Infinite paths with bounded or recurrent partial sums

We consider problems of the following type. Assign independently to each vertex of the square lattice the value +1, with probability p, or −1, with probability 1 −p. We ask whether an infinite path π exists, with the property that the partial sums of the ±1s along π are uniformly bounded, and whether there exists an infinite path π' with the property that the partial sums along π' are equal to zero infinitely often. The answers to these question depend on the type of path one allows, the value of p and the uniform bound specified. We show that phase transitions occur for these phenomena. Moreover, we make a surprising connection between the problem of finding a path to infinity (not necessarily self-avoiding, but visiting each vertex at most finitely many times) with a given bound on the partial sums, and the classical Boolean model with squares around the points of a Poisson process in the plane. For the recurrence problem, we also show that the probability of finding such a path is monotone in p, for p≥?. Received: 10 January 2000 / Revised version: 14 August 2000 / Published online: 9 March 2001     

Weyl transforms associated with the Heisenberg group

In this paper, we define the Wigner transform and the corresponding Weyl transform associated with the Heisenberg group. We established some harmonic analysis results. Then we present that the Weyl transform with the Sp-valued symbol in Lp (p∈[1,2]) is not only bounded but also compacted, while when 2<p<+∞, the Weyl transform is not a bounded operator.     

On spherical expansions of zonal functions on Euclidean spheres

This paper describes a new approach to the problem of computing spherical expansions of zonal functions on Euclidean spheres. We derive an explicit formula for the coefficients of the expansion expressing them in terms of the Taylor coefficients of the profile function rather than (as done usually) in terms of its integrals against Gegenbauer polynomials. Our proof of this result is based on a polynomial identity equivalent to the canonical decomposition of homogeneous polynomials and uses only basic properties of this decomposition together with simple facts concerning zonal harmonic polynomials. As corollaries, we obtain direct and apparently new derivations of the so-called plane wave expansion and of the expansion of the Poisson kernel for the unit ball. Received: 26 January 2007     

On the α-amenability of hypergroups

Let UC(K) denote the Banach space of all bounded uniformly continuous functions on a hypergroup K. The main results of this article concern the α-amenability of UC(K) and quotient and product of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is α-amenable if and only if α = 1. Author’s address: Dietlinden Stra?e 16, 80802 München, Germany     

Site-specific ϕ- and ψ-torsion angle determination in a uniformly/extensively 13C- and 15N-labeled peptide

A solid-state rotational-echo double resonance (REDOR) NMR method was introduced to identify the ?- and ψ-torsion angle from a ¹H–¹⁵N or ¹H–¹³C′ spin system of alanine-like residues in a selectively, uniformly, or extensively ¹⁵N-/¹³C-labeled peptide. When a C_α(i) or a ¹⁵N peak is site-specifically obtainable in the NMR spectrum of a uniformly ¹⁵N/¹³C-labeled sample system, the ψ- or ?-torsion angle specified by the conformational structure of peptide geometry involving ¹⁵N(i)–¹H_αi–¹⁵N(i + 1) or ¹³C′(i − 1)–¹H^Ni–¹³C′(i) spin system can be identified based on ¹³C_α- or ¹⁵N-detected ¹H_α–¹⁵N or ¹H_N–¹³C REDOR experiment. This method will conveniently be utilized to identify major secondary motifs, such as α-helix, β-sheet, and β-turn, from a uniformly ¹⁵N-/¹³C-labled peptide sample system. When tested on a ¹³C-/¹⁵N-labeled model system of a three amino acid peptide Gly–[U–¹³C, ¹⁵N]Ala–[U–¹³C, ¹⁵N]Leu, the ψ-angle of alanine obtained experimentally, ψ = −40 ± 30°, agreed reasonably well with the X-ray determined angle, ψ = −39°.     

A 43Ca and 13C NMR study of the chemical interaction between poly(ethylene-vinyl acetate) and white cement during hydration

⁴³Ca and ¹³C NMR methods were used to study the chemical interaction of poly(ethylene–vinyl acetate) (PEVAc) admixture in commercial-grade white cement. From ⁴³Ca NMR it is shown both that PEVAc induces modest changes in the hydrated cement structure, and that hydrated commercial cement is significantly more complex than models that have been used for its structure in past work. The ¹³C NMR results show that the PEVAc hydrolysis occurs early in the cement hydration acceleration period, with a rate well-fit by an exponential decay using a time constant of 6±1 days.     

退火处理Fe43Co43Hf7B6Cu1非晶合金的正电子湮没研究

对熔体急冷法制备的Fe₄₃Co₄₃Hf₇B₆Cu₁非晶合金进行了200,300,400和500 ℃保温30 min的退火处理,用正电子湮没寿命谱、X射线衍射、穆斯堡尔谱等方法研究了退火后试样的结构及结构缺陷变化.结果表明,在非晶合金的制备态,正电子主要在非晶基体相空位尺寸的自由体积中湮没,湮没寿命τ₁为158.4 ps,强度I₁关键词： 43Co₄₃Hf₇B₆Cu₁非晶')" href="#">Fe₄₃Co₄₃Hf₇B₆Cu₁非晶 退火处理 正电子湮没寿命 结构与结构缺陷     

Anisotropic shearlet transforms for L2

In this paper, we present a new anisotropic generalization of the continuous shearlet transformation. This is achieved by means of an explicit construction of a family of reproducing Lie subgroups of the symplectic group. We study the properties of this new family of anisotropic shearlet transformations. In particular, we provide an analog of the Calder43;n admissibility condition for anisotropic shearlet reproducing functions.     

Spectral multipliers for Laplacians with drift on Damek–Ricci spaces

We prove a multiplier theorem for certain Laplacians with drift on Damek–Ricci spaces, which are a class of Lie groups of exponential growth. Our theorem generalizes previous results obtained by W. Hebisch, G. Mauceri and S. Meda on Lie groups of polynomial growth.