Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

Experimental results of a high Q quasioptical reflection cavity

A quasi-optical reflection cavity intended to be used as the resonant load of a submillimeter wavelength oscillator has been designed, constructed, and tested. The resonator consists of three elements in cascade: a high Q, high finesse folded Fabry-Perot resonator, a lower Q, low finesse Fabry-Perot resonator, and a Littrow mounted diffraction grating. The resonator exhibits a Q of 6600 and 2.5 dB of loss at 63 GHz. The design can be scaled to 1 THz, where waveguide structures become impractical, to serve as the resonator for high frequency quantum well resonant tunneling device oscillators.     

Radiation Effects on Concentrated Potassium Hexacyanoferrate(III) Solutions

The neutron irradiated potassium hexacyanoferrate(III) solutions were analyzed for Fe(CN)₆^4?, Fe(CN)₆^3?, and Prussian blue. The retention values (1.1%) were constant throughout the pH and concentration ranges studied, and did not change with the length of irradiation. The complex behavior of the radiochemical yield of the Fe(CN)₆^4? and Prussian blue was attributed to the competition of the various reactions involved in the irradiation.     

High-speed techniques for estimating t1, t2, and density images

This work presents methods for estimating relaxation times T1 and T2 and proton density using a real time digital video processor. This device performs each mathematical step of the fitting algorithms in one video frame interval (1/30 s). Two-point fits of T1 and T2 may be generated in approximately 15 video frame intervals or about 0.5 s; generation of a T2 image from four acquired images requires about 30 video frame intervals or about 1 s. The hardware is common to many commercial MR scanners and requires no array processor. Such high-speed techniques can expedite the clinical use of computed images and facilitate the implementation of image synthesis.     

Strong-coupling effects in high-T c superconductors

It is conceivable that the high-T _c superconducting perovskites are conventional electronphonon superconductors. In this case one expects significant strong-coupling effects because of the unusually high ratiok _B T _c / of the order 0.1 and greater. We use a set of reasonable models for the Eliashberg function ² F() (which takes into account available information on the phonon spectra and which fit the measuredT _c 's) and calculate strong-coupling effects in the specific heatc _s (T)/T _c , the ratio ₀/k _B T _c , the critical fieldsH _c (T) andH _c2 (T) including Pauli limiting, and other measurable quantities. Strongcoupling corrections turn out to be in the range of 0 to about 100%, depending on the quantity of interest. We discuss the perspectives of using strong-coupling effects as indicators for conventional electron-phonon superconductivity in the new materials.