Analytic families of semihyperbolic generalized polynomial-like mappings

We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we associate to each analytic family of semihyperbolic GPLs a weakly regular analytic family of conformal graph directed Markov systems with the Hausdorff dimension of the limit sets equal to the Hausdorff dimension of the Julia sets of the corresponding semihyperbolic GPLs.     

Nontrivial solutions for Neumann problems with an indefinite linear part

In this paper, we consider a semilinear Neumann problem with an indefinite linear part and a Carathéodory nonlinearity which is superlinear near infinity and near zero, but does not satisfy the Ambrosetti-Rabinowitz condition. Using an abstract existence theorem for C¹-functions having a local linking at the origin, we establish the existence of at least one nontrivial smooth solution.     

Non‐homogeneous infinitely many sites discrete‐time model with exact coalescent

Kingman's coalescent is among the most fertile concepts in mathematical population genetics. However, it only approximates the exact coalescent process associated with the Wright–Fisher model, in which the ancestry of a sample does not have to be a binary tree. The distinction between the approximate and exact coalescent becomes important when population size is small and time has to be measured in discrete units (generations). In the present paper, we explore the exact coalescent, with mutations following the infinitely many sites model. The methods used involve random point processes and generating functionals. This allows obtaining joint distributions of segregating sites in arbitrary intervals or collections of intervals, and generally in arbitrary Borel subsets of two or more chromosomes. Using this framework it is possible to find the moments of the numbers of segregating sites on pairs of chromosomes, as well as the moments of the average of the number of pairwise differences, in the form that is more general than usually. In addition, we demonstrate limit properties of the first two moments under a range of demographic scenarios, including different patterns of population growth. This latter part complements results obtained earlier for Kingman's coalescent. Finally, we discuss various applications, including the analysis of fluctuation experiments, from which mutation rates of biological cells can be inferred. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic differential equations with jump reflection at time-dependent barriers

We study existence, uniqueness and approximation of solutions of stochastic differential equations with jump reflection at time-dependent barriers. The basic idea in proofs consists in applying new existence and stability theorems on deterministic one-dimensional Skorokhod problem. Our results are new even in the classical case of one reflecting barrier.     

Isosceles-orthogonality preserving property and its stability

For real normed spaces, we consider the class of linear operators, preserving approximately the relation of isosceles-orthogonality. We show some general properties of such mappings. Next, we examine whether an approximately orthogonality preserving mapping admits an approximation by an orthogonality preserving one. In regard to this, we generalize some results obtained earlier for inner product spaces with standard orthogonality relation.     

Carbon-13 Kinetic Isotope Effects in the Decarbonylation Of Liquid Formic Acid in Water Solution

Abstract

Carbon-13 kinetic isotope effects (¹³C KIEs) in the decarbonylation of formic acid diluted with water 1:1 (V:V) has been studied in the 130–181°C temperature interval in sealed vacuum all glass reactions vessels. The experimental ¹³C KIEs are higher than the ¹³C KIEs values extrapolated from low 50–100°C temperature interval ¹³C KIEs observed in the decarbonylation of water free liquid formic acid but less than ¹³C KIEs expected theoretically assuming the complete carbon—oxygen (¹³C[sbnd]¹⁶O) bond rupture in the transition state. For instance the (k₁₂/k₁₃) KIE found in this study is 1.0375 at 170.2°C while the “full” ¹³C KIE is expected to be 1.0429 at this temperature. The ¹³C KIE extrapolated to 170.2°C from the low temperature data published earlier is 1.0299. - The Arrhenius activation energy for the decarbonylation of formic acid in 1:1 water solution E = 31.3 kcal/mol is by 6 kcal/mol higher than that which was obtained with 99,9% pure formic acid (E = 25,660 kcal/mol). The entropy of activation ΔS ^≠ increased from -21.4 e.u. (pure formic acid) to -15.3 e.u. in the decarbonylation of formic acid diluted with water 1:1. The increases of the enthalpy of activation, of the entropy of activation and partly of the carbon-13 kinetic isotope effect observed in the decarbonylation of formic acid in water solution have been rationalized by suggesting isotopic equilibria interfering the pure kinetic fractionation of ¹³C and intervention of the water molecules into the process of transfer of protons to the formic acid molecules lowering the absolute rate of their decomposition.     

Das Auflösungsvermögen des Szintiscanners “Szintitest” bei der Nierenszintigraphie

Der vom VEB Vakutronik WIB Dresden hergestellete Szintiscanner “Szintitites” wird auf seine Einsatzmöglichlichkeit für die Nierenszintigraphic geprüft. Dazu werden Szintigramme von Modellen aufgenommen, die in ihren Impulsdichten in der Gröβenordnung liegen, wie sie nach Applikation von 300 500µCi¹³¹ J-Hippuran über den Nieren und dem anderen Gewebe der Patienten gefunden werden. Zum Einsatz kommt dabei der Konuskollimator mit einer Apertur von 12 mm. Die besser auflösenden 9- und 19- Kanal-Kollimatoren scheiden für die Nierenszintigraphie mit dem “Szintitest” aus, da ihre Effektivität zu gering ist. Die Einflüsse der Abtastgeschwindigkeit, einer bestimmten Untergrundzählrate und eines variablen Abstandes zwischen Scanner und Objekt werden untersucht. Dabei zeigt sich, daβ ein Körperoberfläche, nicht erreicht werden kann. Das Auflösungsvermögen als 2 cm auch im günstigsten Fall von etwa 8 cm Abstand von der Nierenoberfläche, d. h. 2 4 cm von der Köperoberfläche, nicht werden kann. Das Auflösungsvermögen verschlechtert sich dagegen noch je nach Abstand und Untergrun von 2 auf 3 cm.