Approximation of an Inverse Initial Problem for a Biparabolic Equation

In this paper, we consider the problem of finding the initial distribution for the linear inhomogeneous and nonlinear biparabolic equation. The problem is severely ill-posed in the sense of Hadamard. First, we apply a general filter method to regularize the linear nonhomogeneous problem. Then, we also give a regularized solution and consider the convergence between the regularized solution and the sought solution. Under the a priori assumption on the exact solution belonging to a Gevrey space, we consider a generalized nonlinear problem by using the Fourier truncation method to obtain rigorous convergence estimates in the norms on Hilbert space and Hilbert scale space.     

Stability of a mixed additive and quadratic functional equation in quasi-Banach spaces

We study the stability of functional equations in quasi-Banach spaces where the quasi-norm is not assumed to be a p-norm. To overcome the modulus of concavity greater than 1 and the discontinuity of quasi-norms we use the squeeze inequality presented in an explicit revision of Aoki–Rolewicz Theorem  [13, Theorem 1]. As illustrations, we prove an extension of the stability of a mixed additive and quadratic functional equation in p-Banach spaces to quasi-Banach spaces with better approximation. The technique may be used to prove extensions of other results on the stability of functional equations in p-Banach spaces to quasi-Banach spaces.     

Embedding theorems and Kahlerity for 1-convex spaces

Unless the contrary is explicitly stated, allℂ-analytic spaces considered here are assumed to be non compact, countable at infinity and of bounded Zariski dimension. The author gratefully acknowledges the generous support from the N.S.F. Grant #MCS 81-02266. Also he would like to thank Prof. H. Hironaka for bringing this problem to his attention.     

Nonlinear integration on Lp-spaces

For a Banach space E and for 1 ? p < ∞ let ?p<∞ let L_E^p(μ) = L_E^p(S,B,μ) denote all Bochner p-integrable E-valued functions on a measure space (S,B,μ). Under study are convergence theorems for integrals of functions in L_E^p(μ) with respect to Nemytskii measures. Weak integrals are then denoted to Hammerstein operators, and a study of topologies generated by vector measures leads to a characterization of compact Hammerstein operators.     

Quasielastic scattering of light by a photoexcited electron-hole plasma induced in a GaAs layer in the presence of InAs quantum dots

The development of a method for registering quasielastic electronic light scattering spectra in the near-IR region, which makes it possible to detect light scattering by a photoexcited electron-hole plasma induced in a GaAs layer in the presence of a self-organized ensemble of InAs quantum dots, is reported. A substantial resonance intensification of such scattering, two orders of magnitude greater than the values established for the bulk material, is observed, and the main mechanism of such scattering is determined.     

On compactifiable strongly pseudoconvex threefolds

In contrast with the 2-dimensional case, we would like to exhibit here an example of a compactifiable strongly pseudoconvex threefold X such that a) the analytic Kodaira dimension κ(X)=3 and b) its exceptional subvariety S is projective algebraic; yet X is not quasi-projective.     

Systematic control of the packing density of self-assembled monolayers using bidentate and tridentate chelating alkanethiols

The structural and interfacial properties of self-assembled monolayers (SAMs) on gold derived from the adsorption of a series of 1,1,1-tris(mercaptomethyl)alkanes (i.e., CH3(CH2)mC[CH2SH]3, where m = 9, 11, 13, 15) were investigated. The new SAMs, which possess uniformly low densities of alkyl chains, were characterized by ellipsometry, contact angle goniometry, and polarization modulation infrared reflection absorption spectroscopy. Additional analysis of the SAMs by X-ray photoelectron spectroscopy permitted a direct calculation of the packing densities of the SAMs on gold. The results as a whole, when compared to those obtained on SAMs generated from normal alkanethiols (CH3(CH2)m+2SH), 2-alkylpropane-1,3-dithiols (CH3(CH2)mCH[CH2SH]2), and 2-alkyl-2-methylpropane-1,3-dithiols (CH3(CH2)mC(CH3)[CH2SH]2) having analogous chain lengths, demonstrate that the 1,1,1-tris(mercaptomethyl)alkanes afford SAMs with alkyl chains having the lowest packing density and least conformational order.     

A review of progress on nano-aperture VCSELInvited Paper

This paper reviews the progress on nano-aperture vertical-cavity surface-emitting lasers (VCSELs). The design, fabrication, and polarization control of nano-aperture VCSELs are reviewed. With the nanoaperture evolving from conventional circular and square aperture to unique C-shaped, H-shaped, I-shaped, and bowtie-shaped aperture, both the near-field intensity and near-field beam confinement from nanoaperture VCSELs are significantly improved. As a high-intensity compact light source with sub-100-nm spot size, nano-aperture VCSELs are promising to realize many new near-field optical systems and applications.