A Revision of the Trapezoidal Branch-and-Bound Algorithm for Linear Sum-of-Ratios Problems

In this paper, we point out a theoretical flaw in Kuno [(2002)Journal of Global Optimization 22, 155–174] which deals with the linear sum-of-ratios problem, and show that the proposed branch-and-bound algorithm works correctly despite the flaw. We also note a relationship between a single ratio and the overestimator used in the bounding operation, and develop a procedure for tightening the upper bound on the optimal value. The procedure is not expensive, but the revised algorithms incorporating it improve significantly in efficiency. This is confirmed by numerical comparisons between the original and revised algorithms. The author was partially supported by the Grand-in-Aid for Scientific Research (C)(2) 15560048 from the Japan Society for the Promotion of Science.     

Modeling of chemical tracer transport in the atmospheric environment and its impact on the global climate

Continental regions are experiencing rapid environmental changes due to expansion of industrial activities and land uses in different types of agricultural productions, burning of fossil fuels, etc., which lead to the emanation of huge amount of smog aerosol particulates and chemicals in the atmosphere. Information about these chemical tracers has been found from Indian Ocean Experiment (INDOEX), Intergovernmental Panel for Climate Change (IPCC) assessment reports as well as from other sources. The results of these computations may be interpreted by the chemical tracer transport model. In this paper, we have used a global atmospheric model in which the optical properties and the concentrations of the chemical tracers and aerosols have been incorporated. The aerosols and chemicals are transported in the atmospheric environment by the model cumulus convection and through the model semi-Lagrangian advection process . Thus, they are globally distributed along with the wind flow. The model has been used in studying the impact of the tropospheric chemical perturbations on the global environment.     

Construction of a CPA contraction metric for periodic orbits using semidefinite optimization

A Riemannian metric with a local contraction property can be used to prove existence and uniqueness of a periodic orbit and determine a subset of its basin of attraction. While the existence of such a contraction metric is equivalent to the existence of an exponentially stable periodic orbit, the explicit construction of the metric is a difficult problem.In this paper, the construction of such a contraction metric is achieved by formulating it as an equivalent problem, namely a feasibility problem in semidefinite optimization. The contraction metric, a matrix-valued function, is constructed as a continuous piecewise affine (CPA) function, which is affine on each simplex of a triangulation of the phase space. The contraction conditions are formulated as conditions on the values at the vertices.The paper states a semidefinite optimization problem. We prove on the one hand that a feasible solution of the optimization problem determines a CPA contraction metric and on the other hand that the optimization problem is always feasible if the system has an exponentially stable periodic orbit and the triangulation is fine enough. An objective function can be used to obtain a bound on the largest Floquet exponent of the periodic orbit.     

不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

Global fittings of NNO and NNO vibrational-rotational line positions using the effective Hamiltonian approach

An effective Hamiltonian built up to sixth order in the Amat-Nielsen ordering scheme describing all rovibrational energy levels in the ground electronic state and containing in explicit form all resonance interaction terms due to the approximate relations between harmonic frequencies ω₁≈2ω₂ and ω₃≈4ω₂ was applied to model the observed rovibrational line positions (collected from the literature) of ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O isotopologues of nitrous oxide. For ¹⁴N¹⁵N¹⁶O, 124 effective Hamiltonian parameters were fitted to near 28 000 observed line positions covering the 0.8-8860 cm⁻¹ spectral range. The RMS of the weighted fit is 0.00126 cm⁻¹ and dimensionless standard deviation is 1.48. For ¹⁵N¹⁴N¹⁶O, 121 effective Hamiltonian parameters were fitted to more than 31 000 observed line positions covering the same spectral interval. The RMS of the weighted fit is 0.00185 cm⁻¹ and dimensionless standard deviation is 1.85. In both cases the models describe all available line positions with precision compatible to the measurement uncertainties. A number of local resonance perturbations was found and discussed. Among these perturbations there are interpolyad resonance Coriolis interactions. A comparison of HITRAN-2008 data with the calculations based on the fitted models is presented.     

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。     

Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints

We present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions. The authors are grateful to the referees for constructive comments and suggestions which have contributed to the final preparation of the paper. Z.Y. Wu’s current address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Victoria, Australia. The work of this author was completed while at the Department of Applied Mathematics, University of New South Wales, Sydney, Australia.     

带有多项式非线性项的高维反应扩散方程有限差分格式的长时间行为

本文考虑了一类带有多项式非线性项的高维反应扩散方程．建立了一个全离散的有限差分格式,并证明了差分解的存在唯一性．分析了由差分格式生成的离散系统的动力性质,在对差分解先验估计的基础上得到了离散动力系统的整体吸引子的存在性．最后证明了差分格式的长时间稳定性和收敛性．