Errata Corrige: General Ekeland's Variational Principle for Set-Valued Mappings

Journal of Optimization Theory and Applications -     

Nizhnik方程组的一个非线性变换和多重孤子解

用齐次平衡原则导出了一个非线性变换,通过该变换Nizhnik方程组化为一个齐2次方程.用Hirota方法可求出齐2 次方程的一列解.将其代入非线性变换,得Nizhnik方程组的多重孤子解.详细分析了二重孤子解.     

Symmetry and optimal control in economics

This paper provides a new simple version of Noether's theorem. From symmetries of dynamic optimal programs, this theorem gives invariant quantities along optimal paths. It is suited to optimal control programs especially for economic models. Applications in growth economics are given.     

Rearrangement inequalities for functionals with monotone integrands

The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F(u₁,…,u_m) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂_i∂_jF for all i≠j. This paper concerns the regularity assumptions on F and the equality cases. It is shown here that extended Hardy-Littlewood and Riesz inequalities are valid for supermodular integrands that are just Borel measurable. Under some nondegeneracy conditions, all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant (i.e., measure-preserving maps for the Hardy-Littlewood inequality, translations for the Riesz inequality). The proofs rely on monotone changes of variables in the spirit of Sklar's theorem.     

An error analysis and the mesh independence principle for a nonlinear collocation problem

A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton's method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution method. Simple techniques are applied for estimating certain discretization and iteration constants that are used in the formulation of a mesh refinement strategy and an efficient multilevel method. Several mesh refinement strategies for solving a test problem are compared numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Minimum principle for mixtures with memory

This work concerns the theory of viscoelastic composites which are modelled as mixtures of two interpenetrating solid continua. First it is given a characterization of the boundary-initial value problem in which the initial conditions are incorporated into the field equations. Then a minimum principle for the dynamic theory is established.     

Relationship between basicity and nucleophilicity

The empirical concepts of basicity and nucleophilicity are related but not strictly proportional. Hence, the aim of this study is to help in elucidating the range where both concepts are directly proportional. To do this, the relationship between a recently introduced nucleophilicity index and the proton affinity (PA) of several families of bases has been studied. A good correlation between the PA and the nucleophilicity index using HF and HCN as electrophilic partner has been found. Our studies show that the correlation exists only when the interaction is soft–soft in character and for strong bases with weak acids. However, the relationship is not only valid for exothermic reactions as it has been previously postulated but also for endothermic reactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields

We prove suitable versions of the weak maximum principle and of the maximum propagation for solutions u of a differential inequality Hu?0. Here H=_∑i,jai,j(z)ZiZj+Z₀ is a differential operator structured on the vector fields Zj's, whereas u belongs to an appropriate intrinsic class of regularity modelled on the Zj's.     

An invariance principle for Azéma martingales

An invariance principle for Azéma martingales is presented as well as a new device to construct solutions of Emery's structure equations.     

Consistent relations in the method of reducibility in the cluster variation method

A redundancy is noted in the set of Lagrange multipliers—effective fields and effective interactions—used in the expressions of the reduced density matrices given by Morita⁽⁴⁾ in some problems with less symmetry⁽⁶⁾. The expressions of the reduced density matrices without this redundancy are given. An argument showing that a certain expression of the free energy in terms of the Lagrange multipliers is stationary with respect to the variations of these is presented.