Electronic correlation in the quantum Hall regime

Two‐dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many‐particle ground state and its excitations are studied in detail at fractional filling factors for spin‐polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.     

The effects of preventive vocal hygiene education on the vocal hygiene habits and perceptual vocal characteristics of training singers

The purpose of the present study was to determine the effects of vocal hygiene education on the vocal hygiene behaviors and perceptual vocal characteristics of untrained singers. Eleven adult untrained singers served as subjects. They attended four 1-hour class sessions on vocal hygiene, including anatomy and physiology of the phonatory mechanism, vocally abusive behaviors, voice disorders commonly seen in singers, and measures to prevent voice disorders. Pre- and postinstruction surveys were used to record subjects' vocal abuses and their perceptions of their speaking and singing voice. They also rated their perceived value of vocal hygiene education. Results revealed minimal changes in vocal hygiene behaviors and perceptual voice characteristics. The subjects did report a high degree of benefit and learning, however.     

Propagation of self-gravitating density waves in the deDonder gauge: the physical importance of gauge solutions and the problem of initial conditions

The propagation of perturbations on a spatially flat Robertson-Walker background is studied within linear perturbation theory in deDonder gauge and for comparison in synchronous gauge. The metric perturbations should be determined uniquely by the density/pressure perturbations, therefore only two initial conditions, namely for the density contrast and its time derivative, should be needed. Since the number of fundamental solutions for the density perturbations is higher than 2 in both gauges (6 resp. 3) an additional reduction of possible initial conditions, resp. a physically motivated exclusion of solutions, is needed. It is shown that the common treatment of excluding the so-called gauge solutions (solutions which can be gauged to zero in an already chosen gauge) leads to unphysical results. If gauge solutions are excluded the density perturbation solutions are the same in both gauges. But the correct Newtonian limit — which is present in deDonder gauge but not in synchronous gauge — is bound to the differences in the two gauges for large spatial scales of perturbations. Furthermore, compressional wave solutions should vanish for infinite spatial scales of perturbations (isotropy), but this is guaranteed in deDonder gauge by gauge solutions again. Gauge solutions should therefore not be taken as unphysical.     

Modules of piecewise polynomials and their freeness

Partially supported by NSF Grant DMS-9004123 and ARO through MSI Cornell (DAAG 29-85-C-0018)     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption

In the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation ?Δu + g(x, u) = 0 in a smooth domain Ω ? ?^N, for a general class of positive nonlinearities. This class includes every space independent, monotone increasing g which satisfies the Keller‐Osserman condition as well as degenerate nonlinearities g_α,q of the form g_α,q (x, u) = d(x, ?Ω)^α |u|^q?1 u, with α > ?2 and q > 1. The boundary trace is given by a positive regular Borel measure which may blow up on compact sets. In the second part we concentrate on the family of nonlinearities {g_α,q}, determine the critical value of the exponent q (for fixed α > ?2) and discuss (a) positive solutions with an isolated singularity, for subcritical nonlinearities and (b) the boundary value problem for ?Δu + g_α,q (x, u) = 0 with boundary data given by a positive regular Borel measure (possibly unbounded). We show that, in the subcritical case, the problem possesses a unique solution for every such measure. © 2003 Wiley Periodicals, Inc.