Semigroups for Generalized Birth-and-Death Equations in lp Spaces

We prove the existence of C₀ semigroups related to some birth-and-death type infinite systems of ODEs with possibly unbounded coefficients, in the scale of spaces l^p, For some particular cases we also provide a characterization of the spectra of their generators. For the proof of the generation theorem in the case p > 1 we extend the Chernoff perturbation result ([9]) on relatively bounded perturbations of generators. The results presented here have been used in [5] and they play important role for analysing chaoticity of dynamical systems considered there. As a by-product of our approach we obtain a result related to the classical Shubin theorem [20]. We show that this theorem, saying that for a class of bounded infinite matrices the spectrum of the corresponding maximal operator in l^p is independent on cannot be extended to unbounded matrices.     

Beiträge zur Chemie der Alkylverbindungen von Übergangsmetallen. XIII. Über die Reaktion von Vanadinsäure-triisopropylester mit Zinkdimethyl—Zur Kenntnis des Methylvanadinoxiddiisopropoxids

Contributions to the Chemistry of Transition Metal Alkyl Compounds. XIII. the Reaction of Vanadium Isopropyl Ester with Dimethyl Zinc. — On the Formation of CH₃VO(i-OC₃H₇)₂ Dimethyl zinc reacts with ortho vanadium acid triisopropyl ester forming methyl zinc isopropoxide (CH₃Zn-i-OC₃H₇)_n and methyl vanadium oxide diisopropoxide CH₃VO(i-OC₃H₇)₂. The new σ-organovanadium compound was isolated and thoroughly characterized.     

Polyolefins - poly(ethylene oxide) blends: Structure and properties

Structure and properties of polyolefins-poly(ethylene oxide) (PEO) blends were studied by combination of thermal analysis, light microscopy and fluorescence probe technique. Mixing and preparation conditions influence the calorimetric behavior, changing heat and temperature of melting and crystallinity degree of blended polymers. Values of the static mechanical parameters as well as flow characteristic parameters of the blends are lower for the higher PEO fraction in the samples. Fluorescence investigation of pyrene (changes in the vibrational fine structure) showed a nonhomogeneous distribution of the probe molecules between polyolefin and PEO environment. From these data the partition coefficient between polyolefin and PEO phase can be calculated and correlated with the crystallinity changes of the mixture composition.     

Efficiency of second harmonic generation for partially coherent light in anisotropic crystals

This paper analyzes the second harmonic generation (SHG) efficiency of light with partial temporal coherence due to depolarization effects in birefringent media. It discusses relations between SHG efficiency fading, light source spectrum, crystal birefringence, and phase matching conditions. The efficiency of SHG pumped by the partially coherent light beam that may depolarize light in nonlinear birefringent crystal is also analyzed. The basic theory of SHG with its modification for partially coherent light with depolarization and some numerical calculations of the SHG process are described. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 207, May 17–20, 2007, Świnoujście, Poland     

On the initial layer and the existence theorem for the nonlinear Boltzmann equation

The truncated Hilbert expansion including the initial layer terms is considered. This enables us to replace the singulary perturbed Boltzmann equation by a weakly nonlinear equation. In this way the existence of a strong solution of the Boltzmann equation is obtained for initial data close enough to a local Maxwellian. The solution exists in the physically significant time interval on which smooth solutions to the Euler equations exist.     

Sur la solution fondamentale de l'équation aux dérivées partielles du type parabolique

Résumé L'auteur construit la solution fondamentale pour l'équation aux dérivées partielles du type parabolique à deux variables indépendantes en partant de celle de l'équation construite parJ. Hadamard. à Mauro Picone pour son 70^me anniversaire.     

Stochastic differential equations for the kinetic and hydrodynamic equations

A finite system of stochastic interacting particles is considered. The system approximates the solutions of the kinetic equations (the Boltzmann equation, the Boltzmann-Enskog equation) as well as the solutions describing the macroscopic evolution of fluids: the Euler and the Navier-Stokes hydrodynamic equations.     

Radon concentration of outdoor air: measured by an ionization chamber for radioisotope monitoring system at radioisotope institute

Gas-flow ionization chambers for radioisotope (RI) monitoring systems at RI institutes throughout Japan are commonly used to measure RIs which leak from the RI institutes. Before the Japan’s 2011 Tohoku earthquake [11 March 2011, moment magnitude (M _w) 9.0], ionization current data measured with a gas-flow ionization chamber at the RI institute of Fukushima Medical University were found to change. The question we must raise is whether the variation ionization current can be considered to the variation of outdoor radon concentration. The conversion factors (from ionization current to radon concentration in air) of the gas-flow ionization chamber can be obtained by measuring four levels of radon concentration (outdoor air, indoor air, high level and radon-free gas) with an AlphaGUARD monitor and the chamber itself. The two gas-flow ionization chambers consist of the air intake and terminal exhaust duct of the RI institute. It was found that the radon concentration in the exhaust air was the same as that in the air intake. This study provided evidence that variations of outdoor radon concentration could be determined using gas-flow ionization chambers for RI monitoring systems.