Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Enhancing the Success of African-American Students in the Sciences: Freshman Year Outcomes

The Meyerhoff Program is an intensive, multicomponent program focused on enhancing the success of talented African-American students in science and engineering at a predominantly white, medium-sized university. The program components, taken together, address the four primary factors emphasized in the research literature as limiting minority student performance and persistence in science: knowledge and skills, motivation and support, monitoring and advising, and academic and social integration. Outcome analyses indicated that the first three cohorts of Meyerhoff students (total N=69) achieved an overall GPA (mean=3.5) significantly greater than that of an African-American historical comparison sample (mean=2.8) of comparably talented science students at the university. This difference was even greater for first year science GPA (means of 3.4 and 2.4, respectively), and in specific science and mathematics courses. Observational and questionnaire data indicated that the Meyerhoff program study groups, peerbased community, financial scholarships, summer bridge program and staff appear to be especially important contributors to student success. Implications of the findings for enhancing the success of African-American and other underrepresented populations in science are discussed.     

On the conditions under which a satellite orbit intersects the surface of a central body of finite radius in the restricted double-averaged three-body problem

This paper is concerned with the applied problem of choosing long-living orbits of artificial Earth satellites whose evolution under the influence of gravitational perturbation from the Moon and the Sun may result in the collision of the satellite with the central body, as was shown by M.L. Lidov for the well-known example of “Vertical Moon.” We use solutions of the completely integrable system of evolution equations obtained by Lidov in 1961 by averaging twice the spatial circular restricted three-body problem in the Hill approximation. In order to apply the integrability of this problem in practice, we study the foliation of the manifold of levels of first integrals and the change of motion under crossing the bifurcation manifolds separating the foliated cells. As a result, we describe the manifold of initial conditions under which the orbit evolution leads to an inevitable collision of the satellite with the central body. We also find a lower bound for the practical applicability of the results, which is determined by the presence of gravitational perturbations caused by a polar flattening of the central body. Original Russian Text ? V.I. Prokhorenko, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 156–173.     

Investigation of the structural elements of a fullerene within the static-fluctuation approximation of the Hubbard model

The anticommutator Green’s functions, correlation functions, and ground-state energies for closed atomic structures that consist of five or six atoms and are structural elements of a fullerene are calculated within the static-fluctuation approximation of the Hubbard model. The results of the calculations are analyzed and compared with the data available in the literature.     

Indistinguishability of particles or independence of the random variables?

After establishing the formula of information, we turn to two cases: to the independent case and to the dependent case. If the characteristics of the particles (e.g., the energy) as random variables are independent, we come in the discrete case to the Boltzmann distribution, while in the continuous case we come to the Gibbs formula-irrespectively of whether the particles are distinguishable or not. Our effort is nimed at clarity of the ideas, not at their mathematical completeness. Supported by the Hungarian National Foundation for Scientific Research (grant No. T 016384 and No. 4007-016237) Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part III.     

Parameterization of all solutions of the three chains completion problem

The family of all solutions of the three chains completion problem with a prescribed tolerance is described explicitly. It is shown that this family can be parameterized by a natural set of contractive upper triangular operators. As an application all solutions to a suboptimal nonstationary Nehari problem are described.     

Stable solutions of a system of two connected Chua cells

We investigate a nonlinear chain of two Chua oscillators and its stable solutions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1567–1569, November, 1998.     

Effect of p-toluensulfonic acid on oxidation of polyethylene and polyethylene-poly-p-methylstyrene blends

p-Toluensulfonic acid retards oxidation of polyethylene and, to a greater extent, of polyethylene-poly-p-methylstyrene blends. The real antioxidant is p-cresol, formed by p-toluensulfonic acid transformation in oxidizing polyethylene and, in blends, through peroxidation and subsequent acid-catalyzed decomposition of hydroperoxides of poly-p-methylstyrene.