Alternative Second-Order Conditions in Constrained Optimization

New formulations are given for the second-order necessary conditions in parameter optimization with equality constraints. The new conditions are shown to be equivalent to previously known conditions by using the properties of projection matrices. The various conditions require different computational tools. As one of the obtained conditions requires standard computational tools (i.e., matrix inversion and eigenvalue computation), it might be useful in applications (e.g., real-time optimization schemes), when these standard tools are already in use.     

DIFFERENT EFFECTS OF RAD GENES OF SACCHAROMYCES CEREVISIAE ON INCISIONS OF INTERSTRAND CROSSLINKS AND MONOADDUCTS IN DNA INDUCED BY PSORALEN PLUS NEAR UV LIGHT TREATMENT

Abstract— The RAD1, RAD2, RAD3 and RAD4 genes of Saccharomyces cerevisiae are required for incising DNA containing UV induced pyrimidine dimers or psoralen plus 360 nm light induced interstrand crosslinks. We have now determined if these genes are also required for incising DNA at psoralen plus 360 nm light induced monoadducts. For distinguishing between incision breaks occurring at crosslinks and at monoadducts. we have used the cdc9-2 mutant, defective in DNA ligase activity at the restrictive temperature, and the radl-2 cdc9-2, rad2-5 cdc9-2 , rad3-2 cdc9-2 and rad4-4 cdc9-2 double mutant combinations. We conclude that the radl, rad2 , and rad4 mutants are defective in incising DNA both at crosslinks and monoadducts, whereas the rad3 mutant is proficient in incising DNA at monoadducts but not at crosslinks.     

Affinely Prime Dynamical Systems

This paper deals with representations of groups by "affine" automorphisms of compact,convex spaces,with special focus on "irreducible" representations:equivalently "minimal" actions.When the group in question is PSL(2,R),the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations.This analysis shows that,surprisingly,all these representations are equivalent.In fact,it is found that all irreducible affine representations of this group are equivalent.The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces.If it holds for the "universal strongly proximal space"of the group (to be defined),then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.     

Structural Analysis in the Dynamical Modelling of Chemical Engineering Systems

The dynamical modelling of physical (bio-)chemical processes based on first principles considerations is analysed from a structural point of view. Based on a classification of the variables and equations that occur in such models, we propose a general framework that can help to organise the model in a transparent way and to analyse efficiently its solv- ability properties. We show that a well-known tool in the theory of nonlinear dynamical systems, the Zero Dynamics Algorithm, can be used in the analysis of higher index mod- els and also in index reduction. The symbolic computations involved in this algorithm are readily available in the form of nonlinear system analysis packages. The proposed methods are illustrated by a few simple concrete examples. Keywords : First principles modelling, differential-algebraic systems, index reduction.