On convergence of Lavrentiev regularization for semilinear parabolic optimal control problems with pointwise control and state constraints

We consider Lavrentiev regularization for a class of semilinear parabolic optimal control problems with control constraints and pointwise state constraints and review convergence results for local solutions under Slater type assumptions as well as quadratic growth conditions. Moreover, we state a local uniqueness result for local optima under the assumptions of strict separability of the active sets as well as a second order sufficient condition for the regularized solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identifying almost invariant sets in stochastic dynamical systems

We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius-Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered.     

A block‐size bound for Steiner 6–wise balanced designs

If B is a block in a proper Steiner 6–wise balanced design then |B| ≤ v/2. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 141–145, 2000     

Asymptotic completeness forN-body Stark Hamiltonians

We prove asymptotic completeness for short- and long-rangeN-body Stark Hamiltonians with local singularities of at most Coulomb type. Our results include the usual models for atoms and molecules.Research partially supported by NSF grant DMS 9307147.     

Synthesis and electrochemical properties of mono- and (±)-1,2-dialkylferrocenes and alkylferrocenium hexafluorophosphates in aqueous and micellar media

Absract Simple methods have been developed for the preparation of a series ofn-alkylferrocenes H(CH₂) _n Fc (n = 3, 5–8, or 12) based on Friedel-Crafts acylation of ferrocenes followed by reduction of the corresponding ketones with Zn amalgam. The properties of H(CH₂) _n Fc and the corresponding ferrocenium ions in micellar aqueous solutions and the behavior of water-soluble cations H(CH₂) _n Fc⁺ in the absence of micelles were studied by cyclic voltammetry. In all cases, the formal redox potentials of ferrocenes (E ^o) increase linearly asn increases up to 8. Whether micelles are present or not, the corresponding correlation equation has the following form:E ^o= + n, where = 29 mV in all cases. The synthesis of (±)-1-ethyl-2-methylferrocene from racemic -dimethylaminoethylferrocene is reported.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2575–2581, October 1996.     

PHOTOREACTIVITY OF HYDROXYPSORALENS AND THEIR PHOTOBIOLOGICAL EFFECTS IN BACILLUS SUBTILIS*

Abstract— Although psoralen and many substituted psoralens are potent skin-photosensitizing agents, hydroxypsoralens are not. A satisfactory molecular interpretation of this structural specificity has been given in terms of dissociation of the hydroxyl group of 5- and 8-hydroxypsoralens in their excited states. The dissociation process in the S₁ state effectively competes with S₁→T₁ intersystem crossing, thus reducing the photoreactive T₁ population. The T₁ states of the anions are more delocalized than those of neutral psoralens so that they are less reactive toward photocycloaddition with pyrimidine bases of DNA. The lack of significant phosphorescence of hydroxypsoralens in ionizing solvent or in the presence of base at low temperatures (14–77 K.) indicates ineffective S₁→T₁ and/or effective T₁→S₀ intersystem crossing. These factors make hydroxypsoralens unreactive, electronically and kinetically, as skin photosensitizers, which are known to react with DNA. In correlation with the hydroxypsoralens' spectroscopic characterization, they are also found to be ineffective or less effective photosensitizers in Bacillus subtilis.     

High-performance liquid chromatography of seized drugs at elevated pressure with 1.7 microm hybrid C18 stationary phase columns

High-performance liquid chromatography (HPLC) separation of drugs at elevated pressure with 1.7 microm hybrid C18 stationary phase columns was investigated. This technique, which uses instrumentation engineered to handle the narrow peaks and high back pressures generated by 1.7 microm particle columns, provided significantly better resolution and/or faster analysis than conventional HPLC and capillary electrophoresis (CE). The use of 2mm internal diameter (i.d.) columns of 3-10 cm length has been evaluated for the separation of basic and neutral drugs, drug profiling, and general screening (including acidic drugs). For these applications, compared to conventional HPLC and CE, it provided up to 12x and 3x faster analyses, respectively. Precision was excellent for both isocratic and gradient analyses. For retention time and peak area, RSDs of < or =0.1% were obtainable. Fifteen anabolic steroids and esters were well separated in a 2.5 min gradient. For drug profiling, compared to HPLC and CE, approximately twice as many peaks were resolved. HPLC at elevated pressure is also well suited as a general screening technique. Twenty-four solutes of varying drug classes including narcotic analgesics, stimulants, depressants, hallucinogens, and anabolic steroids were fully separated in a 13.5 min gradient.