New synthesis of hexamethyltungsten(VI); hexamethylrhenium(VI) and dioxotrimethylrh enium(VII)

A new synthesis of hexamethyltungsten involves the reaction of WCl₆ and AlMe₃, while interaction of AlMe₃ and ReOMe₄ gives ReMe₆; a dioxorhenium(VII) methyl, ReO₂ Me₃, is reported.     

Integer points on the curve

We completely solve diophantine equations of the form where is a positive integer, using a reduction to some quartic elliptic equations, which can be solved with well known methods.

     

QoS provision in wireless access networks: a routing perspective considering mobility

Future wireless communications are expected to provide mobile users access to the desired service with the appropriate quality at any place. The essential elements for assembling such a vision are mobility, quality of service (QoS) provision and scalability, which are expected to be merged into the design process of wireless access networks. Internet mobility support is currently entering a mature phase in which scalable solutions provide low loss or even seamless handovers in cellular and heterogeneous mobile environments. Wireless and mobile QoS architectures extend the equivalent Internet approaches in order to accommodate the requirements associated with the presence of wireless links and mobility. Nevertheless, none of the popular mobility proposals combined with wireless and mobile QoS architectures encounter QoS in the routing function, leaving the QoS provision underutilized. QoS routing (QoSR) complements existing QoS architectures, enhancing application performance especially in the case of congestion, while providing efficient resource management. However, QoSR was originally designed for fixed IP networks without taking mobility into account. This paper investigates the interaction of QoSR in wireless access networks, identifying key points for the efficient cooperation with mobility and existing QoS architectures. Copyright © 2009 John Wiley & Sons, Ltd.     

Ancient shrinking spherical interfaces in the Allen–Cahn flow

We consider the parabolic Allen–Cahn equation in ${\mathbb{R}}^n$, $n\ge 2$,

$u_t=\mathrm{\Delta }u+(1?u^2)u\text{ in }{\mathbb{R}}^n\times (?\infty ,0].$

We construct an ancient radially symmetric solution $u(x,t)$ with any given number k of transition layers between ?1 and +1. At main order they consist of k time-traveling copies of w with spherical interfaces distant $O(\log ?|t|)$ one to each other as $t\to ?\infty$. These interfaces are resemble at main order copies of the shrinking sphere ancient solution to mean the flow by mean curvature of surfaces: $|x|=\sqrt{?2(n?1)t}$. More precisely, if $w(s)$ denotes the heteroclinic 1-dimensional solution of $w^{″}+(1?w^2)w=0$$w(\pm \infty )=\pm 1$ given by $w(s)=\tanh ?\left(\frac{s}{\sqrt{2}}\right)$ we have

$u(x,t)\approx \sum _{j=1}^k{(?1)}^{j?1}w(|x|?{\rho }_j(t))?\frac{1}{2}(1+{(?1)}^k)\text{ as }t\to ?\infty$

where

${\rho }_j(t)=\sqrt{?2(n?1)t}+\frac{1}{\sqrt{2}}(j?\frac{k+1}{2})\log ?\left(\frac{|t|}{\log ?|t|}\right)+O(1),j=1,\dots ,k.$

     

Application of the hybrid Hopkins–Abbe method in full-chip OPC

The hybrid Hopkins–Abbe method is presented and shown to resolve the problem of the traditional Hopkins theory, namely the requirement for constant mask diffraction efficiencies. Simulation of electromagnetic scattering from the mask that takes into account the oblique angles of incidence from the illumination is performed by application of the domain decomposition method that is extended for offaxis illumination. Examples of 45 nm and 32 nm lines and spaces through pitch and through focus are presented to demonstrate the validity and accuracy of the hybrid Hopkins–Abbe method. The results obtained are in excellent agreement with a rigorous and independent (third party) simulator.     

On properties of random dissections and triangulations

In this work we study properties of random graphs that are drawn uniformly at random from the class consisting of biconnected outerplanar graphs, or equivalently dissections of large convex polygons. We obtain very sharp concentration results for the number of vertices of any given degree, and for the number of induced copies of a given fixed graph. Our method gives similar results for random graphs from the class of triangulations of convex polygons.     

Where galaxies really come from

The fundamental paradox of the incompatibility of the observed large-scale uniformity of the Universe with the fact that the age of the Universe is finite is overcome by the introduction of an initial period of superluminal expansion of space, called cosmic inflation. Inflation can also produce the small deviations from uniformity needed for the formation of structures in the Universe such as galaxies. This is achieved by the conjunction of inflation with the quantum vacuum, through the so-called particle production process. This mechanism is explained and linked with Hawking radiation of black holes. The nature of the particles involved is discussed and the case of using massive vector boson fields instead of scalar fields is presented, with emphasis on its distinct observational signatures. Finally, a particular implementation of these ideas is included, which can link the formation of galaxies, the standard model vector bosons and the observed galactic magnetic fields.     

Rumor spreading on random regular graphs and expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well‐studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d ‐regular graphs with n vertices. We show that with probability 1 ‐ o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d lnn rounds, where Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo‐random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 ‐ o(1), where \begin{align*}C = \lim_{d\to\infty}C_d = \frac{1}{\ln2} + 1\end{align*}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Using Goffman's concepts to explore collaborative interaction processes in elementary school mathematics

The present paper describes the combined implementation of two approaches which are based on the work of Erving Goffman and focus on the analysis of the interactional participation structures. Our aim is to examine the ways that differing interpretations of the ongoing interactions may lead the students to adopt differing roles, which in turn affects the process of negotiating and establishing shared meanings. For this purpose we analyse the interaction processes in one ‘expert’ group within the ‘Jigsaw’ form of cooperation (Aronson, 1978 Aronson, E. 1978. The jigsaw classroom, Beverly Hills, CA: Sage.  [Google Scholar]), decomposing the participants’ roles according to their interactional status and their interpersonal effect. Our analysis points out the different roles that emerge in the process of collaborative interaction, and the influence of these roles on group achievement and individual learning possibilities.