Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection

We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m$m$-player stopping games and a new kind of m$m$-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided.     

Comparison theorems for weak splittings of bounded operators

Summary Comparison theorems for weak splittings of bounded operators are presented. These theorems extend the classical comparison theorem for regular splittings of matrices by Varga, the less known result by Wonicki, and the recent results for regular and weak regular splittings of matrices by Neumann and Plemmons, Elsner, and Lanzkron, Rose and Szyld. The hypotheses of the theorems presented here are weaker and the theorems hold for general Banach spaces and rather general cones. Hypotheses are given which provide strict inequalities for the comparisons. It is also shown that the comparison theorem by Alefeld and Volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators.This work was supported by the National Science Foundation grants DMS-8807338 and INT-8918502     

The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct edge-slopes in such a drawing of a planar graph with maximum degree Δ. We show that the planar slope number of every planar partial 3-tree and also every plane partial 3-tree is at most O(Δ ⁵). In particular, we answer the question of Dujmovi? et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f(Δ) slopes.     

On the reflexivity of subspaces of Toeplitz operators on the hardy space on the upper half-plane

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ^∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L ¹ spaces.     

Precision Penning trap mass measurements of rare isotopes produced by projectile fragmentation

The low-energy beam and ion trap facility LEBIT at NSCL/MSU is at present the only facility where precision experiments are performed with stopped rare isotope beams produced by fast-beam fragmentation. LEBIT combines high-pressure-gas stopping with advanced ion manipulation techniques to provide brilliant low-energy beams. So far these beams have mainly been used for mass measurements on short-lived rare isotopes with a 9.4T Penning trap mass spectrometer. Recent examples include ^70m Br , located at the proton dripline, ³²Si and the iron isotopes ^63-65Fe . While the measurement of ³²Si helps to solve a long-standing dispute over the validity of the isobaric multiplet mass equation (IMME) for the A = 32 , T = 2 multiplet, the mass measurements of ^65m,g Fe marked the first time a nuclear isomeric state has been discovered by Penning trap mass spectrometry.     

On a new set-valued stochastic integral with respect to semimartingales and its applications

We present a new approach to a concept of a set-valued stochastic integral with respect to semimartingales. Such an integral, called set-valued stochastic up-trajectory integral, is compatible with the decomposition of the semimartingale. Some properties of this integral are stated. We show applicability of the new integral in set-valued stochastic integral equations driven by multidimensional semimartingales. The uniqueness theorem is presented. Then we extend the notion of the set-valued stochastic up-trajectory integral to definition of a fuzzy stochastic up-trajectory integral with respect to semimartingales. A result on uniqueness of a solution to fuzzy stochastic integral equations incorporating the new fuzzy stochastic up-trajectory integral driven by the multidimensional semimartingale is stated.     

Silicate Xerogels with Dopant-Induced Chirality

A series of silicate xerogels with entrapped chiral amino acids have been obtained via sol-gel technology. The transparent, glassy samples obtained exhibit chirality in the bulk due to the presence of the entrapped asymmetric molecules. Measurements of the optical activity of the doped xerogel samples revealed that the entrapment did not significantly influence the optical activity observed for liquid solutions of the amino acids. Thus, the sol-gel method enables the preparation of amorphous optical materials exhibiting properties of strictly spatially defined molecular systems. Apart from the obvious optical applications, such porous materials with asymmetric centers might find interesting applications in chiral chemical syntheses and separations.     

Nucleophilic Substitution at Tetracoordinate Phosphorus. Stereochemical Course and Mechanisms of Nucleophilic Displacement Reactions at Phosphorus in Diastereomeric cis- and trans-2-Halogeno-4-methyl-1,3,2-dioxaphosphorinan-2-thiones: Experimental and DFT Studies

Geometrical cis- and trans- isomers of 2-chloro-, 2-bromo- and 2-fluoro-4-methyl-1,3,2-dioxaphosphorinan-2-thiones were obtained in a diastereoselective way by (a) sulfurization of corresponding cyclic P^III-halogenides, (b) reaction of cyclic phosphorothioic acids with phosphorus pentachloride and (c) halogen–halogen exchange at P^IV-halogenide. Their conformation and configuration at the C₄-ring carbon and phosphorus stereocentres were studied by NMR (¹H, ³¹P) methods, X-ray analysis and density functional (DFT) calculations. The stereochemistry of displacement reactions (alkaline hydrolysis, methanolysis, aminolysis) at phosphorus and its mechanism were shown to depend on the nature of halogen. Cyclic cis- and trans-isomers of chlorides and bromides react with nucleophiles (HO⁻, CH₃O⁻, Me₂NH) with inversion of configuration at phosphorus. DFT calculations provided evidence that alkaline hydrolysis of cyclic thiophosphoryl chlorides proceeds according to the S_N2-P mechanism with a single transition state according to the potential energy surface (PES) observed. The alkaline hydrolysis reaction of cis- and trans-fluorides afforded the same mixture of the corresponding cyclic thiophosphoric acids with the thermodynamically more stable major product. Similar DFT calculations revealed that substitution at phosphorus in fluorides proceeds stepwise according to the A–E mechanism with formation of a pentacoordinate intermediate since a PES with two transition states was observed.     

Chromatographic and Computational Studies of the Physicochemical Properties of Cholinesterase Inhibitors — Alkyl- and Arylcarbamate Derivatives of N-Benzylpiperidine and N-Benzylpiperazine

JPC – Journal of Planar Chromatography – Modern TLC - This paper reports an investigation of physicochemical properties of four series of carbamates of 3-hydroxy and...