An asymptotic estimate of the edge effects in the high frequency Kirchhoff diffraction theory for 3-d problems

In the context of wave propagation through a three-dimensional acoustic medium, an analytical approach to estimate the boundary effects in the high-frequency (single) diffraction by thin rigid obstacles is developed. Starting from the classical Kirchhoff (approximate) representation, explicit formulas regarding three sample cases are obtained. The improvement with respect to previous approaches, usually based on refinements of the classical Ray Theory, is evaluated by comparison with the results from a direct numerical solution of the main integrals involved.     

Smoothk-gonal curves with another fixed pencil

Let X be a smooth curve of genus g with two pencils, sayg _k ¹ andg _m ¹ . Here we show that, in general, dim|rg _k ¹ +ug _m ¹ | has the expected dimension and construct examples in which dim |rg _k ¹ +ug _m ¹ | has a prescribed value.     

High-level ab initio calculations for the four low-lying families of minima of (H2O)20. II. Spectroscopic signatures of the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms hydrogen bonding networks

We report the first harmonic vibrational spectra for each of the lowest lying isomers within the four major families of minima of (H2O)20, namely, the dodecahedron, fused cubes, face-sharing pentagonal prisms, and edge-sharing pentagonal prisms. These were obtained at the second-order Moller-Plesset perturbation level of theory (MP2) with the augmented correlation consistent basis set of double zeta quality (aug-cc-pVDZ) at the corresponding minimum energy geometries. The computed infrared (IR) spectra are the first ones obtained from first principles for these clusters. They were found to contain spectral features, which can be directly mapped onto the distinctive spectroscopic signatures of their constituent tetramer, pentamer, and octamer fragments. The dodecahedron spectra show the richest structure in the OH stretching region and are associated with the most redshifted OH vibrations with respect to the monomer. The lowest lying edge-sharing pentagonal prism isomer displays intense IR active vibrations that are redshifted by approximately 600 cm(-1) with respect to the water monomer. Furthermore the most redshifted, IR-active OH stretching vibrations for all four networks correspond to hydrogen bonded OH groups, which exhibit the following two common characteristics: (i) they belong to fragments which have a "free" OH stretch and (ii) they act as donors to a neighboring water molecule along a "dimerlike" (strong) hydrogen bond. The zero-point energy corrected MP2/CBS (complete basis set) limit binding energies D(0) for the four isomers are -163.1 kcal/mol (edge-sharing pentagonal prism), -160.1 kcal/mol (face-sharing pentagonal prism), -157.5 kcal/mol (fused cubes), and -148.1 kcal/mol (dodecahedron).     

On the maximum feasible subsystem problem,IISs and IIS-hypergraphs

 We consider the Max FS problem: For a given infeasible linear system A x≤b, determine a feasible subsystem containing as many inequalities as possible. This problem, which is NP-hard and also difficult to approximate, has a number of interesting applications in a wide range of fields. In this paper we examine structural and algorithmic properties of Max FS and of Irreducible Infeasible Subsystems (IISs), which are intrinsically related since one must delete at least one constraint from each IIS to attain feasibility. First we provide a new simplex decomposition characterization of IISs and prove that finding a smallest cardinality IIS is very difficult to approximate. Then we discuss structural properties of IIS-hypergraphs, i.e., hypergraphs in which each edge corresponds to an IIS, and show that recognizing IIS-hypergraphs subsumes the Steinitz problem for polytopes and hence is NP-hard. Finally we investigate rank facets of the Feasible Subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system. In particular, using the IIS-hypergraph structural result, we show that only two very specific types of rank inequalities induced by generalized antiwebs (which generalize cliques, odd holes and antiholes to general independence systems) can arise as facets. Received: December 2000 / Accepted: November 2002 Published online: February 14, 2003 RID="⋆" ID="⋆" Part of this work was done while the first two authors were with the School of OR&IE, Cornell University, USA. A preliminary version appeared in the Proceedings of the 10th IPCO conference [7], held in Graz, Austria, June 1999. This work was supported by NSF grant DMS-9527124. Key words. infeasible linear systems – feasible subsystems – Irreducible Infeasible Subsystem (IIS) – IIS-hypergraphs – independence systems – feasible subsystem polytope – rank facets     

Hydrosilylation of terminal alkynes with alkylidene ruthenium complexes and silanes

[reaction: see text] Ruthenium alkylidene complexes 1-3 mediate hydrosilylation of alkynes with silanes. When triethoxy- or triphenylsilanes are used as silylating agents, the reaction affords alpha-substituted vinylsilanes as major products.     

Rhenium(V) complexes with Schiff bases: Synthesis and reaction mechanisms

Summary Some isomers of the ReOX₂LPPh₃ complexes [X = Cl or Br and L =N-methylsalicylideneiminate,N-phenylsalicylideneiminate, halfN,N'-ethylenebis(salicylideneiminate) or 8-hydroxyquinolinate] have been synthesized and characterized. Two different mechanisms for reaction of thetrans-ReOX₃(PPh₃)₂ complexes (X = Cl or Br) with the Schiff bases are supported by qualitative studies on such parameters as the Schiff base ligand form, concentration of free triphenylphosphine ligand, reaction solvent and temperature.