Synthesis of Spiranes by Cyclocondensation of 2-Phenacylbenzothiazole with Hydrazines and o-Hydroxybenzaldehydes

2-Phenacylbenzothiazole reacts with hydrazines and o-hydroxybenzaldehydes to give hydrazones and chalcones. These compounds tend to isomerize to benzothiazole-2-spiro-3'-pyrazoles and benzo[b]pyran-2-spiro-2'-benzothiazoles, respectively.     

A Study of Drop Size Distribution in Multistage Bubble Extractor

Results obtained in determining experimentally the mean volume-surface drop diameter of the dispersed phase in a multistage bubble extractor are presented.     

Magnetic field penetration into half-space for type-II superconductors of the second kind

Equations that simulate the magnetic induction and current density distributions in half-space in view of the power I-V characteristic are derived. The magnetization front velocity is determined for a given mean rate of external magnetic field variation at the boundary of the sample. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. An analytical solution that simulates the power variation of the magnetic field at the boundary is given. The Bean generalized model describing the current density distribution near the critical current is considered. It is shown that solutions like shock waves may arise beyond the applicability domain of the Bean model.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

Modification of GaAs by medium-energy N<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> ions

The modification of GaAs with a 2500-eV beam containing N ₂ ⁺ and Ar⁺ ions is examined with Auger electron spectroscopy. Most implanted nitrogen atoms are found to react with the matrix, substituting arsenic atoms to produce a several-nanometer-thick layer of the single-phase GaAs_1−x N_x (x=6%) solid solution. The GaN phase is absent. Displaced arsenic atoms and nitrogen atoms unreacted with the matrix are present in the layer and on its surface. The former segregate, whereas the latter form molecules.     

IR-induced nonlinear optics in Ge-doped Bi12TiO20 large-sized nanocrystallites

Photoinduced non-linear optical effects in large-sized (up to 25 nm) nanocrystallites (NC) of Ge-doped Bi₁₂TiO₂₀ (BTO:Ge) incorporated within olygoether photopolymer matrix have been studied. Photoinduced second harmonic generation (PISHG) was measured. Nd:YAG pulsed laser (λ=1.06 μm) was used as a source of photoinducing light. As a fundamental light source for the SHG and two-photon absorption, Er:LiYF₄ laser (λ=2.065 μm) was used. We have found that with increasing IR pump power density, the output doubled frequency SHG signal (λ=1.03 μm) increases and achieves its maximum value at the pump power density about 0.45 GW/cm² and NC size about 12 nm.The values of second-order optical susceptibilities were almost 20% larger than for the pure BTO NC single crystals. With decreasing temperature below 60 K, the SHG signal increases achieving maximal value at LHeT.     

Fracture strength of class II slot cavities restored with polymerizable restorative materials

This study compared the fracture strength of Class II slot cavities restored with polymerizable restorative materials. Sixty, caries-free, posterior teeth were divided into five groups of 12 teeth. The Class II slot cavities were prepared. The teeth were restored with two packable composites (Filtek P60, Surefil), a microhybrid composite (Filtek Z250)and two ormocer (Definite, Admira). The restorations were then subjected to fracture resistance tests. The marginal ridges of the restorations were loaded at an angle of 13.5° to the long axis of the tooth in an Universal Testing Machine until failure. Analysis of mean forces indicated that, Filtek P60, Surefil and Filtek Z250 exhibited better performance than Definite and Admira. The tested resin composites differed in their mechanical properties. This study suggested that fracture behavior were highly influenced by the filler system. Overall, Filtek P60, Surefil, Filtek Z250, demonstrated good fracture resistance. Copyright © 2003 John Wiley & Sons, Ltd.     

Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting and show the connections of adjoint processes to dynamic programming. The result is applied to financial optimization problems.