An Optimal Alternative Theorem and Applications to Mathematical Programming

Given a closed convex cone P with nonempty interior in a locally convex vector space, and a set , we provide various equivalences to the implication

一类n维泛函微分方程的正周期解

应用Leray-Schauder不动点定理,证明一类n维滞后型泛函微分方程至少存在一个正的周期解的一个充分条件.这类方程的正周期解问题已被一些文献研究,论文的研究方法和这些文献的研究方法不同,所得结果也不互相包含.     

Hexafluoro-2-propanol as a potent cosolvent for chemical ligation of membrane proteins

The study on membrane proteins is an important challenge mainly because of their very poor solubility in various solvents.The traditional recombinant expression strategy and the native chemical ligation method both have difficulty in generating sufficient amounts of desired proteins with high efficiency.Previous studies have shown that multiply fluorinated alcohols exhibit good ability to dissolve difficult peptide sequences,especially hexafluoro-2-propanol (HFIP).In the present study we systematically stud...     

Periodic solutions for semi-linear evolution inclusions

In this paper, we study the periodic problem for semi-linear evolution inclusion. Using techniques from multivalued analysis and fixed point theorems, we establish existence theorems under the one-sided Lipschitz condition. First we prove existence theorems for nonconvex and convex problem. Second, we look for extremal periodic solutions and prove the relaxation theorem.     

The classical Yang-Baxter equation on alternative algebras: The alternative D-bialgebra structure on Cayley-Dickson matrix algebras

We consider the Yang-Baxter equations on alternative algebras and prove that the bialgebras induced by the solutions to these equations are alternative D-bialgebras. We describe the alternative D-bialgebra structure on Cayley-Dickson matrix algebras.     

Basic representations for Eisenstein series from their differential equations

In this paper we provide a new approach for the derivation of parameterizations for the Eisenstein series. We demonstrate that a variety of classical formulas may be derived in an elementary way, without knowledge of the inversion formulae for the corresponding Schwarzian triangle functions. In particular, we provide a new derivation for the parametric representations of the Eisenstein series in terms of the complete elliptic integral of the first kind. The proof given here is distinguished from existing elementary proofs in that we do not employ the Jacobi-Ramanujan inversion formula relating theta functions and hypergeometric series. Our alternative approach is based on a Lie symmetry group for the differential equations satisfied by certain Eisenstein series. We employ similar arguments to obtain parameterizations from Ramanujan's alternative signatures and those associated with the inversion formula for the modular J-function. Moreover, we show that these parameterizations represent the only possible signatures under a certain assumed form for the Lie group parameters.     

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Fréchet Spaces

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Fréchet spaces, combined with the semigroup theory.     

Approximation by randomly weighting method in censored regression model

Censored regression (“Tobit”) models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis. This work was supported by National Natural Science Foundation of China (Grant No. 10471136), PhD Program Foundation of the Ministry of Education of China, and Special Foundations of the Chinese Academy of Sciences and University of Science and Technology of China     

Unified finite element discretizations of coupled Darcy–Stokes flow

In this article, we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy's law in the rest of the domain, and where the solutions in the two domains are coupled by proper interface conditions. All the methods proposed here utilize the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor–Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions are straightforward. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009