Extended affine Weyl groups and Frobenius manifolds

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F(t₁, ..., t_n) of WDVV equations of associativity polynomial in t₁, ..., t_n-1, exp t_n.     

Lipids from Flowers and Leaves of <Emphasis Type="Italic">Artemisia annua</Emphasis> and Their Biological Activity

Chemical, chromatographic, and spectral methods were used to show that the main components of the lipid extract of flowers and leaves are free and bound aliphatic and cyclic alcohols (sterols and triterpenols) and essential oil. It was shown that the lipid extract of Artemisia annua has a positive influence on skin metabolism and possesses anti-inflammatory activity.__________Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 226–229, May–June, 2005.     

混合极性溶剂乙二醇／水中正负离子表面活性剂SDS／CTAB的界面性质研究

正负离子混合表面活性剂由于其特异的自组织行为及良好的稳定性,已成为研究生物膜和用于生物活性物质分离分析的理想模型[1-2],近年来,该体系在界面化学性质中得到了广泛的研究,但是由于正负电性中和,其水溶液很不稳定,一旦超过临界胶束浓度(CMC),极易发生沉淀,从而失去表面活性,使其应用受到限制.     

Measurements of surface coordinates and slopes by shearography

This paper represents an optical method which is based on speckle-shearing interferometry for the measurement of surface coordinates and slopes. The technique enables generation of carrier fringes which measure surface coordinates, or displacement derivative fringes which measure surface slope. The theory of the method as well as some experimental results are presented.     

A method for constructing the polar cone of a polyhedral cone,with applications to linear multicriteria decision problems

The necessary and sufficient conditions for solution sets of linear multicriteria decision problems are given in the first part of this paper. In order to find the solution sets by applying the theorem describing the conditions, the constructions of the open polar cone and the semi-open polar cone of a given polyhedral cone are required.A method of construction of the polar cone, open polar cone, and semi-open polar cone is presented. For this purpose, edge vectors of the polar cone are introduced and characterized in terms of the generating vectors of a given polyhedral cone. It is shown that these polar cones are represented by the edge vectors.Numerical examples of linear multicriteria decision problems are solved to illustrate the construction of the polar cones and to explain the application of the theorem to obtain the solution sets.The author is grateful to Professor P. L. Yu for helpful comments concerning the development of Theorem 2.1.     

Fast direct solvers for Poisson equation on 2D polar and spherical geometries

A simple and efficient class of FFT‐based fast direct solvers for Poisson equation on 2D polar and spherical geometries is presented. These solvers rely on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the second‐ and fourth‐order finite difference discretizations. Using a grid by shifting half mesh away from the origin/poles, and incorporating with the symmetry constraint of Fourier coefficients, the coordinate singularities can be easily handled without pole condition. By manipulating the radial mesh width, three different boundary conditions for polar geometry including Dirichlet, Neumann, and Robin conditions can be treated equally well. The new method only needs O(MN log₂ N) arithmetic operations for M × N grid points. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 56–68, 2002     

Magnetic and magneto-optical properties of Co-P films prepared by chemical deposition

Features in the formation of chemically deposited polycrystalline Co-P films with thicknesses of a few nanometers are established by analyzing film surface morphology and variation in the film magnetization. It is shown that in the thickness range below 30 nm the polar Kerr effect value θ_K changes nonmonotonically and depends on a wavelength of the incident light. For the films thicker than 30 nm, this value depends weakly on both the thickness and the wavelength. These features in the θ_K behavior are attributed to the Faraday effect, which is revealed at small thicknesses upon light reflection from the lower surface of a magnetic layer. It is found that the Faraday effect in the Co-P films exceeds that in the Co films by a factor of more than two. This effect is assumed to be caused by the presence of a Pd underlayer in the samples under study.     

Metric characterization of apartments in dual polar spaces

Let Π be a polar space of rank n and let Gk(Π), k∈{0,…,n−1} be the polar Grassmannian formed by k-dimensional singular subspaces of Π. The corresponding Grassmann graph will be denoted by Γk(Π). We consider the polar Grassmannian Gn−1(Π) formed by maximal singular subspaces of Π and show that the image of every isometric embedding of the n-dimensional hypercube graph Hn in Γn−1(Π) is an apartment of Gn−1(Π). This follows from a more general result concerning isometric embeddings of Hm, m?n in Γn−1(Π). As an application, we classify all isometric embeddings of Γn−1(Π) in Γn^′−1(Π^′), where Π^′ is a polar space of rank n^′?n.     

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.