A threshold for the size of random caps to cover a sphere

Consider a unit sphere on which are placed N random spherical caps of area 4p(N). We prove that if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH8aapcaaIXaaaaa!454E!\[\overline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) < 1\], then the probability that the sphere is completely covered by N caps tends to 0 as N , and if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWaaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH+aGpcaaIXaaaaa!4551!\[\underline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) > 1\], then for any integer n>0 the probability that each point of the sphere is covered more than n times tends to 1 as N .     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.     

稀土高碳当量灰口铸铁组织与性能的研究

本文研究了利用稀土合金改善高碳当量灰口铸铁质量的可能性,稀土合金对高碳当 量灰口铸铁组织和性能影响的规律,以及稀土夹杂物在铸铁各相中分布的规律．发现了 稀土合金加入量与铸铁的机械性能之间明显的对应关系——“双峰值效应”。对稀土高 碳当量灰口铸铁的某些高温机械、物理、化学性能进行了研究。结果表明稀土合金加入 到高碳当量灰口铸铁中以后能净化铁水,改善组织,并提高其性能．     

WO3/(TiO2-SiO2)催化剂的表面分散状态及催化性能的研究

用气相流动吸附法制备复合载体,用浸渍法制备WO3/(TiO2-S iO2)催化剂.应用LRS和TPR技术研究WO3在复合载体TIO2-S iO2表面的分散状态,发现TiO2在S iO2表面的分散可增强WO3与载体之间的相互作用,提高WO3在载体表面的分散阈值.另外TPR实验证明,TiO2的存在不仅大大改善WO3的分散状态,而且使WO3在TiO2-S iO2的还原温度升高,WO3与载体之间的作用增强.负载于经TiO2调变的S iO2上的催化剂其HDS、HYD、BHD活性高于负载于单纯S iO2上的催化剂的活性.     

MoO3、NiO、ZnO在小表面金红石上的分散行为

Dispersion of MoO3, NiO, ZnO on rutile TiO2 with low specific surface area was studied with Mercury Porosimeter, SEM, XPS and Ammonia Extraction method. The dispersion thresholds of MoO3, NiO, ZnO on three rutile TiO2 carriers were obtained with XPS, and com-pared with those on anatase TiO2 with high specific surf are area. Ammonia Extraction method was used to identify the surface oxide species interarting with support surface in different strength and it was found that the proportions of oxides that can not be extracted by ammonia extraction are different for MoO3, NiO and ZnO which are supported on rutile TiO2.     

Raman spectra of olivine solid solutions (FexMg1−x )2SiO4 and spin-vibration interaction

Room temperature Raman spectra of synthesized powder (Fe_xMg_1?x )₂SiO₄ solid solutions are obtained. Frequency trend of all modes versus composition shows clearly the existence of a step at x = 0.3. A step-like behavior of vibration frequencies at the given composition that coincides with the percolation threshold for the olivine lattice is related to the appearance of magnetic excitations in the disordered magnetic medium owing to the spin-vibration interaction.     

基于PSO磁悬浮球系统自适应灰预测控制

目的 针对磁悬浮球系统非线性不稳定和滞后性的问题,提出一种基于粒子群优化的自适应灰色预测 PID (Proportion Integration Differentiation)复合控制策略。 方法 通过在 PID 控制模块的反馈环中引入具有等维新息特征的灰色预测器,对系统误差进行及时反馈修正,以提高控制系统的响应速度和鲁棒性;同时,融合粒子群智能算 法对控制器参数迭代优化,以提高控制系统控制精度和抗干扰能力;最后,在 MATLAB / Simulink 环境下搭建仿真 平台进行对比实验。 结果 验证基于粒子群优化的自适应灰预测控制系统模型的超调量、峰值时间、调节时间显著 改善。 结论 证实该策略可以有效抑制系统滞后性,具有良好的稳定性和鲁棒性。     

“灰箱”的辩识与控制——一种简便实用的自适应控制方法

以在蒸汽机车锅炉减温群控系统中成功地实现自适应控制为例,介绍一种用单板机对“灰箱”进行在线辩识和自校正调节的方法,并提出了简化的自适应控制算式.     

基于新型核与灰度序列的时滞GM(1,N)模型及其应用

为了解决GM(1,N)模型在新型核与灰度的基础上,对驱动项的延迟作用机理不明确的问题,将时滞参数引入到GM(1,N)模型的驱动项中,构建了基于新型核与灰度的时滞GM(1,N)模型,分析了时滞参数的辨识方法,讨论了新模型的建模机理。为了更好地对该模型的有效性进行验证,将优化的时滞GM(1,N)模型对南京市的雾霾进行预测分析,选择GM(1,N)模型、一元回归模型与文中的优化模型进行对比。结果显示,优化模型对PM₁₀浓度的拟合精度更高,且误差均控制在5%之内,从而验证了提出的优化模型适用于具有时滞特征数据的模拟和预测。     

考虑顾客便利半径和质量阈值的竞争设施选址问题

在竞争设施选址问题中,顾客选择行为是决定设施占领市场份额的重要因素,其描述了需求在设施之间的分配方式。为了贴近顾客真实的光顾行为,本文提出了一种考虑顾客便利半径和质量阈值的顾客选择规则,并研究了在该规则下市场中新进入公司的竞争设施选址问题。提出了一种基于排名的遗传算法(RGA)求解该问题,并将该算法与经典遗传算法(GA)和基于排名的离散优化算法(RDOA)进行了比较,结果说明了算法的有效性以及模型中质量阈值的重要性。