Geometric and analytic views in existence theorems for optimal control. III. Weak solutions

Existence theorems are proved for weak optimal solutions of problems of optimization with distributed and boundary control. Many examples are given. Application is made of recent remarks on closure properties of linear and nonlinear operators. Recent geometric, topological, and analytical views are brought to bear on the underlying seminormality conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45209/1/10957_2004_Article_BF00934060.pd

Geometric and analytic views in existence theorems for optimal control. II. Distributed and boundary controls

Existence theorems are proved for Lagrange problems of optimization in a given domain G with possibly unbounded distributed controls in G and on the boundary of G , and with functional relations on G and on the boundary represented by closed operators, not necessarily linear. The case where the functional relations are partial differential equations is emphasized. Recent work concerning the reduction or elimination of seminormality requirements is taken into account. Many examples are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45200/1/10957_2004_Article_BF00933208.pd

Closure theorems for orientor fields and weak convergence

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46195/1/205_2004_Article_BF00250438.pd

Like grandparents, like parents: Empirical evidence and psychoanalytic thinking on the transmission of parenting styles

The authors discuss the issue of intergenerational transmission of parenting from an empirical and psychoanalytic perspective. After presenting a framework to explain their conception of parenting, they describe intergenerational transmission of parenting as a key to interpreting and eventually changing parenting behaviors. Then they present (1) the empirical approach aimed at determining if there is actually a stability across generations that contributes to harsh parenting and eventually maltreatment and (2) the psyphoanalytic thinking that seeks to explain the continuity in terms of representations and clinical phenomena. The authors also discuss the relationship between the attachment and the caregiving systems and hypothesize a common base for the two systems in childhood experience. Finally, they propose the psychoanalytic perspective as a fruitful theoretical framework to integrate the evidence for the neurophysiological mediators and moderators of intergenerational transmission. Psychoanalytically informed research can provide clinically relevant insights and hypotheses to be tested

Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained

Qualitative study of a class of nonlinear boundary value problems at resonance

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25816/1/0000379.pd

Existence theorems for abstract multidimensional control problems

In the present paper, the author discusses an abstract formulation of control problems involving general operators ℒ : S → V , ℳ : S → Y from a Banach space S into space V and Y of vector functions in a fixed domain with components in L p , p ⩾1. For this general formulation, the author states closure theorems, lower closure theorems, and existence theorems for an optimal solution. It is then shown that the problems of control involving Dieudonné-Rashevski partial differential equations previously considered by the author are particular cases of the present formulation. Finally, it is shown by examples that problems of control involving usual partial differential equations, linear or not, as well as other functional relations, can be framed in the present formulation. The present work concerns problems with distributed controls . Work concerning problems with distributed as well as boundary controls is forthcoming.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45235/1/10957_2004_Article_BF00926601.pd

Existence theorems for multidimensional Lagrange problems

Existence theorems are proved for multidimensional Lagrange problems of the calculus of variations and optimal control. The unknowns are functions of several independent variables in a fixed bounded domain, the cost functional is a multiple integral, and the side conditions are partial differential equations, not necessarily linear, with assigned boundary conditions. Also, unilateral constraints may be prescribed both on the space and the control variables. These constraints are expressed by requiring that space and control variables take their values in certain fixed or variable sets wich are assumed to be closed but not necessarily compact.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45188/1/10957_2004_Article_BF00936648.pd

Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding

We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding process shows that it proceeds in jumps between well-defined, local free energy minima. Closer analysis of the different local minima allows us to reveal secondary, parallel pathways as well as dead ends.Comment: 7 page

An elementary proof of an equivalence theorem relevant in the theory of optimization

The authors give an elementary proof of an equivalence theorem of analysis which is often used in optimization theory. The theorem asserts that certain conditions are equivalent to weak convergence in L 1 . One is the Dunford-Pettis condition concerning absolute integrability. Two others are expressed in terms of Nagumo functions, and can be thought of as growth properties. The original proofs of the various parts of the theorem are scattered in different and specialized mathematical publications. The authors feel it useful to present here a straightforward proof of the various parts in terms of standard Lebesgue integration theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45221/1/10957_2004_Article_BF00938425.pd