Improving continuity of Voronoi-based interpolation over Delaunay spheres

There are two types of the discontinuity of the original Voronoi-based interpolants: one appears on the data sites and the other on the Delaunay spheres. Some techniques are known for reducing the first type of the discontinuity, but not for the second type. This is mainly because the second type of the discontinuity comes from the coordinate systems used for the interpolants. This paper proposes a sequence of new coordinate systems, called the kth-order standard coordinates, for all nonnegative integers k, and shows that the interpolant generated by the kth-order standard coordinates have C^k continuity on the Delaunay spheres. The previously known Voronoi-based interpolants coincide with the cases k=0 and k=1. Hence, the standard coordinate systems constructed in this paper can reduce the second type of the discontinuity as much as we want. In addition, this paper derives a formula for the gradient of the standard coordinates.     

Thermoelectric power of antiferromagnetic semiconductors near the néel temperature

Thermoelectric power in antiferromagnetic semiconductors is calculated in the vicinity of the Néel temperature by assuming the presence of the well-defined propagating modes (magnon) and a temperature-dependent magnon velocity. Carriers are specified by the mobile carriers in a broad band with an isotropic effective mass. Magnons and carriers are coupled via the sd-interaction. Anomaly near T_N does not result from the diffusion term S_diff. and it is ascribed to the magnon-drag contribution S_drag which is obtained from

$S_{drag}=?{\displaystyle \sum _{\mathit{q}}\mathit{R}(\mathit{q}){\mathit{c}}_m\left(q\right)/3e}$

,where R(q) is the momentum transfer ratio between the magnon system and carriers, c_m(q) denotesthe specific heat of the magnon q. The assumed temperature dependence of the magnon velocity makesSdru divergent at T_N with T_N ? T → +0 and it might be removed in consideration of the magnon frequency spreading. Except this divergence the calculation provides a qualitative explanation for the anomalous feature in MnTe.     

Reversible disulfur monoxide (S2O)-forming retro-Diels-Alder reaction. disproportionation of S2O to trithio-ozone (S3) and sulfur dioxide (SO2) and reactivities of S2O and S3

5,6-Di-tert-butyl-2,3,7-trithiabicyclo[2.2.1]hept-5-ene 7-endo-oxide (4) was prepared by addition of S(2)Cl(2) to 3,4-di-tert-butylthiophene 1-oxide (3) in high yield. The oxidation of 4 with dimethyldioxirane gave a 7:1 isomeric mixture of 5,6-di-tert-butyl-2,3,7-trithiabicyclo[2.2.1]hept-5-ene 2-endo-7-endo-dioxide (5a) and 2-exo-7-endo-dioxide (5b) quantitatively. The thermally labile 5 was shown to undergo a retro-Diels-Alder reaction that produces S(2)O and 3 in a reversible way. The resulting S(2)O was trapped by Diels-Alder reactions with dienes to give 3,6-dihydro-1,2-dithiin 1-oxides in good yields. In the absence of the dienes, S(2)O disproportionates to SO(2) and S(3), and the resulting S(3) underwent a 1,3-dipolar cycloaddition with 3 on its syn-pi-face with respect to the S[double bond]O bond to give a trithiolane derivative, whereas in the presence of excess norbornene, it produced the 1,3-dipolar cycloadduct with norbornene in good yield. Thus, the retro-Diels-Alder reaction of 5 functions as an S(2)O and S(3) source. DFT calculations at the B3LYP/6-311+G(3df,2p) level were carried out in order to explain why S(2)O disproportionates to SO(2) and S(3) and why S(2)O acts as a dienophile and not a 1,3-dipole, whereas O(3) and S(3) serve as 1,3-dipoles.     

An efficient chemical fixation of nitric oxide: convenient and practical synthesis of 1,2,3-oxadiazole 3-oxides

Nitric oxide reacts efficiently with alkynyllithium at low temperature producing 1,2,3-oxadiazole 3-oxides in good yields.     

A geometric view of Krylov subspace methods on singular systems

We give a geometric framework for analysing iterative methods on singular linear systems A x = b and apply them to Krylov subspace methods. The idea is to decompose the method into the ?(A) component and its orthogonal complement ?(A)^?, where ?(A) is the range of A. We apply the framework to GMRES, GMRES(k) and GCR(k), and derive conditions for convergence without breakdown for inconsistent and consistent singular systems. The approach also gives a geometric interpretation and different proofs of the conditions obtained by Brown and Walker for GMRES. We also give examples arising in the finite difference discretization of two‐point boundary value problems of an ordinary differential equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Multifunctional Core–Shell Silica Nanoparticles for Highly Sensitive 19F Magnetic Resonance Imaging

¹⁹F magnetic resonance imaging (¹⁹F MRI) is useful for monitoring particular signals from biological samples, cells, and target tissues, because background signals are missing in animal bodies. Therefore, highly sensitive ¹⁹F MRI contrast agents are in great demand for their practical applications. However, we have faced the following challenges: 1) increasing the number of fluorine atoms decreases the solubility of the molecular probes, and 2) the restriction of the molecular mobility attenuates the ¹⁹F MRI signals. Herein, we developed novel multifunctional core–shell nanoparticles to solve these issues. They are composed of a core micelle filled with liquid perfluorocarbon and a robust silica shell. These core–shell nanoparticles have superior properties such as high sensitivity, modifiability of the surface, biocompatibility, and sufficient in vivo stability. By the adequate surface modifications, gene expression in living cells and tumor tissue in living mice were successfully detected by ¹⁹F MRI.     

A Study of Electronic Equalization Scheme Enabling Optically Pre-Filtered 1 bit/s/Hz DWDM Transmission

A numerical simulation shows that by using electronic equalizers 1 bit/s/Hz spectral efficiency can be attained with the same signal quality as a 0.8 bit/s/Hz system. Waveform distortion due to optical band-limiting is corrected with nearly 3 dB improvement of the Q-penalty.