The Transition Products in Substitutional Photochemistry of [Mo(CN)8]4− – Theoretical Approach. X-ray Crystal Structure of (AsPh4)[W(bpy)(CN)6]

The single crystal X-ray structure of (AsPh₄)[W(bpy)(CN)₆] is described. The structure of octa- and hepta-coordinated intermediates of substitutional photolysis of [Mo(CN)₈]⁴⁻ ion in aqueous media were determined by performing semi-empirical calculations. On the basis of obtained results as well as on empirical data the photolysis scheme has been postulated.     

Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants no. 2 P03A 003 25 and no. 4 T07A 027 26.     

Alloy formation in mechanically activated mixtures

The physical mixtures of hydroxocarbonates of Cu and Ni with aluminium were activated using a laboratory planetary mill. The chemical reactions and alloy formations as the effects of grinding were followed by the phase analysis of solid products based on the thermogravimetry and X-ray diffractometry. Experimental evidence indicates that the nature of reactions and products of mechanical activation was dependent on the amount of aluminium and time of grinding. This revised version was published online in July 2006 with corrections to the Cover Date.     

Physical Analysis of a Possibility to Reach the 1.30-μm Emission from the GaAs-Based VCSELs with the InGaAs/GaAs Quantum-Well Active Regions and the Intentionally Detuned Optical Cavities

Physical aspects of an operation of the GaAs-based InGaAs/GaAs quantum-well (QW) VCSELs with the intentionally detuned optical cavities have been considered in the present paper using the comprehensive three-dimensional self-consistent optical–electrical–thermal-gain simulation. In GaAs-based structures, very good DBR resonator mirrors and a very efficient methods to confine radially both the current spreading and the electromagnetic field with the aid of oxide apertures may be applied. It has been found using the above simulation that even currently available immature technology enables manufacturing the above devices emitting radiation of wavelengths over 1.20 μm. In particular, while the room-temperature 1.30-μm lasing emission is still beyond possibilities of the InGaAs/GaAs QW VCSELs, these structures may offer analogous 1.25-μm emission, especially for the high-power and/or high-temperature operation.     

Interpolation of Bilinear Operators Between Quasi-Banach Spaces

We study interpolation, generated by an abstract method of means, of bilinear operators between quasi-Banach spaces. It is shown that under suitable conditions on the type of these spaces and the boundedness of the classical convolution operator between the corresponding quasi-Banach sequence spaces, bilinear interpolation is possible. Applications to the classical real method spaces, Calderón-Lozanovsky spaces, and Lorentz-Zygmund spaces are presented. The author is supported by the National Science Foundation under grant DMS 0099881. The author is supported by KBN Grant 1 P03A 013 26.     

Current and shot noise in two capacitively coupled single electron transistors with an atomic sized spacer

The currents and their fluctuations in two capacitively coupled single electron transistors are determined in the limit of sequential tunnelling. Our considerations are restricted to the case when the islands (dots) of the transistors are atomic-sized, which means each of them has only one single electronic level available for the tunnelling processes. The Coulomb interactions of accumulated charges on the both single electron transistors lead to the effect of the negative differential resistance. An enhancement of the current shot-noise was also found. Spectral decomposition analysis indicated the two main contributions to the shot-noise: low- and high-frequency fluctuations. It was found that the low frequency fluctuations (polarization noise) are responsible for a strong enhancement of the current noise. Received 9 October 2001 / Received in final form 8 March 2002 Published online 9 July 2002     

Characterization of continuous distributions in terms of moments of extremal statistics

We give characterizations of continuous distributions in terms of moments of order statistics when the sample size is random. In particular, we characterize uniform, exponential, Pareto, and logistic distributions. Special cases of a random sample size (logarithmic series, geometrical, truncated binomial, truncated negative binomial, and truncated Poisson distribution) are also considered. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

Uniform persistence for nonautonomous and random parabolic Kolmogorov systems

The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems.     

Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K ^A of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K ^A and SA is deduced. Furthermore, the rigidity of the functor K ^A is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed.