Multiresolution approximation of the vector fields on T^3

Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical vectors, we proved the orthogonal decomposition of L^2(T^3) which is a synthesis of the Hodge decomposition of the differential 1- or 2-form on T^3 and the Beltrami decomposition that decompose the space of solenoidal vector fields into the eigenspaces of curl operator. In the course of proof, a general construction procedure of the divergence-free orthonormal complete basis from the basis of scalar function space is presented. Applying this procedure to MRA of L^2(T^3), we discussed the MRA of vector fields on T^3 and the analyticity and regularity of vector wavelets. It is conjectured that the solenoidal wavelet basis must break r-regular condition, i.e. some wavelet functions cannot be rapidly decreasing function because of the inevitable singularities of helical vectors. The localization property and spatial structure of solenoidal wavelets derived from the Littlewood-Paley type MRA (Meyer's wavelet) are also investigated numerically.Comment: LaTeX, 33 Pages, 3 figures. submitted to J. Math. Phy

Hawaii's Federally Subsidized Public School Lunch Program and the Hawaii Department of Education's Food Safety Requirements for It

This fact sheet provides general considerations of using Hawaii-grown produce in the public school lunch program. Items covered include freshness, self-sufficiency, sustainability, economic viabiity, and Department of Education requirements

Dynamical mean field theory of optical third harmonic generation

We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation, we observe a nontrivial approximate {\em scaling} function describing the THG spectra in all Mott insulators, independent of the gap magnitude.Comment: 4 eps figure

In vivo precision of the GE Lunar iDXA for the measurement of visceral adipose tissue in adults: the influence of body mass index.

CoreScan is a new software for the GE Lunar iDXA, which provides a quantification of visceral adipose tissue (VAT). The objective of this study was to determine the in vivo precision of CoreScan for the measurement of VAT mass in a heterogeneous group of adults. Forty-five adults (aged 34.6 (8.6) years), ranging widely in body mass index (BMI 26.0 (5.2)  kg/m(2); 16.7-42.4 kg/m(2)), received two consecutive total body scans with repositioning. The sample was divided into two subgroups based on BMI, normal-weight and overweight/obese, for precision analyses. Subgroup analyses revealed that precision errors (RMSSD:%CV; root mean square standard deviation:% coefficient of variation) for VAT mass were 20.9 g:17.0% in the normal-weight group and 43.7 g:5.4% in overweight/obese groups. Our findings indicate that precision for DXA-VAT mass measurements increases with BMI, but caution should be used with %CV-derived precision error in normal BMI subjects.European Journal of Clinical Nutrition advance online publication, 15 October 2014; doi:10.1038/ejcn.2014.213

Nonlinear Optical Response Functions of Mott Insulators Based on Dynamical Mean Field Approximation

We investigate the nonlinear optical susceptibilities of Mott insulators with the dynamical mean field approximation. The two-photon absorption (TPA) and the third-harmonic generation (THG) spectra are calculated, and the classification by the types of coupling to external fields shows different behavior from conventional semiconductors. The direct transition terms are predominant both in the TPA and THG spectra, and the importance of taking all types of interaction with the external field into account is illustrated in connection with the THG spectrum and dcKerr effect. The dependence of the TPA and THG spectra on the Coulomb interaction indicate a scaling relation. We apply this relation to the quantitative evaluation and obtain results comparable to those of experiments.Comment: 14 pages, 12 figure

Charge dynamics of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} as a correlated electron system with the ideal tetragonal lattice

We report the reflectivity and the resistivity measurement of Ca_{2-x}Na_{x}CuO_{2}Cl_{2} (CNCOC), which has a single-CuO2-plane lattice with no orthorhombic distortion. The doping dependence of the in-plane optical conductivity spectra for CNCOC is qualitatively the same to those of other cuprates, but a slight difference between CNCOC and LSCO, i.e., the absence of the 1.5 eV peak in CNCOC, can be attributed to the smaller charge-stripe instability in CNCOC. The temperature dependence of the optical onductivity spectra of CNCOC has been analyzed both by the two-component model (Drude+Lorentzian) and by the one-component model (extended-Drude analysis). The latter analysis gives a universal trend of the scattering rate Gamma(omega) with doping. It was also found that Gamma(omega) shows a saturation behavior at high frequencies, whose origin is the same as that of resistivity saturation at high temperatures.Comment: 8 pages, 11 figures, to be published in Phys. Rev.

Nonlinear Optical Response of Spin Density Wave Insulators

We calculate the third order nonlinear optical response in the Hubbard model within the spin density wave (SDW) mean field ansatz in which the gap is due to onsite Coulomb repulsion. We obtain closed-form analytical results in one dimension (1D) and two dimension (2D), which show that nonlinear optical response in SDW insulators in 2D is stronger than both 3D and 1D. We also calculate the two photon absorption (TPA) arising from the stress tensor term. We show that in the SDW, the contribution from stress tensor term to the low-energy peak corresponding to two photon absorption becomes identically zero if we consider the gauge invariant current properly.Comment: we use \psfrag in figur

Microcracks, spall and fracture in glass : A study using short pulsed laser shock waves

Copyright 1998 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics, 83(7), 3583-3594, 1998 and may be found at http://dx.doi.org/10.1063/1.36657