Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Asymptotic Analysis of the Current-Voltage Curve of a pnpn Semiconductor Device

We consider the one-dimensional steady-state semiconductor deviceequations modelling a pnpn device. There are two relevant scalingsof the equations corresponding to small and large applied voltages.In both scalings, the semiconductor equations can be consideredas singularly perturbed. It turns out that the small-voltagescaling breaks down for current values between two saturationcurrents. In that interval, the large-voltage scaling has tobe employed. For both scalings, we derive the first-order termsof an asymptotic expansion and show that the reduced problemhas a solution. An example verifies that the current-voltagecurves obtained have the expected qualitative structure.     

Synthesis and properties of the nanocomposite of zink oxide and poly(amic acid)

The composite comprised of zinc oxide quantum dots and poly(amic acid) (PAAc) was prepared and studied by X-rays diffraction, X-ray photoelectron spectroscopy, light scattering, UV absorbance and UV fluorescence. The UV absorbance of the ZnO/PAAc composite was found to be much larger than that of its components taken separately. The fluorescence of the ZnO/PAAc composite was found to be shifted to longer wavelengthes in comparison with pure ZnO. The presence of the dopant dodecylbenzenesulfonic acid was found to affect the observed fluorescence.     

Optical absorption spectra of linear and cyclic thiophenes—selection rules manifestation

We theoretically study the size-dependent relation between absorption spectra of thiophene-based oligomers and the corresponding cyclothiophenes. In our approach based on a Frenkel exciton Hamiltonian, we demonstrate that the geometry and selection rules determine the observed relations between the spectra.     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003