Convergence rate of approximate solutions to weakly coupled nonlinear systems

We study the convergence rate of approximate solutions to nonlinear hyperbolic systems which are weakly coupled through linear source terms. Such weakly coupled systems appear, for example, in the context of resonant waves in gas dynamics equations.

This work is an extension of our previous scalar analysis. This analysis asserts that a One Sided Lipschitz Condition (OSLC, or -stability) together with -consistency imply convergence to the unique entropy solution. Moreover, it provides sharp convergence rate estimates, both global (quantified in terms of the -norms) and local.

We focus our attention on the -stability of the viscosity regularization associated with such weakly coupled systems. We derive sufficient conditions, interesting for their own sake, under which the viscosity (and hence the entropy) solutions are -stable in an appropriate sense. Equipped with this, we may apply the abovementioned convergence rate analysis to approximate solutions that share this type of -stability.

     

EPR study of electron spin polarization in the photoexcited triplet state of chlorophyll a and b

The photoexcited triplet states of chlorophyll à and b are studied by the EPR method at ≈85 K using modulated light excitation. Both compounds show anomalous EPR line intensities and transient kinetics, indicating electron spin polarization (ESP) in the photoexcited triplet state. EPR studies, using Mg-tetraphenyl porphyrin (MgTPP) dissolved in n-octane show that ESP occurs also in that solvent. It is shown that the zero field splitting (ZFS) parameters of MgTPP depend strongly on the solvent. From the analysis of the data for chlorophyll a and b we evaluate: (1) the population rate constants (k_p); (2) the ratio between the population rate constants (A_p) (p = x, y, z) and, (3) the spin lattice relaxation rate W. In both chlorophylls the in-plane component, x, is predominantly populated and depopulated. The ZFS parameters have been also determined for the above compounds.     

General Approximate Solutions for some Common Inventory Models

Employing a group of general approximations introduced elsewhere, we derive explicit approximate solutions to the standard newsboy problem, to some (Q, r) models recently developed, and to a periodic review order up to R model. The solutions obtained are general in that no distributional assumptions need to be specified prior to their derivation, and merely knowledge of the first three or four moments (of the relevant random variables) is required. The accuracy achieved is satisfactory, while algebraic simplicity is preserved.     

RESEARCH NOTE

A previous report [Freeman et al. (1986) Photochem. Photobiol. 43S, 93S] indicated that irradiation of human skin in situ with 385 or 405 nm radiation produced detectable levels of pyrimidine dimers in DNA. Since these wavelengths are absorbed poorly by DNA, these results suggested that DNA damage was sensitized by other absorbing molecules present in skin. Examination of two experimental aspects of the previous work indicates that (1) the static gel electrophoresis method for DNA dispersion used in lesion determination gave accurate values of the levels of induced dimers, and (2) the DNA damage apparently induced by 385 nm was actually induced by shorter wavelength UV present in the 20 nm bandpass beam of the monochromator. The current results indicate that monochromatic 385 and 405 nm radiation are ineffective in dimer production in human skin in situ.     

Perfect sets of random reals

We show that the existence of a perfect set of random reals over a modelM ofZFC does not imply the existence of a dominating real overM, thus answering a well-known open question (see [BJ 1] and [JS 2]). We also prove that (the product of two copies of the random algebra) neither adds a dominating real nor adds a perfect set of random reals (this answers a question that A. Miller asked during the logic year at MSRI). The first author would like to thank the MINERVA-foundation for supporting him. The second author would like to thank the Basic Research Foundation (the Israel Academy of Sciences and Humanities) for supporting him.     

Quartet Pair and Radical Quartet Pair Mechanisms of Electron Spin Polarization Developed within Nonbonded Dimers

Novel mechanisms of the electron spin polarization were reported. Effect of spin-selective interactions within the photo-excited preexisting molecular dimers was utilized. Processes occurring within dimers and upon escape from the dimer cage were considered.     

Trivalent Copper Complexes with 1,4,8,11-Tetramethyl-1,4,8,11-tetraazacyclotetradecane in Aqueous Solutions. A Pulse Radiolysis and Electrochemical Study

The mechanisms and kinetics of the formation and decomposition of the complexesCu^IIIL_aq and [LCu^IIIN₃]²⁺ are reportedand discussed.     

Forcing axioms and the Galvin number

Periodica Mathematica Hungarica - We study the Galvin property. We show that various square principles imply that the cofinality of the Galvin number is uncountable (or even greater than $$\aleph...