On ``Time-Periodic' Black-Hole Solutions to Certain Spherically Symmetric Einstein-Matter Systems

This paper explores black hole solutions of various Einstein-wave matter systems admitting a time-orientation preserving isometry of their domain of outer communications taking some point to its future. In the first two parts, it is shown that such solutions, assuming in addition that they are spherically symmetric and the matter has a certain structure, must be Schwarzschild or Reissner-Nordström. Non-trivial examples of matter for which the result applies are a wave map and a massive charged scalar field interacting with an electromagnetic field. The results thus generalize work of Bekenstein [1] and Heusler [13] from the static to the periodic case. In the third part, which is independent of the first two, it is shown that Dirac fields preserved by an isometry of a spherically symmetric domain of outer communications of the type described above must vanish. It can be applied in particular to the Einstein-Dirac-Maxwell equations or the Einstein-Dirac-Yang/Mills equations, generalizing work of Finster, Smoller and Yau [10, 8, 9 and also 7].     

Global Optimization: On Pathlengths in Min-Max Graphs

Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric.     

On the mechanism of the N,N‐dimethyl amination of Grignard reagents: a kinetic study

A direct kinetic study is reported for the electrophilic amination of substituted phenylmagnesium bromides with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine in THF. Rate data, Hammett relationship, and activation entropy are consistent with a S_N2 displacement involving the attack of carbanions to sp³N in the amination reagent (AR). Copyright © 2007 John Wiley & Sons, Ltd.     

Can Sobolev Inequality Be Written for Sharma-Mittal Entropy?

In this paper, we focus on Sobolev inequality in the context of Sharma-Mittal entropy. Using this new inequality, generalized entropic uncertainty relation in accordance with Sharma-Mittal entropy is derived and the pseudoadditivity relation has been obtained. This new entropic uncertainty relation has then been applied to physical examples such as one dimensional harmonic oscillator and Pösch-Teller potential. Finally, it has been shown that for certain values of the parameters of Sharma-Mittal measure, the present results reduce to the corresponding results of Shannon, Renyi and Tsallis measures.     

Periodic Solutions and Approximate Symmetries

Assuming that a dynamical system (DS) has a periodic solutionwith period T in the neighborhood of an equilibrium, a newDS can be obtained which governs approximately the motion oftrajectories in the neighborhood of the periodic orbit. Approximatesymmetries and first integrals have been discussed for this DS. Theresults have been demonstrated on the Helmholtz oscillator.     

On Tauberian theorems for (<Emphasis Type="Italic">A,k</Emphasis>) summability method

Let (u _n ) be a sequence of real numbers. In this paper we introduce some Tauberian conditions in terms of regularly generated sequences for (A, k) summability method.     

Zur Kenntnis einiger Triazole und ihrer Abkömmlinge

Ohne Zusammenfassung     

Solid‐State NMR investigations of anhydrous proton‐conducting acid–base poly(acrylic acid)– poly(4‐vinyl pyridine) polymer blend system: A study of hydrogen bonding and proton conduction

NMR studies of the structure and dynamics of a system composed of the acidic polymer poly(acrylic acid) (PAA) and the basic polymer poly(4‐vinyl pyridine) (P4VP) are presented. This system aims at the application of anhydrous proton‐conducting membranes that can be used at elevated temperatures at which the proton conduction of hydrated membranes breaks down. The ¹H NMR measurements have been preformed under fast magic angle spinning (MAS) conditions to achieve sufficient resolution and the applied ¹H NMR methods vary from simple ¹H MAS to double‐quantum filtered methods and two‐dimensional ¹H double‐quantum spectroscopy. The dynamic behavior of the systems has been investigated via variable temperature ¹H MAS NMR. ¹³C cross‐polarization MAS NMR provides additional aspects of dynamic and structural features to complete the picture. Different types of acidic protons have been identified in the studied PAA‐P4VP systems that are nonhydrogen‐bonded free acidic protons, hydrogen‐bonded dicarboxylic dimers, and protons forming hydrogen bonds between carboxylic protons and ring nitrogens. The conversion of dimer structures in dried PAA to free carboxylic acid groups is accomplished at temperatures above 380 K. However, the stability of hydrogen‐bonding strongly depends on the hydration level of the polymer systems. The effect of hydration becomes less apparent in the complexes. An inverse proportionality between hydrogen‐bonding strength and proton conduction in the PAA‐P4VP acid–base polymer blend systems was established. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 138–155, 2009