Preliminary experiment of fluorescent X-ray computed tomography to detect dual agents for biological study

The simultaneous observation of various information, such as blood flow, tissue metabolism and distribution of receptors, is quite important in order to understand the functional state of biomedical objects. The simultaneous detectability of contrast agents by fluorescent X-ray computed tomography (FXCT) with synchrotron radiation is examined in this study. The system consisted of a silicon (111) double-crystal monochromator, an X-ray slit system, a scanning table, a PIN diode, a highly purified germanium detector and an X-ray charge-coupled device (CCD) camera. The monochromatic X-ray beam energy was adjusted to 37.0 keV and collimated into a pencil beam of 1 x 1 mm. The fluorescent spectra of the K alpha lines for iodine and xenon were detected simultaneously. FXCT could image the distribution of both iodine and xenon agents in a phantom clearly and the contrast ratio was significantly better than that of transmission X-ray computed tomography images.     

A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature

Consider a simply-connected Riemann surface represented by a Speiser graph. Nevanlinna asked if the type of the surface is determined by the mean excess of the graph: whether mean excess zero implies that the surface is parabolic, and negative mean excess implies that the surface is hyperbolic. Teichmüller gave an example of a hyperbolic simply-connected Riemann surface whose mean excess is zero, disproving the first of these implications. We give an example of a simply-connected parabolic Riemann surface with negative mean excess, thus disproving the other part. We also construct an example of a complete, simply-connected, parabolic surface with nowhere positive curvature such that the integral of curvature in any disk about a fixed basepoint is less than times the area of disk, where 0$"> is some constant.

     

Quantification of cerebral metabolites in glioma patients with proton MR spectroscopy using T2 relaxation time correction

This study was aimed to investigate the significance of absolute concentration of metabolites in glioma patients using proton MR spectroscopy (MRS) with T2 relaxation time correction using three different echo times. The absolute concentrations of metabolites in 7 normal subjects and in 23 gliomas (10 low-grade, 13 high-grade) were obtained by proton MRS using a tissue water signal as an internal standard. The signal intensities of metabolites and tissue water were corrected by T2 relaxation time. In low-grade glioma, the T2 relaxation time of NAA was shorter, and T2 relaxation time of water was prolonged as compared to normal subjects (p < 0.001). In high-grade glioma, the T2 relaxation time of NAA (p < 0.001) and T2 relaxation time of Cr (p < 0.01) were shorter, and T2 relaxation time of water (p < 0.001) was prolonged as compared to normal subjects. Moreover, high-grade gliomas revealed a shorter T2 relaxation time of Cr than low-grade gliomas (p < 0.05). In glioma, NAA and Cr concentration were decreased, and Cho were increased as compared to normal subjects. Moreover, high-grade glioma revealed a significant lower Cr (p < 0.001) and Cho (p < 0.01) concentration compared to low-grade gliomas. Low Cr concentration is the most reliable indicator of malignancy in glioma. Cho concentration did not correlate with malignancy in gliomas.     

Clarithromycin form I determined by synchrotron X‐ray powder diffraction

The structure of the metastable form I polymorph of the macrolide antibiotic clarithromycin, C₃₈H₆₉NO₁₃, was determined by a powder diffraction method using synchrotron radiation. The space group of form I is P2₁2₁2. The initial model was determined by a molecular replacement method using the structure of clarithromycin form 0 as a search model, and the final structure was obtained through Rietveld refinements. In the form I crystal structure, the clarithromycin molecules are aligned parallel along the a axis in a head‐to‐tail manner with intermolecular hydrogen bonds between the hydroxy O atoms. The dimethylamine groups of the clarithromycin molecule interdigitate between neighbouring head‐to‐tail clarithromycin alignments. The novel crystal packing found in form I provides a mechanism that describes the transformation of form 0 to form I.     

The mixing time of the giant component of a random graph

We show that the total variation mixing time of the simple random walk on the giant component of supercritical and is . This statement was proved, independently, by Fountoulakis and Reed. Our proof follows from a structure result for these graphs which is interesting in its own right. We show that these graphs are “decorated expanders” — an expander glued to graphs whose size has constant expectation and exponential tail, and such that each vertex in the expander is glued to no more than a constant number of decorations. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 383–407, 2014     

Bounds on path connectivity

The path-connectivity of a graph G is the maximal k for which between any k pairs of vertices there are k edge-disjoint paths (one between each pair). An upper bound for the path-connectivity of n^q(q<1) separable graphs [6] is shown to exist.If the edge-connectivity of a graph is K_E then between any two pairs of vertices and for every $\text{t?}\text{K}{}_{\mathrm{E}}$ there exists a t?t′?t+1 such that there are t′ paths between the first pair and $\text{K}{}_{\mathrm{E}}\text{?t′}$ between the second pair. All paths are edge-disjoint.     

The distance between homotopy classes of <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-valued maps in multiply connected domains

Certain Sobolev spaces of S ¹-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different homotopy classes in such spaces is considered. In particular, several types of one-dimensional and two-dimensional domains are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are sharp but are not achieved. The first author’s work of was supported in part by NSF grant 0503887. The second author’s research of was supported by G.S. Elkin research fund.     

On the solid state of hydrogen fluoride: A self-consistent crystal field study

A recently developed self-consistent crystal field (SCCF ) method is applied to two suggested crystal structures of solid hydrogen fluoride, polar and nonpolar, respectively. Constrained geometry optimizations are performed and the results are compared with experiment and previous theoretical studies. Comparisons are also made with a previous SCCF study on hydrogen cyanide. The Pauli repulsion, dispersion, and “classical” crystal field contributions to the lattice energy are calculated. © 1993 John Wiley & Sons, Inc.