Local Nash Equilibrium in Multiparty Politics

We present a model of multi-party, spatial competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form . This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists.In the final section of the paper some empirical work is reviewed in order to obtain some insights into why parties do not simply converge to an electoral center in order to maximize expected vote shares.     

Percolation in the hyperbolic plane

We study percolation in the hyperbolic plane and on regular tilings in the hyperbolic plane. The processes discussed include Bernoulli site and bond percolation on planar hyperbolic graphs, invariant dependent percolations on such graphs, and Poisson-Voronoi-Bernoulli percolation. We prove the existence of three distinct nonempty phases for the Bernoulli processes. In the first phase, , there are no unbounded clusters, but there is a unique infinite cluster for the dual process. In the second phase, , there are infinitely many unbounded clusters for the process and for the dual process. In the third phase, , there is a unique unbounded cluster, and all the clusters of the dual process are bounded. We also study the dependence of in the Poisson-Voronoi-Bernoulli percolation process on the intensity of the underlying Poisson process.

     

K-generic Projective Planes have Morley Rank Two or Infinity

We show that K-generic projective planes have Morley rank either two or infinity. We also show give a direct argument that such planes are not Desarguesian. Mathematics Subject Classification: 03C45, 05C90, 51A35.     

Shinjulactone C,a new quassinoid ith a 1α, 12α:5α, 13α-dicyclo-9βH-picrasane skeleton from ailanthus altissima SWINGLE

A new non-bitter quassinoid, named shinjulactone C ($\text{1}$), was isolated from the root bark of $\text{Ailanthus altissima}$ SWINGLE and shown to be 1α, 12α:5α, 13α-dicyclo-1β, 12β, 20-trihydroxy-9β$\text{H}$-picras-3-ene-2, 11, 16-trione by X-ray diffraction method.     

Boundary trace of reflecting Brownian motions

We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.Mathematics Subject Classification (2000):Primary 60G17, 60J60, Secondary 28A80, 30C35, 60G52, 60J50     

Uniqueness of positive solutions for singular problems involving the -Laplacian

We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: on a bounded smooth domain with zero boundary condition. We also characterize all positive solutions of in .

     

Optimum spray congealing conditions for masking the bitter taste of clarithromycin in wax matrix

The effects of operating conditions in the spray-congealing process on the release and the micromeritic properties of clarithromycin (CAM) wax matrix were evaluated. CAM wax matrix with 30% CAM, 60% glyceryl monostearate (GM) and 10% aminoalkyl methacrylate copolymer E (AMCE) was manufactured at various atomizer wheel speeds and liquid feed rates with a spray dryer. Release of CAM from the matrix exhibited a two-phase pattern, probably due to the dissolution of the fine portions broken on the surface of the matrix. The slope and the extrapolated y-intercept of the subsequent release pattern were defined as the release rate and the initial amount of release of CAM from the matrix, respectively. These release parameters, as well as the volume median diameter and the specific surface area of matrix, were selected as response variables, and multiple regression analysis was performed. For specific surface area and initial amount of release, a minimum point was observed on the contour curve when the atomizer wheel speed was constant and the liquid feed rate was varied. For the release rate, a maximum point was observed on the contour curve under the same conditions. These points were considered preferable for masking the bitter taste of CAM preparation. Microscopic observation revealed that a small spherical matrix with a smooth surface could be obtained with a high atomizer wheel speed and optimum liquid feed rate. This matrix also possessed excellent properties for taste masking, with small initial amount of release and subsequent high rate of release. In conclusion, the congealing speed of melt droplets was the dominant factor in masking the bitter taste of CAM.     

The influence of ligand side chain on the enantioselectivity of Lewis acid catalyzed Diels-Alder reactions

The enantioselective Lewis acid-catalyzed Diels-Alder reaction of 3-(2-propenoyl)-1,3-oxazolidin-2-one 8 with cyclopentadiene was examined using a series of chiral mox ligands 2-6, deferring in the side chain at 2-position of the chiral oxazoline and in the nature of the substituent at the chiral center (4-position) of the oxazoline ring, and a combination of N-[(1R)-2-chloro-1-phenylethyl]-2-[(4R)-4-phenyl-4,5-dihydrooxazol-2-yl]butyramide 2-MgI(2)-I(2) was the most efficient catalyst.     

A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.