The effect of complexing processes on energy transfer Tl+→Gd3+ and Tl+→Tb3+ in glass

T. Shevchenko Kiev University, 252022 Kiev, Pr. Akad. Glushakova, 6, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 3, pp. 192–196, May–June, 1995.     

Miscible blends of modified poly(aryl ether ketones) with aromatic polyimides

The phase behavior of binary blends of poly(ether ether ketone) (PEEK), sulfonated PEEK, and sulfamidated PEEK with aromatic polyimides is reported. PEEK was determined to be immiscible with a poly(amide imide) (TORLON 4000T). Blends of sulfonated and sulfamidated PEEK with this poly(amide imide), however, are reported here to be miscible in all proportions. Blends of sulfonated PEEK and a poly(ether imide) (ULTEM 1000) are also reported to be miscible. Spectroscopic investigations of the intermolecular interactions suggest that formation of electron donoracceptor complexes between the sulfonated/sulfamidated phenylene rings of the PEEKs and the n-phenylene units of the polyimides are responsible for this miscibility. © 1993 John Wiley & Sons, Inc.     

Existence of black hole solutions for the Einstein-Yang/Mills equations

This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge groupSU(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/r ², asr tends to infinity.Research supported in part by the NSF, Contract No. DMS-89-05205Research supported in part by the DE, Contract No. De-FG 02-88 EF 25065     

Optimal convex hull algorithms on enhanced meshes

In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.This work was supported by NASA under grant NCCI-99.Additional support by the National Science Foundation under grant CCR-8909996 is gratefully acknowledged.     

Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers

We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self-induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two-dimensional spatial optical solitons. We apply the matrix criterion for stability of these two-parameter solitons, and verify it by direct numerical simulations.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.     

Generation of 0.2-TW 5.5-fs optical pulses at 1 kHz using a differentially pumped hollow-fiber chirped-mirror compressor

Optical pulses with 1.1-mJ energy and 5.5-fs duration have been generated at 1-kHz repetition rate from a chirped pulse amplification Ti:Sapphire laser incorporating a differentially pumped hollow-fiber chirped-mirror compressor. The effects of self-focusing and multi-photon ionization during the beam propagation were minimized by differentially pumping the hollow fiber filled with neon. The spectral broadening at the hollow-fiber compressor was optimized by adjusting gas pressure, laser intensity, and laser chirp, covering from 540 nm to 950 nm. PACS 42.65.Jx; 42.65.Re