基于等额本息按揭贷款的脉冲增加还款模型

利用一阶线性差分方程建立了每隔半年增加还款一次的按揭贷款数学模型,并通过实例说明了其在经济生活中的具体应用.     

Symmetries in Projective Multiresolution Analyses

We give an equivariant version of Packer and Rieffel’s theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analysis. Suppose that the scaling functions are invariant with respect to some finite group action. We give sufficient conditions for the existence of wavelets with similar invariance. Research supported in part by the Research Council of Norway, project number NFR 154077/420. Some of the final work was also done with the support from the project NFR 170620/V30.     

Simultaneous quantification of five major constituents in stems of Dracaena plants and related medicinal preparations from China and Vietnam by HPLC–DAD

A high‐performance liquid chromatographic (HPLC) method was developed for the simultaneous quantification of five major bioactive constituents in the stems of resiniferous Dracaena plants from China and Vietnam, as well as those in the related traditional Chinese medicinal preparations. A diode array detector with the wavelength of 330 nm was used to monitor resveratrol, 7,4′‐dihydroxyflavone and pterostilbene, while loureirin A and loureirin B were monitored at 280 nm. The five constituents were separated on an Agela SB C₁₈ column by gradient elution using 0.008% (v/v) formic acid solution (A) and acetonitrile (B) as the mobile phase. The validation of the method included recovery, linearity, accuracy and precision (intra‐ and inter‐day variation). The range of recoveries of this method was 98.1–104.9%, with all the constituents showing good linearity (r² > 0.9999). The accuracy and precision were satisfactory, with the overall intra‐ and inter‐day variation being less than 4%. The present method has been successfully applied for the determination of all five constituents in 21 related herbal samples including 10 D. cochinchinensis stem samples, seven D. cambodiana stem samples and four purchased medicinal preparations. The contents of these constituents were analyzed using principal component analysis, which can efficiently identify raw herb of Dracaena from different sources. The study may be considered helpful to the quality control of Dracena plants and its medicinal preparations. Copyright © 2009 John Wiley & Sons, Ltd.     

Harmonic maps into loop spaces of compact Lie groups

We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ¹ into ΩG are related to Yang-Mills G-fields on ℝ⁴. This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics”     

The multivariate N-Component resolution problem with minimum assumptions

The present state of the minimum assumption multivariate component resolution theory is outlined. Some new developments are presented: limiting function domains; the analytical expression for the limiting function; efficient algorithms for defining the FIRPOL and INNPOL hyperpolyhedrons. A very low resolution data set is analyzed.     

Integral formula of Minkowski type and new characterization of the Wulff shape

Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.     

PrincipalG-bundles on nodal curves

LetG be a connected semisimple affine algebraic group defined over C. We study the relation between stable, semistable G-bundles on a nodal curveY and representations of the fundamental group ofY. This study is done by extending the notion of (generalized) parabolic vector bundles to principal G-bundles on the desingularizationC ofY and using the correspondence between them and principal G-bundles onY. We give an isomorphism of the stack of generalized parabolic bundles onC with a quotient stack associated to loop groups. We show that if G is simple and simply connected then the Picard group of the stack of principal G-bundles onY is isomorphic to ⊕_m Z,m being the number of components ofY.     

Barth type vanishing theorem

In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.      

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.