The spectrum of Nd in rare earth orthoaluminates. The trigonal to orthorhombic transition study of the level

Some structural and spectroscopic features of rare earth orthoaluminates are examined.The trigonal→ orthorhombic transition is studied in a series of Nd_xSm_1−xAlO₃ compounds. The evolution of the crystal structure is followed by X-ray analysis and optical absorption. The free ion and crystal field parameters of Nd³⁺ (4f³ configuration) are determined in LuAlO₃:Nd³⁺.The anomaly of the calculated splitting of the levels is slight, but well characterized in NdAlO₃. The spin correlated crystal field and orbitally correlated crystal field models are tested as well as an empirical correction which was proposed earlier.     

微分代数多项式系统的可解集

本文对一般微分代数方程给出了几类可解集的概念，并讨论了多项式微分代数方程的可解集，得到子多项式系统具有唯一解。特别是有多于一个的解的条件，并得到了低次多项式在一定意义下的充分必要条件。     

Predictability and model selection in the context of ARCH models

Most of the methods used in the ARCH literature for selecting the appropriate model are based on evaluating the ability of the models to describe the data. An alternative model selection approach is examined based on the evaluation of the predictability of the models in terms of standardized prediction errors. Copyright © 2005 John Wiley & Sons, Ltd.     

彩票发行方案的合理性评价

本文根据目前常见的彩票销售规则及相应的奖金设置方案，综合分析了高项奖奖金额和低项奖中奖率对彩民的吸引力等因素，将发行方案的合理性问题归结为发行方案对彩民的吸引力上，引入了表示彩民心理趋向的偏好系数，构造了吸引力函数，同时综合考虑了封顶值等因素，对现行常见的29种彩票发行方案进行了综合评价。     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Radial and angular correlation in heliumlike ions

In the framework of nonrelativistic variational formalism a new type of basis set is proposed, to estimate separately the effect of radial and angular correlations on the ground‐state energy for helium isoelectronic sequence H^? to Ar¹⁶⁺. Effect of radial correlation is incorporated by using multiexponential functions arising from product basis sets suitably formed out of Slater‐type one‐particle orbitals. The angular correlation can be switched on by incorporating an expansion in terms of basis involving interparticle coordinates. With a set of six‐term Slater‐type one‐particle basis and five‐term interparticle expansion, the ground‐state energy of helium is estimated as ?2.9037236 (a.u.) compared with the multiterm variational estimates ?2.9037244 (a.u.) due to Pekeris and Thakkar and Smith and Drake. Matrix elements of different operators in the ground state have been calculated and found to be in good agreement with available accurate results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

Collaborative distributed decision making for large scale disaster relief operations: Drawing analogies from robust natural systems

One of the most ignored, but urgent and vital challenges confronting society today is the vulnerability of urban areas to extreme events. Current organization of response systems, predominantly based on a command and control model, limits their effectiveness and efficiency. Particularly, in decision‐making processes where a large number of actors may be involved. In this article, a new distributed collaborative decision‐making model is proposed to overcome command and control limitations encountered in stressful, hostile, chaotic, and large‐scale settings. This model was derived by borrowing concepts from the collective decision making of honeybees foraging, a successful process in solving complex tasks within complex settings. The model introduced in this article was evaluated through differential equations, i.e., continuous analysis, and difference equations, i.e., discrete analysis. The most important result found is that the best available option in any large‐scale decision‐making problem can be configured as an attractor, in a distributed and timely manner. We suggest that the proposed model has the potential to facilitate decision‐making processes in large‐scale settings. © 2005 Wiley Periodicals, Inc. Complexity 11:28–38, 2005     

On the orthogonality of natural modes of vibration

The natural modes of a discrete linear system are orthogonal with respect to the mass and stiffness matrices in a generalized sense. However, these modes are usually not orthogonal to each other in the ordinary sense. The purpose of this paper is to document a number of conditions under which the modes are also orthogonal in an ordinary fashion.