Editor\u27s Remarks

Welcome to the first issue of the Journal of Research on the College President, an outlet for the National Lab for the Study of the College President. The Lab is a new research unit within the College of Education and Health Professions at the University of Arkansas, and has been created to conduct research and provide leadership on the study of the American College President. Through policy briefings, publications, workshops, grant writing, and hosting speakers, the NLSCP provides national direction for research on college leaders

Some results on chromatic number as a function of triangle count

A variety of powerful extremal results have been shown for the chromatic number of triangle-free graphs. Three noteworthy bounds are in terms of the number of vertices, edges, and maximum degree given by Poljak \& Tuza (1994), and Johansson. There have been comparatively fewer works extending these types of bounds to graphs with a small number of triangles. One noteworthy exception is a result of Alon et. al (1999) bounding the chromatic number for graphs with low degree and few triangles per vertex; this bound is nearly the same as for triangle-free graphs. This type of parametrization is much less rigid, and has appeared in dozens of combinatorial constructions. In this paper, we show a similar type of result for $\chi(G)$ as a function of the number of vertices $n$, the number of edges $m$, as well as the triangle count (both local and global measures). Our results smoothly interpolate between the generic bounds true for all graphs and bounds for triangle-free graphs. Our results are tight for most of these cases; we show how an open problem regarding fractional chromatic number and degeneracy in triangle-free graphs can resolve the small remaining gap in our bounds

SO(5)-Symmetric Description of the Low Energy Sector of a Ladder System

We study a system of two Tomonaga-Luttinger models coupled by a small transverse hopping (a two-chain ladder). We use Abelian and non-Abelian bosonisation to show that the strong coupling regime at low energies can be described by an SO(5)$_1$ WZW model (or equivalently 5 massless Majorana fermions) deformed by symmetry breaking terms that nonetheless leave the theory critical at T=0. The SO(5) currents of the theory comprise the charge and spin currents and linear combinations of the so-called pi operators (S.C. Zhang, Science 275, 1089 (1997)) which are local in terms both of the original fermions and those of the effective theory. Using bosonisation we obtain the asymptotic behaviour of all correlation functions. We find that the 5 component ``superspin'' vector has power law correlations at T=0; other fermion bilinears have exponentially decaying correlations and the corresponding tendencies are suppressed. Conformal field theory also allows us to obtain the energies, quantum numbers, and degeneracies of the low-lying states and fit them into deformed SO(5) multiplets.Comment: 17 pages, ReVTeX, 1 eps figure include

High field magnetotransport in composite conductors: the effective medium approximation revisited

The self consistent effective medium approximation (SEMA) is used to study three-dimensional random conducting composites under the influence of a strong magnetic field {\bf B}, in the case where all constituents exhibit isotropic response. Asymptotic analysis is used to obtain almost closed form results for the strong field magnetoresistance and Hall resistance in various types of two- and three-constituent isotropic mixtures for the entire range of compositions. Numerical solutions of the SEMA equations are also obtained, in some cases, and compared with those results. In two-constituent free-electron-metal/perfect-insulator mixtures, the magnetoresistance is asymptotically proportional to $|{\bf B}|$ at {\em all concentrations above the percolation threshold}. In three-constituent metal/insulator/superconductor mixtures a line of critical points is found, where the strong field magnetoresistance switches abruptly from saturating to non-saturating dependence on $|{\bf B}|$, at a certain value of the insulator-to-superconductor concentration ratio. This transition appears to be related to the phenomenon of anisotropic percolation.Comment: 16 pages, 3 figure

Fake Exponential Brownian Motion

We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian motions. The ideas extend to other diffusions.Comment: 8 page

Physical Coupling Schemes and QCD Exclusive Processes

I discuss application of the BLM method to obtain commensurate scale relations connecting QCD exclusive amplitudes to other observables, in particular the heavy quark potential.Comment: 7 pages, Latex, uses l-school.sty. Talk given at "New Nonperturbative Methods and Quantization on the Light Cone," Les Houches, France, 24 Feb.-7 March 1997. To appear in the proceeding