Poisson boundaries of discrete groups of matrices

If μ is a probability measure on a countable group there is defined a notion of the Poisson boundary for μ which enables one to represent all bounded μ-harmonic functions on the group. It is shown that for discrete groups of matrices this boundary can be identified with the boundary of the corresponding Lie group.     

On minimum congestion routing in rearrangeable multihop lightwave networks

In this article we consider the problem of minimizing the congestion in logically rearrangeable multihop lightwave networks. Namely, we consider a network in which each node is equipped with a small number of transmitters and receivers, and tuning a transmitter at nodei and a receiver at nodej to the same wavelength creates a logical link (i, j) through which traffic could be sent. For a given traffic matrix-the matrix of flows between nodes—the objective is to find the best connectivity diagram and the corresponding flow assignment so that the maximal flow on any link is minimized. We develop a tabu search heuristic that yields a suboptimal connectivity diagram and an optimal flow assignment on it. Computational experiments are conducted on some benchmark data sets, on a real-world traffic matrix, and on some randomly generated problems of larger dimension. The results are compared with known results from the literature and with a known greedy approach. The results suggest that a tabu search—based heuristic is a promising approach for handling this NP-hard combinatorial problem. In addition, we discuss the performance of the method in view of different patterns of input data.     

Interfacial tension between low molecular weight polymers from the static analysis of cylindrical drops and their break-up dynamics

A spinning drop tensiometer was used to measure the interfacial tension between the coexisting phases of mixtures of low molecular weight polypropylene glycol, M_w = 1000, and polyethylene glycol, M_w = 300, 400, or 550. Two types of experiments gave concordant interfacial tensions. First, the static analysis of the equilibrium diameter of cylindrical drops according to Vonnegut and, second, Tomotika's dynamic analysis of Rayleigh instabilities caused by a sharp decrease of the angular speed. The end-pinching process also lead to the break-up of the drops and it was characterized by a rapid expansion of the hemispherical ends followed by a slower pinching step. The pinching rate increases as the final angular speed decreases while the growth rate of Rayleigh instabilities shows no definite trends in the range 118-245 rad · s^?1. It is shown that the end-pinching of long cylindrical drops can be analyzed in terms of short fiber retraction to get the interfacial tension. © 1995 John Wiley & Sons, Inc.     

Crystal structures of high-T c oxides

A comprehensive review of structure work on high-T _c oxides as reported during the years 1987 and 1988 is given. Thirteen structures are refined from X-ray single-crystal and/or neutron powder diffraction data:I. (Ba_1–x ,K _x )BiO₃ (T _c =30 K),II. (La_2–x , Sr _x )CuO₄ (T _c =40 K),III. (Nd, Ce, Sr)₂CuO₄ (T _c =28 K),IV. (Nd_2–x , Ce _x )CuO₄ (T _c =24 K),V. YBa₂Cu₃O₇ (T _c =90 K),VI. YBa₂Cu₄O₈ (T _c =80 K),VII. Y₂Ba₄Cu₇O₁₄ (T _c =40 K),VIII. Pb₂Sr₂NdCu₃O₈ (T _c =70 K),IX. TlBa₂CaCu₂O₇ (T _c =103 K),X. TlBa₂Ca₂Cu₃O₉ (T _c =120 K),XI. Tl₂Ba₂CuO₆ (T _c =90 K),XII. Tl₂Ba₂CaCu₂O₈ (T _c =112 K),XIII. Tl₂Ba₂Ca₂Cu₃O₁₀ (T _c =125 K). Except forI (perovskite type),II (K₂NiF₄ type) andIV (Nd₂CuO₄ type) they represent new structure types. Structure data, bond distances, structure drawings and calculated X-ray powder diffraction patterns are given for each compound. Structural features and correlations with superconductivity are discussed. The review contains 301 citations.     

Rigidity Result for Certain Three-Dimensional Singular Spaces and Their Fundamental Groups

In this paper, we introduce a particularly nice family of locally CAT(−1) spaces, which we call hyperbolic P-manifolds. For X³ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X³ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometry rigidity for these spaces.     

Small covering designs by branch-and-cut

 A Branch-and-Cut algorithm for finding covering designs is presented. Its originality resides in the use of isomorphism pruning of the enumeration tree. A proof that no 4-(10, 5, 1)-covering design with less than 51 sets exists is obtained together with all non isomorphic 4-(10, 5, 1)-covering designs with 51 sets. Received: August 16, 2000 / Accepted: July 18, 2001 Published online: September 5, 2002     

Intramolekulare Cycloadditionen Mit Azomethin-Yliden: Synthese und NMR-Untersuchungen einiger Paracyclophan-Derivate vom Makrolid-Typ

Intramolecular Cycloaddition Reactions with Azomethine Ylides: Synthesis and NMR Investigations of Some Macrolide-Type Paracyclophanes Several aziridine derivatives bearing a para-substituted phenyl group have been prepared as precursors of azomethine ylides for intramolecular 1,3-dipolar cycloadditions. Upon heating in refluxing toluene, the expected reactions take place resulting in the regioselective formations of the pairs of diastereoisomers 14 / 15 and 16 / 17 , respectively. As indicated by the sharply decreasing yield in the a -series (< 5%), a useful application of this method for preparing paracyclophane compounds is restricted to derivatives with more than 11 bridging atoms. The results of detailed ¹H- and ¹³C-NMR investigations with the pyrrolidino-annulated cyclophanes are discussed with respect to the configuration at the five-membered heterocycles and to the conformational flexibility of the bridges.     

Rang maximal pourT_{P^n }

Letk be an algebraically closed field,P ⁿ the n-dimensional projective space overk andT _P ⁿ the tangent vector bundle ofP ⁿ . In this paper I prove the following result: for every integerl, for every non-negative integers, ifZ _s is the union ofs points in sufficiently general position inP ⁿ , then the restriction mapH ⁰(P ⁿ ,T _P ⁿ (l)) →H ⁰(Z _s,T _P ⁿ (l)_{|z s} ) has maximal rank. This result implies that the last non-trivial term of the minimal free resolution of the homogeneous ideal ofZ _s is the conjectured one by the Minimal Resolution Conjecture of Anna Lorenzini (cf. [Lo]).     

Averaging regularity results for PDEs under transversality assumptions

Let u = u(x,y) and f = f(x,y) be two functions related by a PDE P(x,y,D_x,D_y)u = f; the regularity of the y-average ∫ u(x,·)dy as a function of x is investigated knowing that of u and f. Our method consists in reducing P to a microlocal normal form under a natural transversality assumption. The 2-microlocal regularity of u is also determined knowing that of f. These results are then applied to a homogenization problem. This article generalizes the results of [16] and [12] on velocity averaging and homogenization for kinetic equations.