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William O. Bray 《Monatshefte für Mathematik》1993,116(1):1-11
The Fourier inversion formula in polar form is \(f(x) = \int_0^\infty {P_\lambda } f(x)d\lambda \) for suitable functionsf on ? n , whereP λ f(x) is given by convolution off with a multiple of the usual spherical function associated with the Euclidean motion group. In this form, Fourier inversion is essentially a statement of the spectral theorem for the Laplacian and the key question is: how are the properties off andP λ f related? This paper provides a Paley-Wiener theorem within this avenue of thought generalizing a result due to Strichartz and provides a spectral reformulation of a Paley-Wiener theorem for the Fourier transform due to Helgason. As an application we prove support theorems for certain functions of the Laplacian. 相似文献
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A method using a sulfur chemiluminescence detector (SCD) has been developed for the qualitative and quantitative determination of sulfur components in stabilized gasoline-range process streams, including blended gasolines containing between 1 and > 4000 ppm total sulfur. The detection limit per sulfur component was approximately 50 ppb. On-column injection was employed for optimum precision and accuracy. A new probe material was found which did not soften under FID operating conditions. A new method, using a hydrogen sulfide permeation tube, was developed for rapid alignment of the probe in the FID. 相似文献
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It is shown that the B10 spectra for sodium borate glasses are sensitive to the different structural groups in the glasses. Five boron sites are inferred from the data: two 4-coordinated sites and three 3-coordinated sites. The two 4-coordinated boron sites are identified as BO4 units connected to all BO3 units, and BO4 units connected to one BO4 unit and three BO3 units. The three 3-coordinated boron sites are identified as BO3 units connected to: (1) all BO3 units; (2) a mixture of BO3 and BO4 units; and (3) all BO4 units. These five sites can be interpreted in terms of Krogh-Moe's structural model of alkali borate glasses, wherein the fraction of each structural group can be determined for eight sodium borate glasses spanning the compositional range from 0 to 35 mol% Na2O. The resulting fractions are consistent with Krogh-Moe's structural model. 相似文献
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Bray I 《Physical review letters》2002,89(27):273201
The convergent close-coupling method is shown to overcome the remaining discrepancies with experiment of electron-hydrogen ionization. Consequently, this method is able to calculate accurately the Coulomb three-body problems which include electron collisions with hydrogen and helium (within the frozen core model), and helium double photoionization at all incident energies and kinematical or geometrical arrangements of the outgoing electrons. 相似文献