Oscillation for a nonlinear dynamic system on time scales

We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden–Fowler differential and difference equations and many of its extensions. We generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system.     

A Conversation with Robert F. Christy – Part II

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his wartime work at Los Alamos on the critical assembly for the plutonium bomb (“the Christy bomb”); the Alamogordo test, July 16, 1945; the postwar concerns of ALAS (Association of Los Alamos Scientists); his brief return to the University of Chicago and move to Caltech; friendship with and later alienation from Edward Teller; work with Charles and Tommy Lauritsen and William A. Fowler in Caltech’s Kellogg Radiation Laboratory; Freeman Dyson’s Orion Project; work on the meson and RR Lyrae stars; fellowship at Cambridge University; 1950s Vista Project at Caltech; his opposition to the Strategic Defense Initiative; and his post-retirement work for the National Research Council’s Committee on Dosimetry and on inertial-confinement fusion.     

Effect of oceanic current on typhoon-wave modeling in the East China Sea

We use the WAVEWATCH-III model to quantify the effect of oceanic current on typhoon-wave modeling in the East-China-Sea(ECS).Typhoons Jelawat and Saomai in the autumn of 2000 are hindcasted.The oceanic currents in the ECS are mainly constituted of Kuroshio and typhoon-generated currents.The results show distinguishable differences in wave height and wave period under the typhoon conditions.The oceanic current causes the maximum differences,of up to a 0.5 m significant wave height and a 1 s mean wave period.Comparisons between typhoons Jelawat and Saomai show the dependence of the current effect on the typhoon characteristics.     

A Conversation with Robert F. Christy – Part I

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his childhood in British Columbia; his undergraduate years at the University of British Columbia; his graduate work with J. Robert Oppenheimer at Berkeley; and his work on the Manhattan Project, first with Enrico Fermi at the Metallurgical Laboratory of the University of Chicago and then as a member of the Theoretical Division at Los Alamos.     

NONLINEAR STABILITY ANALYSIS OF THE EMDEN–FOWLER EQUATION

In this paper, we qualitatively study radial solutions of the semilinear elliptic equation Δu+uⁿ = 0 with u(0) = 1 and u′(0) = 0 on the positive real line, called the Emden–Fowler or Lane–Emden equation. This equation is of great importance in Newtonian astrophysics and the constant n is called the polytropic index.

By introducing a set of new variables, the Emden–Fowler equation can be written as an autonomous system of two ordinary differential equations which can be analyzed using linear and nonlinear stability analysis. We perform the study of stability by using linear stability analysis, the Jacobi stability analysis (Kosambi–Cartan–Chern-theory) and the Lyapunov function method. Depending on the values of n these different methods yield different results. We identify a parameter range for n where all three methods imply stability.     

SARs of the antiprotozoal action of 6,7-diaryl-bicyclo[2.2.2]octan-2-ols

Abstract  Several 4-amino-6,7-diarylbicyclo[2.2.2]octan-2-ols bearing varying substituents on the aromatic rings were synthesized following a manual method for applying the Hansch approach. All new compounds were tested for their activity against the causative organisms of East African sleeping sickness and malaria tropica. Structure activity relationships are discussed. Graphical abstract        

A note on the existence and uniqueness solutions of the modified error function

This paper shows that the following nonlinear boundary value problem: where δ≥ − 1 and y is defined as a modified error function, can be reduced to the boundary value problems for the generalized Emden‐Fowler equation and Abel differential equation of the second kind in the canonical form, which do not usually have closed‐form solutions. The existence and uniqueness of the solution are established by considering another contraction mapping. Highly accurate approximate solutions of this problem are also provided.     

New approach to the synthesis of tetrazole-containing buta-1,3-diynes: The total synthesis of 1,4-bis(2-(tert-butyl)-2H-tetrazol-5-yl)buta-1,3-diyne

An approach for the total synthesis of 1,4-bis(2-(tert-butyl)-2H-tetrazol-5-yl)buta-1,3-diyne was reported. Developed approach to the synthesis of 1,4-bis(2-(tert-butyl)-2H-tetrazol-5-yl)buta-1,3-diyne can be used for obtaining different 2,5-bis(tetrazol-5-yl)-disubstituted five-membered heterocycles (e.g. thiophenes, pyrroles, furans etc.), as well as tetrazole-containing monomers for the synthesis of new types of electroconductive and high energetic polymers.     

武汉东湖的污染现状与可持续发展对策研究

通过对武汉东湖４０多年来的水生生物、周边环境和水质变化的分析比较，论述了东湖生态系统的人为干扰和变化情况，在对东湖的环境容量研究计算以及最大可持续养鱼量分析的基础上，结合东湖水体的综合功能，提出了武汉东湖可持续发展的对策．