Random walks in random environments on metric groups

Random walks in random environments on countable metric groups with bounded jumps of the walking particle are considered. The transition probabilities of such a random walk from a pointx εG (whereG is the group in question) are described by a vectorp(x) ε ℝ^|W| (whereW ⊏G is fixed and |W|<∞). The set {p(x),x εG} is assumed to consist of independent identically distributed random vectors. A sufficient condition for this random walk to be transient is found. As an example, the groups ℤ ^d , free groups, and the free product of finitely many cyclic groups of second order are considered. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 129–135, January, 2000.     

对称有向图的广义本原指数集

一个有向图Ｄ称为本原有向图,若存在某自然数ｋ,使Ｄ中任一点ｕ到任一点ｖ都有长为ｋ之途径。若Ｄ是一个对称有向图,则Ｄ是本原的当且仅当Ｄ对应的无向图Ｇ连通且至少包含一个奇圈。本文研究最小奇圈长为ｒ的ｎ阶对称本原有向图,完全刻划了第一类广义本原指数集,并部分地解决了第三类广义本原指数集的刻划问题。     

Knotting the MECO Network

The Conferences of the Middle European Cooperation in Statistical Physics (MECO) were created as an attempt to establish and maintain an exchange between scientists in the fields of statistical and condensed matter physics from Western and Eastern countries, overcoming the hurdles of the Iron Curtain. Based on personal remembrance and historical resources, the genesis and further development of MECO meetings is described. The annual meetings were interrupted in 1991 by the Yugoslav War but were re-established in 1993 and continue today. Although the fall of the Iron Curtain and the European Research programs changed the situation for the meetings considerably, the ties created by MECO still are useful to help scientific exchange. The history of European (and not only) statistical physics and the history of the MECO are tightly intertwined. It started in a time where an essential breakthrough has been achieved in statistical physics describing the features near phase transitions. In addition to the merging of solid-state physics and field theory concepts, the application of numerical methods (Monte Carlo methods) added a new pillar besides exact solutions and experiments to check theoretical models. In the following, the scientific emphasis (in general) has changed from the traditional fields of the first MECO to complexity and interdisciplinary themes as well.     

Methoxycyclization of 1,5-Enynes by Coinage Metal Catalysts: Is Gold Always Superior?

Au(I) catalysts promote the intramolecular cycloisomerization of 1,n-enynes, as well as facilitate reactions with alcohols, characteristics that have led to their wide-spread in the synthesis of complex natural products. Literature reports of Cu and Ag species catalyzing the same or similar reactions are much less common. Here, we utilize molecular volcano plots to assess the activity of 45 coinage metal phosphine/phosphite catalysts possessing a variety of stereoelectronic properties for the methoxycyclization reaction of a prototypical 1,5-enyne. Our analysis reveals that the intrinsic properties of gold allow it to be coupled with a wide range of ligands, all of which exhibit high catalytic activity. On the other hand, the coupling of silver and copper with more traditional phosphines, such as triphenylphosphine, leads to catalysts with diminished catalytic ability. The activity of Ag and Cu species, however, can be enhanced by appending ligands with strong π-accepting character, which shifts these species closer to the volcano peak.     

Parameterized Littlewood-Paley Operators and Their Commutators on Lebesgue Spaces with Variable Exponent

In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Littlewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley g*λ-functions, is established on the Lebesgue spaces with variable exponent. Furthermore,the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.     

Mechanical properties of bulk single crystalline nanoporous gold investigated by millimetre-scale tension and compression testing

In this work, the mechanical behaviour of millimetre-scale, bulk single crystalline, nanoporous gold at room temperature is reported for the first time. Tension and compression tests were performed with a custom-designed test system that accommodates small-scale samples. The absence of grain boundaries in the specimens allowed measurement of the inherent strength of millimetre-scale nanoporous gold in tension. The elastic modulus and strength values in tension and compression were found to be significantly lower than values measured with nanoindentation-based techniques and previously reported in the literature, but close to those reported for millimetre-scale polycrystalline samples tested using traditional compression techniques. Fracture toughness was found to be very low, in agreement with the macroscopic brittleness of nanoporous gold, but this is due to the localization of deformation to a narrow zone of ligaments, which individually exhibit significant plasticity and necking.     

Semilinear systems involving multiple critical Hardy-Sobolev exponents and three singular points

In this paper, a semilinear system of elliptic equations is investigated, which involves multiple critical exponents and singular points. By variational methods and analytic techniques, the related best Hardy-Sobolev constants is studied and the existence of positive solutions is established.     

Density and tails of unimodal convolution semigroups

We give sharp bounds for the isotropic unimodal probability convolution semigroups when their Lévy–Khintchine exponent has Matuszewska indices strictly between 0 and 2.     

Selective COSY‐J‐resolved‐HMBC,a new method for improving sensitivity of cross peaks of methine proton signals attached to a methyl group

Improved pulse sequences for measuring long‐range C‐H coupling constants (ⁿJ_C‐H), named selective COSY‐J‐resolved HMBC‐1 and ?2, have been developed. In the spin systems, such as ‐CH_C‐CH_A(CH₃)‐CH_B‐, a methine proton H_A splits into a multiplet owing to several vicinal couplings with protons, resulting in attenuation of its cross‐peak intensity. Therefore, the measurements of ⁿJ_C‐H with H_A are generally difficult in the J‐resolved HMBC or selective J‐resolved HMBC spectrum. With the aim of accurate measurements of ⁿJ_C‐H in such a spin system, we have developed new pulse sequences, which transfer the magnetization of a methyl group to its adjacent methine proton. The proposed pulse sequences successfully enable to enhance the sensitivity of H_A cross peak in comparison with the selective J‐resolved HMBC pulse sequence. Copyright © 2012 John Wiley & Sons, Ltd.