Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{\nu}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions $\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and $\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and [\delta^{(3)}(x)}]^2, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}Comment: 21 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 98 (1997

Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds

Identity Politics Related to the Yao Muslims through A Post-Colonial Theoretical Framework

The study seeks to assess an important question that needs to be asked How can we get a clearer picture of the socio-cultural history of the Yao than that that exists in general among Yaos themselves as well as people who oppose the Yao This is a very large topic and this study will only start to trace some of the important historical facts and perception

Witnesses to a Creation, 27 June 1977

https://egrove.olemiss.edu/civ_pubs/1018/thumbnail.jp

A DECISION-BASED DESIGN PROCESS FOR ECO-INDUSTRIAL PARKS

This thesis presents a new process for designing eco-industrial parks (i.e., EIPs) that identifies the decisions that need to be made during each phase. A literature review about the different EIP development processes in the U.S. and worldwide is conducted to create a general EIP development process. A careful analysis of 21 EIP development processes was conducted to illuminate the different routines associated with each step in these processes. This thesis presents a revised EIP development process that follows the decision-based design principle of aligning all decisions with the involved organizations' most important objectives

Quantum Energy Expectation in Periodic Time-Dependent hamiltonians via Green Functions

Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a {\em probe energy}), we derive a formula for the Laplace time average of its expectation value up to time $T$ in terms of its eigenvalues and Green functions at the circle of radius $e^{1/T}$. Some simple applications are provided which support its usefulness.Comment: 31 page

The Function of Indigenous Law in a Modern Economic and Political State: The Cameroon Scenario

Using Cameroon as a case study, this research examines if a legal system built primarily upon indigenous laws can serve modern economic, political, and social realities. Indigenous laws have several attractive advantages (such as expediency in dispute resolution, and fostering community cohesiveness), and may fully thrive in a homogenous society. However, after examining the realities in Cameroon, the study concludes that since the society has dozens of tribes with values and traditions which are invariably different, and because the country relies on foreign aid, what is advocated is a system whereby indigenous and formal laws co-exist