Optimal strategy of vaccination and treatment in an SIRS model with Markovian switching

Medical treatment and vaccination decisions are often sequential and uncertain. Markov decision process is an appropriate means to model and handle such stochastic dynamic decisions. This paper studies the near‐optimality of a stochastic SIRS epidemic model that incorporates vaccination and saturated treatment with regime switching. The stochastic model takes white noises and color noise into account. We first prove some priori estimates of the susceptible, infected, and recovered populations. Moreover, we establish some sufficient and necessary conditions of the near‐optimality by Pontryagin stochastic maximum principle. Our results show that the two kinds of environmental noises have great impacts on the infectious diseases. Finally, we illustrate our conclusions through numerical simulations.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.     

Control of Ionization in the Interaction of Strong Laser Fields with Dense Nanoplasmas

Different experimental methods to maximize the yield of highly charged ions in silver and xenon clusters interacting with intense and ultra‐short optical laser pulses are discussed. Theoretically, the interaction of strong laser fields with clusters is investigated within the nanoplasma model. The time evolution of the laser intensity has been parametrized. The free optimization of the parameters with a genetic algorithm is an effective but expensive tool to control the plasma dynamics. Comparison is given to the parametric control method in which pulse separation and relative intensity ratio of double‐pulses are varied. This method delivers in the case of silver and xenon clusters pulses quite close to the optimal pulse shape (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

No optimal 1‐planar graph triangulates any nonorientable closed surface

Suzuki [Discrete Math. 310 (2010), 6–11] proved that for any orientable closed surface F² other than the sphere, there exists an optimal 1‐planar graph which can be embedded on F² as a triangulation. However, for nonorientable closed surfaces, the existence of such graphs is unknown. In this article, we prove that no optimal 1‐planar graph triangulates a nonorientable closed surface.     

Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

生态平衡制约下离散尺度结构种群的最优收获

研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构.     

试验优化设计Er3+-Yb3+共掺杂Gd2Ti2O7上转换发光特性

采用溶胶-凝胶（Sol-gel）法制备了Er³⁺-Yb³⁺共掺杂Gd₂Ti₂O₇纳米晶粉末,通过试验优化设计的理论建立了Er³⁺-Yb³⁺掺杂浓度与发光强度的回归方程,利用遗传算法优化计算出方程的最优解Er³⁺、Yb³⁺掺杂浓度分别为5.60%（物质的量分数）和13.43%。Er³⁺-Yb³⁺共掺杂Gd₂Ti₂O₇纳米晶粉末为单一面心立方Gd₂Ti₂O₇相结构,随Yb³⁺共掺杂浓度增加,X射线衍射峰逐渐向高角偏移。在976 nm激光激发下,Er³⁺-Yb³⁺共掺杂Gd₂Ti₂O₇获得了分别对应于Er³⁺的²H_11/2/⁴S_3/2→⁴I_15/2和⁴F_9/2→⁴I_15/2跃迁的绿色和红色上转换发光,且绿色和红色发光均为双光子吸收过程。研究了最优样品上转换发光与温度之间的关系,发现绿色上转换发光具有优良的温度传感特性,对红色上转换发光的温度猝灭进行了解释。     

The optimal cell gap determination of a liquid crystal wavefront corrector from a single photoelectric measurement

It has been a crucial technique to improve the dynamic response characteristics of a liquid crystal wavefront corrector (LCWFC) with optimal cell gap since the LCWFC needs at least 2π (or π) phase modulation in adaptive optics systems (AOSs). We have given a complete process for obtaining the optimal cell gap accurately from a single photoelectric measurement, which can be conducted with a liquid crystal (LC) cell of any known thickness. This method has been analysed theoretically and confirmed experimentally by using a wedge-shaped cell; the experimental results match very well with the theoretical analysis. The response time of an optimal gap cell can be a novel evaluation method of response performance of LC materials.