The dual variational method for n-th order ODEs with multipoint boundary conditions

We discuss the eigenvalue problem for n-th order equations with multipoint boundary conditions. We present the variational method in spite of the fact that the nonlinearity is dependent on the derivative of n/2 order. The results can be applied applied to both sublinear and superlinear cases.     

Hybrid and multi‐point formulations of the lowest‐order mixed methods for Darcy's flow on triangles

Mixed finite element (MFE) and multipoint flux approximation (MPFA) methods have similar properties and are well suited for the resolution of Darcy's flow on anisotropic and heterogeneous domains. In this work, the link between hybrid and MPFA formulations is shown algebraically for the lowest order mixed methods of Raviart–Thomas (RT0) and Brezzi–Douglas–Marini (BDM1) on triangles. The efficiency of the four mixed formulations (Hybrid_RT0, MPFA_RT0, Hybrid_BDM1 and MPFA_BDM1) is investigated on high anisotropic and heterogeneous media and for unstructured triangular discretizations. Numerical experiments show that the MPFA_BDM1 formulation outperforms both Hybrid_RT0 and Hybrid_BDM1 in the case of anisotropic domains and highly unstructured meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

Solution differentiability for parametric nonlinear control problems with control-state constraints

This paper considers parametric nonlinear control problems subject to mixed control-state constraints. The data perturbations are modeled by a parameterp of a Banach space. Using recent second-order sufficient conditions (SSC), it is shown that the optimal solution and the adjoint multipliers are differentiable functions of the parameter. The proof blends numerical shooting techniques for solving the associated boundary-value problem with theoretical methods for obtaining SSC. In a first step, a differentiable family of extremals for the underlying parameteric boundary-value problem is constructed by assuming the regularity of the shooting matrix. Optimality of this family of extremals can be established in a second step when SSC are imposed. This is achieved by building a bridge between the variational system corresponding to the boundary-value problem, solutions of the associated Riccati ODE, and SSC.Solution differentiability provides a theoretical basis for performing a numerical sensitivity analysis of first order. Two numerical examples are worked out in detail that aim at reducing the considerable deficit of numerical examples in this area of research.This paper is dedicated to Professor J. Stoer on the occasion of his 60th birthday.The authors are indebted to K. Malanowski for helpful discussions.     

Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems

We consider the boundary value problem

Weighted Best Local Approximation

In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the Lp spaces and recent results in Orlicz spaces.The notion of balanced point,introduced by Chui et al.in 1984 are extensively used.     

Immobilization/stabilization of lipase fromCandida rugosa

With the aim of fixing the enzyme to the matrix by multiple covalent linkages, lipase from Candida rugosa (formerly cylindracea) has been insolubilized through its amino groups on Sepharose 6B previously activated with 2,3-epoxy-1-propanol. Two main variables that are known to control the number of bonds formed have been tested: the contact time between enzyme and activated support, and the temperature at which the immobilization reaction is carried out. Studies on activity and stability of the different derivatives prepared showed that higher temperatures and longer contact times lead to insolubilized enzymes that are more resistant to inactivation by temperature and the presence of organic solvents. At 50 degrees C and pH 7.2, the insoluble lipase was found to be 140 times more stable than its soluble counterpart.     

Abel-Summability of Eigenfunction Expansions of Three—Point Boundary Value Problems

We study the Abel-summability of the eigenfunction expansions associated with the differential operator L generated by and splitting three-point boundary conditions. It is shown that there is no straightforward analogy between multipoint and twopoint boundary value problems. Counterexamples show that our main results are best possible. Classification. 34L10, 34B10.     

一类非线性二阶三点边值问题的正解

考察了二阶三点边值问题u”（t）＋f（t,u（t））=0,0〈t〈1;αu（O）=βu’（0）,ku（η）=u（1）的正解存在性与多解性,其中允许f（t,u）在t=0,t=1处奇异．利用锥上的Krasnosel’skii不动点定理获得了几个局部存在定理．     

蔗糖衍生物甜味剂的呈味机理及其在三氯蔗糖研究中的应用

简述了甜味剂呈味机理的研究历程,着重介绍了AH-B-X理论和多点结合理论及其在三氯蔗糖研究中的应用,并指出了研究甜味机理的意义,为寻找和合成新型的人工甜味剂提供了理论依据和指导.     

Multipoint Boundary-Value Solution of Two-Point Boundary-Value Problems

An iterative scheme, in which two-point boundary-value problems (TPBVP) are solved as multipoint boundary-value problems (MPBVP), which are independent TPBVPs in each iteration and on each subdomain, is derived for second-order ordinary differential equations. Several equations are solved for illustration. In particular, the algorithm is described in detail for the first boundary-value problem (FBVP) and second boundary-value problem (SBVP). A possible extension to higher-order BVPs is discussed briefly. The procedure may be used when the original TPBVP cannot be solved (does not converge) in a single long domain. It is suitable for implementation on computers with parallel processing. However, that issue is beyond the scope of this paper. The long domain is cut into a large number of subdomains and, based on assumed boundary conditions at the interface points, the resulting local BVPs are solved by any convenient conventional method. The local solutions are then patched by using simple matching formulas, which are derived below, rather than solving large systems of algebraic equations, as it is done in similar existing methods. Assuming that the local solutions are obtained by the most efficient methods, the overall convergence speed depends on the speed of matching. The proposed matching algorithm is based on a fixed-point iteration and has only a linear convergence rate. The rate can be made quadratic by applying standard accelerating schemes, which is beyond the scope of this article.