The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables

We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether S_rD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ￥\rho \to \infty . r? ￥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn S_rDf(\bmx)=\dsf1(2p)^n/2\intli_rD [^(f)](\bxi) e^{\dst iá\bmx,\bxi?} d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}.     

Characterization and Computation of Canonical Tight Windows for Gabor Frames

Let (\gnm)_{n,m ? \Zst}(\gnm)_{n,m\in\Zst} be a Gabor frame for \LtR\LtR for given window gg. We show that the window \ho = \SQI g\ho=\SQI g that generates the canonically associated tight Gabor frame minimizes ||g-h||\|g-h\| among all windows hh generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical \ho\ho is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener--Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho\ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples.     

Contact Interaction of Two Elastic Wedges

We consider the problem of contact of two elastic wedges and assume that only the vertices of the wedges touch before loading. After loading, the edges of both wedges come in contact near their common vertex. We reduce the constructed system of dual integral equations to a Fredholm integral equation of the second kind with difference kernel given on the semiaxis. We analytically solve the Fredholm equation by reducing it to the boundary-value Riemann problem for analytic functions. We obtain an analytic expression for contact stresses.     

Signed graphs for portfolio analysis in risk management

We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable.     

On the Density-Density Critical Indices¶in Interacting Fermi Systems

The behaviour of correlation functions of d=1$ interacting fermionic systems is determined by a small number of critical indices. We prove that one of them is exactly zero. As a consequence, the behavior of the Fourier transform of the density-density correlation at zero momentum is qualitatively unaffected by the interaction, contrary to what happens at , if is the Fermi momentum. The result is obtained by implementing Ward identities in a Renormalization Group approach. Received: 12 November 2001 / Accepted: 25 February 2002?Published online: 2 October 2002     

Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

On Inhomogeneous Diophantine Approximations with Rational Terms and Applications to Elliptic and Trigonometric Functions

We investigate inhomogeneous diophantine approximation problems of the type ¦qθ ? p t- α¦. Lower bounds for the error terms are proved in the case of arbitrarily chosen rational α’s. Applications are given to elliptic and trigonometric functions extending former results of the author and others.     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Interface-related effects on confined excitons in GaAs/AlxGa1−xAs single quantum wells

Confined excitons in non-abrupt GaAs/Al_xGa_1−xAs single quantum wells are studied. The graded interfaces are described taking into account fluctuations in their thickness a and positioning with respect to the abrupt interface picture. Numerical results for confined (0,0),(1,1) and (0,2) excitons in GaAs/Al_0.3Ga_0.7As quantum wells show that while the interfacial fluctuations produce small changes (<0.5 meV) in the exciton binding energies, the confined exciton energies can be red- or blue-shifted as much as 25 meV for wells with mean width of 50 Å and 2 ML wide interfaces.     

Relationship between chemical bond parameters and superconducting temperature in HgBa2Can−1CunO2n+2+δ (n=1, 2, 3, 4)

Bond covalency and valence of elements in HgBa₂Ca_n−1Cu_nO_2n+2+δ (n=1, 2, 3, 4) were calculated and their relationship with T_c was discussed. For both oxygen and argon annealed samples, the results indicated that with the increase of n, the trend of bond covalency of Hg-O and Cu-O was the same or opposite compared with that of superconducting temperature. This may suggest that the magnitudes of Cu-O and Hg-O bond covalency are important in governing the superconducting temperature. For the highest T_c sample, Hg had the lowest valence, implying that lower valence of Hg was preferred in order to produce higher T_c. For fixed n, the valence of Cu in oxygen annealed samples was larger than that in argon annealed samples, indicating that oxygen annealed samples produced more carriers than argon annealed samples.