The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector

We resume our discussion of the new orbifold-string theories of permutation-type, focusing in the present series on the algebraic formulation of the general bosonic prototype and especially the target space-times of the theories. In this first paper of the series, we construct one twisted BRST system for each cycle $j$ in each twisted sector $\sigma$ of the general case, verifying in particular the previously-conjectured algebra $[Q_{i}(\sigma),Q_{j}(\sigma)]_{+} =0$ of the BRST charges. The BRST systems then imply a set of extended physical-state conditions for the matter of each cycle at cycle central charge $\hat{c}_{j}(\sigma)=26f_{j}(\sigma)$ where $f_{j}(\sigma)$ is the length of cycle $j$.Comment: 31 page

Well-posedness of one-way wave equations and absorbing boundary conditions

A one-way wave equation is a partial differential which, in some approximate sense, behaves like the wave equation in one direction but permits no propagation in the opposite one. The construction of such equations can be reduced to the approximation of the square root of (1-s sup 2) on -1, 1 by a rational function r(s) = p sub m (s)/q sub n(s). Those rational functions r for which the corresponding one-way wave equation is well-posed are characterized both as a partial differential equation and as an absorbing boundary condition for the wave equation. We find that if r(s) interpolates the square root of (1-s sup 2) at sufficiently many points in (-1,1), then well-posedness is assured. It follows that absorbing boundary conditions based on Pade approximation are well-posed if and only if (m, n) lies in one of two distinct diagonals in the Pade table, the two proposed by Engquist and Majda. Analogous results also hold for one-way wave equations derived from Chebyshev or least-squares approximation

The connection between non-exponential relaxation and fragility in supercooled liquids

Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature, the non-exponential time dependence of the relaxation, and the possible connection between these two properties. The ferromagnetic Potts model on a square latice is a simple system that is found to exhibit these properties. Our calculations show that in this system the connection between them is associated with the dependence on temperature and time of the average environment of the sites. Some of the consequences of this for understanding the behavior of supercooled liquids are discussed.Comment: 12 pages, 8 figure

Controllability and observabiliy of an artificial advection-diffusion problem

In this paper we study the controllability of an artificial advection-diffusion system through the boundary. Suitable Carleman estimates give us the observability on the adjoint system in the one dimensional case. We also study some basic properties of our problem such as backward uniqueness and we get an intuitive result on the control cost for vanishing viscosity.Comment: 20 pages, accepted for publication in MCSS. DOI: 10.1007/s00498-012-0076-

Systematic approach to cyclic orbifolds

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.Comment: 39 pages, LaTeX. v2,3: references added. v4: typos correcte

Torts—Televising of Professional Act Not a Violation of Civil Rights Law

Gautier v. Pro-Football, Inc., 278 App. Div. 431, 106 N. Y. S. 2d 553 (1st Dept. 1951)

Workmen\u27s Compensation - Traumatic Neurosis Without Physical Injury

Appellee and his co-worker attempted to lower a suspended scaffold on which they were standing, whereupon the scaffold gave way and the coworker fell to his death. Appellee suffered only slight bruises on his leg, but as a result of seeing his fellow employee fall to his death, he sustained severe fright and shock which resulted in a traumatic neurosis preventing him from engaging in the normal duties of his occupation. The lower court awarded appellee judgment for permanent partial disability under the Texas Workmen\u27s Compensation Law. On appeal, held, reversed. Appellee\u27s condition was a mental disease and compensable under Texas law only if it resulted from a compensable physical injury. American General Ins. Co. v. Bailey, (Tex. Civ. App. 1954) 268 S.W. (2d) 528