One cannot hear orbifold isotropy type

We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually isospectral orbifolds with different isotropy types. Finally, we show that the corresponding singular strata of two isospectral orbifolds may not be homeomorphic. Received: 6 October 2005     

Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach

We give a unified approach for studying the existence of multiplepositive solutions of nonlinear differential equations of theform where g, f are non-negativefunctions, subject to various nonlocal boundary conditions.We study these problems via new results for a perturbed integralequation, in the space C[0, 1], of the form where [u], ß[u] are linear functionalsgiven by Stieltjes integrals but are not assumed to be positivefor all positive u. This means we actually cover many more differentialequations than the simple equation written above. Previous resultshave studied positive functionals only, but even for positivefunctionals our methods give improvements on previous work.The well-known m-point boundary value problems are special casesand we obtain sharp conditions on the coefficients, which allowssome of them to have opposite signs. We also use some optimalassumptions on the nonlinear term.     

Fractional Order Analysis of Sephadex Gel Structures: NMR Measurements Reflecting Anomalous Diffusion

We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-(bD)(α)], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4,000 s-mm(-2)). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.     

Non-local boundary value problems of arbitrary order

We give a new unified method of establishing the existence ofmultiple positive solutions for a large number of non-lineardifferential equations of arbitrary order with any allowed numberof non-local boundary conditions (BCs). In particular, we areable to determine the Green's function for these problems withvery little explicit calculation, which shows that studyinga more general version of a problem with appropriate notationcan lead to a simplification in approach. We obtain existenceand non-existence results, some of which are sharp, and givenew results for both non-local and local BCs. We illustratethe theory with a detailed account of a fourth-order problemthat models an elastic beam and also determine optimal valuesof constants that appear in the theory.     

The combinatorics of the bar resolution in group cohomology

We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex K_n whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11].

We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.     

Underwater tunable organ-pipe sound source

A highly efficient frequency-controlled sound source based on a tunable high-Q underwater acoustic resonator is described. The required spectrum width was achieved by transmitting a linear frequency-modulated signal and simultaneously tuning the resonance frequency, keeping the sound source in resonance at the instantaneous frequency of the signal transmitted. Such sound sources have applications in ocean-acoustic tomography and deep-penetration seismic tomography. Mathematical analysis and numerical simulation show the Helmholtz resonator's ability for instant resonant frequency switching and quick adjustment of its resonant frequency to the instantaneous frequency signal. The concept of a quick frequency adjustment filter is considered. The discussion includes the simplest lumped resonant source as well as the complicated distributed system of a tunable organ pipe. A numerical model of the tunable organ pipe is shown to have a form similar to a transmission line segment. This provides a general form for the principal results, which can be applied to tunable resonators of a different physical nature. The numerical simulation shows that the "state-switched" concept also works in the high-Q tunable organ pipe, and the speed of frequency sweeping in a high-Q tunable organ pipe is analyzed. The simulation results were applied to a projector design for ocean-acoustic tomography.     

Novel techniques for the prepartion of synthetic diamond

Abstract

The objectives of this work are two fold: (1) to study the effect of using oxygen-acetylene flame grown synthetic diamond as seed crystals for the high pressure-high temperature conversion of graphite into diamond and (2) to demonstrate the ability to produce small crystallites of diamond by a simple, electron beam evaporation technique. In each case, the production of diamond from graphite was confirmed.     

A radiofrequency coil configuration for imaging the human vertebral column at 7 T

We describe the design and testing of a quadrature transmit, eight-channel receive array RF coil configuration for the acquisition of images of the entire human spinal column at 7 T. Imaging parameters were selected to enable data acquisition in a clinically relevant scan time. Large field-of-view (FOV) scanning enabled sagittal imaging of the spine in two or three-stations, depending upon the height of the volunteer, with a total scan time of between 10 and 15 min. A total of 10 volunteers have been scanned, with results presented for the three subjects spanning the range of heights and weights, namely one female (1.6 m, 50 kg), one average male (1.8 m, 70 kg), and one large male (1.9 m, 100 kg).     

Effect of Precipitation Temperature and Number of Iron Atoms per Molecule on the Structure of Hydrated Iron(III) Oxyhydroxide Ferritin Cores Synthesised in vitro

Hyperfine Interactions - Horse spleen apoferritin was reconstituted with varying numbers of iron atoms per protein shell at 25 and 50°C. Samples with mean particle sizes ranging from...     

A new approach for noninvasive skin blood imaging in microcirculation

A new noninvasive method is proposed for optically imaging blood under skin. A mini-mirror is used to guide the light incident onto the skin surface, while blocking specularly reflected light from the tissue. Moreover, by using two linear polarizers at right angles, the specular reflection can be reduced further, while also blocking the rough surface scattered light. A circular polarizer may be used to obtain the same effect. As a result, the blood flow beneath the surface of skin can be visualized clearly. The effect of the mini-mirror is also analyzed theoretically and experimentally.