Eumeces gilberti

Number of Pages: 3Integrative BiologyGeological Science

Finite dimensional approximations to Wiener measure and path integral formulas on manifolds

Certain natural geometric approximation schemes are developed for Wiener measure on a compact Riemannian manifold. These approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi-group on Riemannian manifolds. The path space is approximated by finite dimensional manifolds consisting of piecewise geodesic paths adapted to partitions $P$ of $[0,1]$. The finite dimensional manifolds of piecewise geodesics carry both an $H^{1}$ and a $L^{2}$ type Riemannian structures $G^i_P$. It is proved that as the mesh of the partition tends to $0$, $$1/Z_P^i e^{- 1/2 E(\sigma)} Vol_{G^i_P}(\sigma) \to \rho_i(\sigma)\nu(\sigma)$$ where $E(\sigma )$ is the energy of the piecewise geodesic path $\sigma$, and for $i=0$ and $1$, $Z_P^i$ is a ``normalization'' constant, $Vol_{G^i_P}$ is the Riemannian volume form relative $G^i_P$, and $\nu$ is Wiener measure on paths on $M$. Here $\rho_1 = 1$ and $$\rho_0 (\sigma) = \exp( -1/6 \int_0^1 Scal(\sigma(s))ds )$$ where $Scal$ is the scalar curvature of $M$. These results are also shown to imply the well know integration by parts formula for the Wiener measure.Comment: 48 pages, latex2e using amsart and amssym

Charmed scalar resonances -- Conventional and four-quark mesons

We propose that there coexist two scalar mesons of different structures (a conventional meson and a four-quark meson) in the recently observed broad bumps just below the large peak of the tensor meson in the D-pi mass distribution. We base this proposal on the interpretation of the charm-strange scalar meson of mass 2317 MeV as a four-quark meson. The strange counterparts of these scalar mesons are also studied.Comment: 4 pages, 0 figures, Revte

Level-of-Aspiration Theory and Initial Stance in Bargaining

This research focuses on the effect of initial stance in bargaining. Following level-of-aspiration theory, the research examines whether the pattern of early concession making modifies the impact of tough vs. soft initial stance. The experiment manipulated opponent\u27s concession pattern (decreasing, constant, increasing) in the early phase of bargaining within an overall tough or soft initial stance. Results indicated that a decreasing concession pattern within the early bargaining extracted larger initial concessions than a constant or increasing concession pattern. Implications for Siegel and Fouraker\u27s (1960) level-of-aspiration theory are discussed