Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Gamow-Teller strength distributions for nuclei in pre-supernova stellar cores

Electron-capture and $\beta$-decay of nuclei in the core of massive stars play an important role in the stages leading to a type II supernova explosion. Nuclei in the f-p shell are particularly important for these reactions in the post Silicon-burning stage of a presupernova star. In this paper, we characterise the energy distribution of the Gamow-Teller Giant Resonance (GTGR) for mid-fp-shell nuclei in terms of a few shape parameters, using data obtained from high energy, forward scattering (p,n) and (n,p) reactions. The energy of the GTGR centroid $E_{GT}$ is further generalised as function of nuclear properties like mass number, isospin and other shell model properties of the nucleus. Since a large fraction of the GT strength lies in the GTGR region, and the GTGR is accessible for weak transitions taking place at energies relevant to the cores of presupernova and collapsing stars, our results are relevant to the study of important $e^-$-capture and $\beta$-decay rates of arbitrary, neutron-rich, f-p shell nuclei in stellar cores. Using the observed GTGR and Isobaric Analog States (IAS) energy systematics we compare the coupling coefficients in the Bohr-Mottelson two particle interaction Hamiltonian for different regions of the Isotope Table.Comment: Revtex, 28 pages +7 figures (PostScript Figures, uuencoded, filename: Sutfigs.uu). If you have difficulty printing the figures, please contact [email protected]. Accepted for publication in Phys. Rev. C, Nov 01, 199

Vector quantization of image subbands: a survey

Subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting, which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization (VQ) provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988, a growing body of research has examined the use of VQ for subband/wavelet transform coefficients. We present a survey of these methods

Complete 0 hbar omega calculations of Gamow-Teller strengths for nuclei in the iron region

Gamow-Teller strengths for selected nuclei in the iron region (A~56) have been investigated via shell-model Monte Carlo calculations with realistic interactions in the complete fp basis. Results for all cases show significant quenching relative to single-particle estimates, in quantitative agreement with (n,p) data. The J=1,T=0 residual interaction and the f_{7/2}-f_{5/2} spin-orbit splitting are shown to play major roles in the quenching mechanism. Calculated B(E2, 2^+_1 -> 0^+_1) values are in fair agreement with experiment using effective charges of e_p=1.1e and e_n=0.1e.Comment: 13 pages + 1 postscript file, Caltech preprint MAP-16

Gamow-Teller strength distributions in fp-shell nuclei

We use the shell model Monte Carlo method to calculate complete 0f1p-shell response functions for Gamow-Teller (GT) operators and obtain the corresponding strength distributions using a Maximum Entropy technique. The approach is validated against direct diagonalization for 48Ti. Calculated GT strength distributions agree well with data from (n,p) and (p,n) reactions for nuclei with A=48-64. We also calculate the temperature evolution of the GT+ distributions for representative nuclei and find that the GT+ distributions broaden and the centroids shift to lower energies with increasing temperature

Nuclear Polarization of Molecular Hydrogen Recombined on a Non-metallic Surface

The nuclear polarization of $\mathrm{H}_2$ molecules formed by recombination of nuclear polarized H atoms on the surface of a storage cell initially coated with a silicon-based polymer has been measured by using the longitudinal double-spin asymmetry in deep-inelastic positron-proton scattering. The molecules are found to have a substantial nuclear polarization, which is evidence that initially polarized atoms retain their nuclear polarization when absorbed on this type of surfac

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Faddeev Calculations of Proton-Deuteron Radiative Capture with Exchange Currents

pd capture processes at various energies have been analyzed based on solutions of 3N-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of $\pi$- and $\rho$-like exchange currents connected to the AV18 NN interaction. Overall good agreement with cross sections and spin observables has been obtained but leaving room for improvement in some cases. Feasibility studies for 3NF's consistently included in the 3N continuum and the 3N bound state have been performed as well.Comment: Minor changes in notation, ps files for figure

Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target

Single-spin asymmetries for semi-inclusive electroproduction of charged pions in deep-inelastic scattering of positrons are measured for the first time with transverse target polarization. The asymmetry depends on the azimuthal angles of both the pion ($\phi$) and the target spin axis ($\phi_S$) about the virtual photon direction and relative to the lepton scattering plane. The extracted Fourier component \cmpi is a signal of the previously unmeasured quark transversity distribution, in conjunction with the so-called Collins fragmentation function, also unknown. The Fourier component \smpi of the asymmetry arises from a correlation between the transverse polarization of the target nucleon and the intrinsic transverse momentum of quarks, as represented by the previously unmeasured Sivers distribution function. Evidence for both signals is observed, but the Sivers asymmetry may be affected by exclusive vector meson productio