On the periodic solutions of a particular Lame equation

We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t).     

苯和甲苯在盐水溶液中活度系数及其盐效应的研究

采用紫外分光光度法测定了24.0℃时苯和甲苯在CH3COONa,(NH4)2SO4,MgSO4,Na2SO4和Na2CO3水溶液中的活度系数(f),它们的lgf-Cs关系符合Setschenow盐效应公式,计算了苯和甲苯在上述5种盐水溶液中的盐析系数。     

Earthquake—generating Structure Revealed by 1999 Sichuan mianzhu Earthquake Sequence with Ms=5.0

Through the accurate determination of hypocenter location,the measurement of the main focal mechanism solutions and the analyses of time dependent processes for Sichuan Mianzhu earthquake sequence with Ms=5.0 occurred along the middle segment of Longmenshan fault zone on November 30,1999,the distribution of focal depth section,the stress relase and seismicity features are given to reveal the earthquake-geneating structure of the earthquake sequence.The obtained results show the activity features for this sequence as follows:(1) There is no obvious foreshock,the accumulated strain energy releases in nearly pulse way,fluctuation of the seismic activity level is not quite evident during the duration of the sequence,and the statistical relation between the large events and the small events is less compatible with the traditional G-R estimation;(2) The epicenters of the earthquake sequence are not distributed on the main Longmenshan piedmont faults emerging out ground,but near the hidden Longmenshan piedmont faults.The direction of epicenter distribution is not very coincident with the fault strikes.The microscopic epicenters are relatively far from the macroscopic epicenters,The focal depths range from 5km to 16km;(3) The fractures of focal fault plane with the NE strike appear out the strike-slip displacement with a few overthrust components under the major principal compressive stress of NNE direction.From these,we consider it should be paid more attentions to the underground hidden faults near the ground fault zone on a large scale for their generating earthquake risk.     

大姚地热动态特征分析

通过大姚高精度水温观测井水地质、井孔条件的分析，震例观测资料、实验观测数据的处理，以及井水水质分析结果，表明大姚水温周期性变化的突出位置是井深75m左右，根本原因是该地层石膏脉稳定释热，含水层热水与井内冷水混合过程中，在通道内形成钙盐类沉淀物（如CaSO4CaCO3），堵塞对流通道，含水层内外压差突破被阻塞通道，热水反复侵入井内，便形成水温周期性变化。地震的孕育、发生和调整过程，由于应力场作用，产生附加地热场，水温基值发生变化，周期畸变或消失，这种附加地热动态是可以恢复的。所以认为大姚地热动态是井区特殊地层地热信息的反映。     

由三元系相图计算活度的方法Ⅱ.有二元同分熔点化合物的体系

利用熔化自由能 ,由具有同分熔点二元化合物的三元系相图计算活度。计算的范围遍及三元相图的液相面、液相线、共熔线和三元低共熔点     

程海断裂带断层泥中石英碎砾表面SEM特征及断层活动状态的分析

根据断层泥中石英碎砾表面SEM特征的鉴定研究，可将程海断裂中、北段断层泥中石英碎砾表面SEM形貌特征分为6类，这表明该段断裂经历了长期多期次活动，强烈活动时间在中晚更新世；5件样品中均未见破裂类(Io)的石英颗粒，表明程海断裂全新世以来强烈活动的频度相对较低。石英碎砾表面机械作用特征的分类统计研究显示：程海断裂中、北段晚更新世以来，断层所经历的活动方式以粘滑活动为主。     

AEKF在星敏感器低频误差补偿中的应用

高分辨率对地观测卫星需要精确的姿态信息来满足后续对地定位等工作,因此姿态确定精度十分重要。星敏感器的低频误差是影响卫星姿态确定精度的重要因素之一,主要是由空间周期性的热环境变化引起的。为进一步提高卫星姿态确定精度,对星敏感器的低频误差产生机理即星敏感器主光轴做周期性扰动进行了分析,设计了星敏感器低频误差补偿方案,建立了考虑星敏感器低频误差在内的组合定姿模型,利用拓维卡尔曼滤波(AEKF)对低频误差进行补偿,并引入RTS平滑滤波进一步提高姿态确定精度。仿真实验表明,设计的星敏感器低频误差补偿方案能有效对其进行补偿,提高卫星姿态确定精度。     

顾及周期项误差和起点偏差修正的北斗卫星钟差预报

根据北斗卫星导航系统星载原子钟自身的物理特性,采用武汉大学IGS数据中心发布的2016年1月1日至2016年11月1日共306天的事后钟差产品进行谱分析。分析结果表明:北斗卫星导航系统的3类卫星钟都存在一定的周期特性;其中GEO和IGSO卫星钟的主周期相对较为明显;GEO卫星钟的主周期依次为12、24、8和6h;IGSO的主周期为24、12、8和6h;而MEO的3个主周期为12.9、6.4和24h。依据各类原子钟的周期特性,同时对各天之间钟差的起始点偏差进行修正,并利用修正模型对北斗卫星钟差进行预报和精度分析。试验结果表明,改进的预报模型能显著提升北斗卫星的钟差预报精度,北斗卫星钟差24h、12h、6h的平均预报精度分别能达到6.55ns、3.17ns和1.76ns。     

西气东输管道工程中卫黄河穿越隧道场地工程地质条件评价

西气东输工程中卫黄河穿越隧道长1197.77m,高4.3m,宽5.6m。隧道入口高于黄河水位28m,出口高于黄河水位45m。隧道顶板高程为1130m。位于黄河水下100m。隧道场地围岩为寒武系磨盘井组灰绿色、银灰色浅变质中厚层细粒长石石英砂岩、千枚状板岩、绢云母化千枚岩。围岩为弱风化Ⅲ～Ⅳ类岩石。透水率为4～67Lu,纵波波速为500～3300m.s-1。BQ为300～400。变形模量为6.11～9.22GPa。泊松比（）0.14～0.24。内摩擦角（）为42.1～44.7。地下水为基岩裂隙水。含水层为寒武系浅变质岩,受大气降水渗入补给,单井涌水量为1.0～50m3.d-1。隧道轴线穿越区岩体较完整较破碎,未有全新活动断层。隧道位置选择和开挖深度设计是可行的。施工和长期运营是安全的。     

周期性的或伴有贯穿流的西边界流跨隙流动的迟滞变异过程

使用1.5层准地转约化重力模式研究了周期性的或伴有贯穿流的西边界流跨隙流动的迟滞变异过程。当西边界流变化的周期比罗斯贝波在缺口处调整的时间尺度大得多时,在雷诺数增加和减少过程的霍夫分叉点都发生延迟,从而产生新的雷诺数迟滞区间;并且西边界流流态转变的临界值变化显著;且周期强迫越短,雷诺数迟滞区间越大。当西边界流变化的周期与罗斯贝波在缺口处调整的时间尺度相当时,西边界流在缺口的流态呈无迟滞的周期性变化,且西边界流入侵西海盆的程度随周期减少而变小。此外,当贯穿流的流量大于西边界流的一半时,会显著影响西边界流在缺口处的迟滞变异过程;西边界流向西入侵程度和流态转变发生的临界雷诺值均发生变化,且贯穿流流量越大变化越大。