Approximate analytical solution to normal emittance of semi-transparent layer of an absorbing, scattering, and refracting medium

A two-step approximate analytical solution for the normal emittance of a plane layer of an absorbing, scattering and refracting medium is derived analytically. The analysis is based on the transport approximation and the two-step solution method for radiative transfer. The high accuracy of the approximate solution, examined by comparing its results to those obtained independently by the discrete ordinates and Monte Carlo methods, makes it suitable for application in combined experimental-analytical studies to identify selected spectral radiative properties of dispersed media in the range of semi-transparency.     

Effective potential in curved space and cut-off regularizations

We consider derivation of the effective potential for a scalar field in curved space-time within the physical regularization scheme, using two sorts of covariant cut-off regularizations. The first one is based on the local momentum representation and Riemann normal coordinates and the second is operatorial regularization, based on the Fock-Schwinger-DeWitt proper-time representation. We show, on the example of a self-interacting scalar field, that these two methods produce equal results for divergences, but the first one gives more detailed information about the finite part. Furthermore, we calculate the contribution from a massive fermion loop and discuss renormalization group equations and their interpretation for the multi-mass theories.     

A monotone version of the Sokolov property and monotone retractability in function spaces

We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X   is monotonically retractable if and only if _Cp(X)$C_p(X)$ is monotonically Sokolov. Besides, a space X   is monotonically Sokolov if and only if _Cp(X)$C_p(X)$ is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R$\mathbb{R}$-quotient images and _Fσ$F_{\sigma }$-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X   and _Cp(X)$C_p(X)$ are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X   such that _Cp(X)$C_p(X)$ has the Lindelöf Σ-property but neither X   nor _Cp(X)$C_p(X)$ is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov.     

Finite determinacy and polynomial normal forms for diffeomorphisms near a strongly 1-resonant fixed point

In this paper we study polynomial normal forms and smooth (C^∞$C^{\infty }$) classification of one kind of diffeomorphisms which have infinite many resonant relations but are finitely determined. We derive a complete list of normal forms of all such germs with arbitrary degeneracy of their nonlinear parts.     

An explicit recursive formula for computing the normal forms associated with semisimple cases

This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm.     

de Sitter空间中法联络平坦的完备类空子流形

该文证明了de Sitter空间中具有平行平均曲率向量的常数量曲率完备类空子流形,如果其法联络是平坦的,且M的截面曲率小于0,或M的第二基本形式模长平方‖σ‖相似文献   

Use of Micelles in the TLC Separation of Polynuclear Aromatic Compounds and Amino Acids

Abstract

The polynuclear aromatic compounds (PNA): anthracene, napthalene, phenanthrene, pyrene, pyrenecarboxaldehyde, benzo (a) pyrene, benzo (e) pyrene, perylene and fluorene can be chromatographed on polyamide TLC sheets using an aqueous micellar solution cf sodium dodecylsulfate (SDS) as the mobile phase. Reversed micellar solutions (of sodium dioctylsulfosuccinate) were used in a reverse phase chromatographic separation of amino acids. Some amino acids tended to streak slightly rather than move as discrete spots. Conditions could be adjusted, however, so that most of the amino acids and all PNA's would move as spots.     

正态定限（Orthant）概率

本文采用不同以往的方法；对正态定限（Ｏｒｔｈａｎｔ）概率积分施行线性变换与极坐标变换；得到了一个新的递推公式，使积分重数至少降低了３重；并推导了四维正态定限概率的表达式，这对进行数值计算是十分有意义的．     

Normal operators and inequalities in norm ideals

In this work we characterize normal invertible operators via inequalities with unitarily invariant norm of elementary operators.