On the placement of an obstacle so as to optimize the Dirichlet heat trace

We prove that among all doubly connected domains of $\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the spherical shell). The supremum is attained when the interior sphere is in contact with the outer sphere.This is shown to be a special case of a more general theorem characterizing the optimal placement of a spherical obstacle inside a convex domain so as to maximize or minimize the trace of the Dirichlet heat kernel. In this case the minimizing position of the center of the obstacle belongs to the "heart" of the domain, while the maximizing situation occurs either in the interior of the heart or at a point where the obstacle is in contact with the outer boundary. Similar statements hold for the optimal positions of the obstaclefor any spectral property that can be obtained as a positivity-preserving or positivity-reversing transform of $Z(t)$,including the spectral zeta function and, through it, the regularized determinant.Comment: in SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 201

Universal inequalities for the eigenvalues of Schrodinger operators on submanifolds

We establish inequalities for the eigenvalues of Schr\"odinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related to inequalities for the Laplacian on Euclidean domains due to Payne, P\'olya, and Weinberger and to Yang, but which depend in an explicit way on the mean curvature. In later sections, we prove similar results for Schr\"odinger operators on homogeneous Riemannian spaces and, more generally, on any Riemannian manifold that admits an eigenmap into a sphere, as well as for the Kohn Laplacian on subdomains of the Heisenberg group. Among the consequences of this analysis are an extension of Reilly's inequality, bounding any eigenvalue of the Laplacian in terms of the mean curvature, and spectral criteria for the immersibility of manifolds in homogeneous spaces.Comment: A paraitre dans Transactions of the AM

Observations of Mare Serenitatis from lunar orbit and their interpretation

Visual observations are investigated of color differences of Serenitatis mare materials from orbit complement photography and other remotely sensed data. The light tan gray inner fill of the Serenitatis basin is younger than the dark blue gray annulus; the latter continues into and appears to be contemporaneous with the fill of Mare Tranquillitatis. Mare ridges occur in both the inner basin fill and the dark annulus of Serenitatis. Ridges are interpreted as the result of structural deformation and up-doming after the solidification of the basaltic lavas. On the southeastern rim of the Serenitatis basin is the darkes blue gray unit within which Apollo 17 landed. Highland massifs surrounding this unit have unstable slopes which are believed to be the result of localized tectonic activity. On the southwest rim of the basin are the dark tan to brown gray mantling materials of the Sulpicius Gallus Formation. Farther west on the rim are dark blue grap patches which resemble the mare material of the Serenitatis dark annulus

On sums of eigenvalues of elliptic operators on manifolds

We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kr{\"o}ger 's bound for Neumann spectra of Laplacians on Euclidean domains [12]. Among the operators we consider are the Laplace-Beltrami operator on compact subdomains of manifolds. These estimates become more explicit and asymptotically sharp when the manifold is conformal to homogeneous spaces (here extending a result of Strichartz [21] with a simplified proof). In addition we obtain results for the Witten Laplacian on the same sorts of domains and for Schr{\"o}dinger operators with confining potentials on infinite Euclidean domains. Our bounds have the sharp asymptotic form expected from the Weyl law or classical phase-space analysis. Similarly sharp bounds for the trace of the heat kernel follow as corollaries.Comment: in Journal of Spectral Theory, 201

An investigation into the pathogenesis of vulvo-vaginal candidosis

OBJECTIVE: To monitor yeasts isolated from women during and between episodes of recurrent vulvo-vaginal candidosis (VVC) to determine whether vaginal relapse or re-infection occurred. METHODS:Women presenting at the genitourinary medicine clinic with signs and symptoms of VVC were recruited to the study (n = 121). A vaginal washing, high vaginal swab (HVS) and rectal swab were taken and the women treated with a single 500 mg clotrimazole pessary.Women were asked to re-attend after 1, 4, and 12 weeks, or when the VVC recurred, when vaginal washings and HVS were repeated. Candida isolates recovered were strain typed using the Ca3 probe and their similarity assessed. Antifungal susceptibility to fluconazole and clotrimazole were determined. RESULTS: Of the women recruited, 47 completed the study, either returning for four visits or suffering a recurrence during the study period. Of the 22 women who experienced recurrence, the same strain was responsible for the initial and recurrent episode in 17 women. For the remaining five women, four had strain replacement and one had a change of species. None of the isolates recovered from the women demonstrated resistance to either clotrimazole or fluconazole. CONCLUSIONS: Our findings support the theory of vaginal relapse and thus may support the use of more prolonged courses of antifungal therapy initially to increase the chances of eradication of the yeast

Molecular gas in nearby powerful radio galaxies

We report the detection of CO(1-0) and CO(2-1) emission from the central region of nearby 3CR radio galaxies (z$<$ 0.03). Out of 21 galaxies, 8 have been detected in, at least, one of the two CO transitions. The total molecular gas content is below 10$^9$ \msun. Their individual CO emission exhibit, for 5 cases, a double-horned line profile that is characteristic of an inclined rotating disk with a central depression at the rising part of its rotation curve. The inferred disk or ring distributions of the molecular gas is consistent with the observed presence of dust disks or rings detected optically in the cores of the galaxies. We reason that if their gas originates from the mergers of two gas-rich disk galaxies, as has been invoked to explain the molecular gas in other radio galaxies, then these galaxies must have merged a long time ago (few Gyr or more) but their remnant elliptical galaxies only recently (last 10$^7$ years or less) become active radio galaxies. Instead, we argue the the cannibalism of gas-rich galaxies provide a simpler explanation for the origin of molecular gas in the elliptical hosts of radio galaxies (Lim et al. 2000). Given the transient nature of their observed disturbances, these galaxies probably become active in radio soon after the accretion event when sufficient molecular gas agglomerates in their nuclei.Comment: 6 pages, including 2 figures,in "QSO Hosts and Their Environments", ed. I. Marquez, in pres

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Quarkonium mass splittings in three-flavor lattice QCD

We report on calculations of the charmonium and bottomonium spectrum in lattice QCD. We use ensembles of gauge fields with three flavors of sea quarks, simulated with the asqtad improved action for staggered fermions. For the heavy quarks we employ the Fermilab interpretation of the clover action for Wilson fermions. These calculations provide a test of lattice QCD, including the theory of discretization errors for heavy quarks. We provide, therefore, a careful discussion of the results in light of the heavy-quark effective Lagrangian. By and large, we find that the computed results are in agreement with experiment, once parametric and discretization errors are taken into account.Comment: 21 pages, 17 figure