律表达为一个二阶锥线性互补模型.在此基础上,在参变量变分原理的框架下,建立了正交各向异性摩擦接触问题的有限元列式.由于避免了对摩擦锥的显式线性化,使得该文模型的变量个数较线性互补模型小很多,而解的精度又高很多.文末通过算例,说明了方法对于正交各向异性摩擦接触分析的有效性.     

键阻断原理构建中孔A型沸石

采用不同类型的有机硅烷化SiO2作为基本合成单元,制备了具有晶内中孔的A型沸石。考察了反应碱度、Si/Al比、晶化时间等合成条件对产品的影响。结果表明,苯胺基丙基三甲氧基硅烷是合成中孔A型沸石的最佳硅烷化试剂;硅烷化试剂的应用,使中孔沸石晶化过程可以通过"键阻断原理"有效控制;沸石的中孔尺寸可以通过不同类型的有机硅烷化试剂进行调控;一定范围内,其外比表面积、中孔体积随SiO2表面硅烷化度的增加而增加。通过沸石晶化过程中的"键阻断",可以制备具有晶内中孔的A型沸石。     

On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation

Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts.     

Error in an approximate wave function and an error minimization scheme

An estimate of error in an approximate wave function for a stationary state is put forward that does not require any information about the exact state. The measure is sensitive and direct. Parameters embedded in a trial wave function can be varied to minimize this error as well, leading to a variational principle. Such a scheme works nicely for bound states and the more so for Siegert states, for which the standard energy minimization principle does not apply. Pilot calculations on the anharmonic oscillator system and the radial Stark effect in the hydrogen atom reveal the worth of the endeavor. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Semiempirical evaluation of the global hardness of the atoms of 103 elements of the periodic table using the most probable radii as their size descriptors

Relying upon the fact that the density functional computation of the global hardness of the atoms of the elements are still at large and there is some mathematical in congruency between the theory and operational formula of finite difference approximation, we have suggested a radial‐dependent ansatz for evaluating global hardness of atoms as: η=a(7.2/r)+b (in eV), where, “a” and “b” are the constants and r is the absolute radius of atoms in angstrom unit. The ansatz is invoked to evaluate the global hardness of atoms of 103 element of the periodic table. The evaluated new set of global hardness is found to satisfy the sine qua non of a reasonable scale of hardness by exhibiting perfect periodicity of periods and groups and correlating the gross physicochemical properties of elements. The inertness of Hg and extreme reactivity Cs atoms are nicely correlated. The chemical reactivity and its variation in small steps in the series of lanthanide elements are also nicely reproduced. The results of the present semiempirical calculation also have strong correlation with the result of some sophisticated DFT calculation for a set of atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010