Biorthogonal bases of compactly supported wavelets

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets. We give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions, and we present a sufficient conditions for the decay of their Fourier transforms. We study the regularity of these biorthogonal bases. We provide several families of examples, all symmetric (corresponding to “linear phase” filters). In particular we can construct symmetric biorthogonal wavelet bases with arbitraily high preassigned regularity; we also show how to construct symmetric biorthogonal wavelet bases “close” to a (nonsymmetric) orthonormal basis.     

Analytic supernova models and black holes

Presented are new analytic solutions to Einstein's field equations with properties normally associated with supernovas. These are the first analytic supernova models with pressure, temperature, and luminosity. These solutions are used to compare a radiative nonzero model (for which the pressure is continuous accross the outer boundary of the star) with a radiative zero model [(standard model) for which the pressure within the star is zero at the outer boundary].     

Equilibrium configurations of rotating charged or gravitating liquid masses with surface tension. II

The equilibrium configurations of rotating charged or gravitating liquid masses with surface tension are investigated. The objective is to discuss in a unified manner configurations of idealized atomic nuclei, rotating liquid drops and rotating idealized astronomical masses. The present paper formulates the problem generally but the applications discussed are mostly to nuclei. These include the estimates of the geometrical characteristics, of the rigid moments of inertia, and of the energies and fission barriers of idealized nuclei throughout the periodic table and with any angular momentum. The existence of super-deformed nuclei, stretched out into cylinderlike configurations by the centrifugal force, is discussed.     

Synchrotron radiation measurements and calculation of core to conduction level transitions in lead chalcogenides

New high resolution reflectivity measurements on PbSe and PbTe using synchrotron radiation (18–26 eV) are studied using an OPW formalism based on recent improved EPM band structure models to determine the angular momentum character of the final conduction band states. Detailed analysis reveals that the reflectivity threshold is shifted to lower energies by 0.8 eV compared to results derived from photoemission and low energy reflectivity data. Electron-hole interactions are suggested as a possible explanation for this shift.     

Pair-states in α-perylene crystal. A theoretical study

The low- and high-temperature emissions from α-perylene are interpreted as originating in, respectively, loosely- and tightly-bound pair complexes. The change-over from one to the other results from thermal expansion and deformation of the lattice and the resulting change in contact distances between the complexing pair and the surrounding molecules. With this model the binding energies, Stokes shifts, lifetimes, and emissive bandwidths associated with the complexes are estimated, as is the activation energy for excimer-exciton migration; the values agree well with the available experimental data.     

Microscopic theory of the static structural properties and phase transformation of Ge

Using the atomic number as the only input, the static structural properties and the pressure-induced phase transformation of Ge are calculated within an ab initio density-functional pseudopotential scheme. Among a set of likely crystal structures, the diamond structure is found to be the most stable. The calculated lattice constant, cohesive energy, and bulk modulus are in excellent agreement with experiment, and the properties of the phase transformation to the β-tin structure under pressure accurately reproduced.     

Wave fronts in elastic membranes

This paper deals with nonlinear wave propagation in hyperelastic membranes from the point of view of wave front analysis. Conditions are formulated under which all three wave types which can propagate sweep out the same system of wave fronts on the membrane. Particular emphasis is placed on the situation arising when the membrane material is homogeneous, uni-directional homogeneous, and homogeneous-isotropic. The general form of the growth-decay equation governing the amplitude of acceleration waves is derived and discussed.     

A novel method for protection and deprotection of the carbonyl groups in 1,2-indanedione by conversion to dioxa-dithiapropellanes

1,2-Indanedione reacts with two equivalents of 2-mercaptoethanol to produce, instead of the expected 1,2-bis(1,3-oxathiolane), a dioxa-dithia[4.4.3] propellane. Other 1,2-indanediones produce analogous compounds. The protecting groups are removed at room temperature with NBS in aqueous acetone, to produce the original diketone.