Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Humanitarian welfare values in a changing social environment: A survey of social work undergraduate students in Beijing and Shanghai

• Summary: Internationally accepted social work values are based on ideas about rights, social justice and equitable resource distribution. Does social work education in China embody similar values? Are these values influenced by culture and the current political/economic environment? The research posed three questions. Do social work students studying in metropolitan China support humanitarian welfare values? Are values affected by demographic backgrounds? Does social work education enhance humanitarian values? A self-administered, standardized questionnaire was distributed in 26 classes of social work students studying in seven universities in Beijing and Shanghai (n = 1328).• Findings: Students do not support humanitarian welfare values strongly; and a decrease in these values was observed in senior students. Significant differences in values were found based on gender and on rural/urban origins. Female students were more likely to agree with humanitarian value statements; rural and urban students tended to agree more with values from which they had potential to benefit.• Applications: Social work knowledge and skills rather than values maybe more immediately relevant to Chinese society. However, independent professional practitioners need a solid foundation of professional values to inform practice and standardize the social work role. There needs to be an ongoing debate in China involving social work educators and practitioners about values and their relation to Chinese society, the ways in which they are influenced by non-Chinese cultures; and how to infuse these consistently into social work curricula in Chinese universities. © The Author(s) 2010.postprin

Determination of Wave Function Functionals: The Constrained-Search--Variational Method

In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. The space of variations is expanded because a search over the functions $\chi$ can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.Comment: 26 pages, 4 figures, 5 table

Making inexpensive drugs for the treatment of Human African Trypanosomiasis

Neglected tropical diseases (NTDs) affect the world’s poorest population; mainly in Africa, Asia, and Latin America. According to the WHO, more than one billion people are affected by NTDs. The connection between these areas is the lack of proper sanitation, and the persistence of the diseases, trap the affected countries in the poverty and disease cycle. African sleeping sickness, a prevalent NTD, is a parasitic infection caused by two parasites from the Trypanosoma brucei species and is transmitted by the tsetse fly or congenitally. The disease is manifested by fever, severe headaches, irritability, extreme fatigue, swollen lymph nodes, and aching muscles and joints. When it reaches the central nervous system it can cause progressive confusion, personality changes, and other neurologic problems. The high-cost and limited number of the drugs contribute to the increase of the cases resulting in a great impact on global health. The goal of our research is to develop inexpensive and effective drugs using low-cost organic starting materials that target the T. brucei parasite. Our target compounds are Mannich bases containing an aromatic moiety. Previous, but limited, studies have shown that this class of compounds demonstrates promising results against T. brucei. Our one step synthesis involves the use of nitro-substituted acetophenones, formaldehyde, and a variety of amines to make Mannich bases under conventional heating and microwave conditions. By changing the nitro-acetophenones and the amines used in the reaction, we hope to develop a robust drug library we can use to screen against T. brucei

On the discrete spectrum of Robin Laplacians in conical domains

We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians on conical domains.Comment: 12 page