保单调有理三次插值

提出了一种构造C^1保单调的有理三次插值函数的方法，所构造的插值函数分子是三次多项式，分母是线性多项式．由于函数表达式中含有调节参数，这使得插值曲线更具灵活性．     

玻色指数二次多项式型算子任意矩阵元的解析表达式

运用多模玻色指数二次多项式算子普通、正规乘积、反正规乘积三种表达式之间的转换关系，给出了多模玻色指数二次多项式算子任意矩阵元的解析表达式．应用本结果，得到了玻色二次多项式型系统配分函数及多模玻色指数二次多项式算子在粒子数、坐标、动量表象的矩阵元和P表示的严格表达式。     

n符号动力学n-1超稳揉序列揉特征多项式

利用Milnor-Thurston揉理论,推导出n符号动力学n-1超稳揉序列揉特征多项式的一个显式表达式.对于单峰、双峰及三峰等低次映射,表达式与已知的结果一致.     

近半个世纪云南持续数年干旱事件时空分布

云南近五十年气候变化趋势与规律研究对于理解和预测区域气候对全球暖化的响应有重要意义.研究基于云南29个气象站点1960-2012年的日降水数据,进行了标准化降水指数(SPI)分析,探讨了过去近五十年云南SPI24的变化趋势,以此确定了三次持续数年的干旱事件,分析了它们的空间演化模式和可能成因.分析结果表明,过去半个多世纪云南降水存在明显的年代际变化规律和变旱变涝趋势;分别在1988-1990年、2004-2007年和2009-2012年经历了三次持续数年的干旱事件.其中1988-1990年和2009-2012年的干旱事件在空间分布模式上表现为以滇南和滇东中部为中心地,向外发展而成覆盖云南大部分的极端干旱;而2004-2007年的干旱区域呈点状分布.在机制方面,持续数年干旱事件可能与大气环流异常持续发展并且受到某一特殊海气模式加持有关.     

保凸有理二次插值

提出了一种构造C^1连续的保凸分段有理二次插值函数的方法，所构造的插值函数分母是线性多项式，分子是二次多项式．由于函数表达式中含有调节参数，这使得插值曲线更具灵活性．     

一类平面分段光滑线性Hamilton系统在多项式扰动下的极限环个数

研究一类平面抛物-椭圆型分段光滑线性Hamilton系统在n次多项式扰动下的极限环个数.计算得到系统一阶Melnikov函数的表达式,利用广义罗尔定理证明了该类平面抛物-椭圆型分段光滑线性Hamilton系统在n次多项式扰动下极限环个数的上界为n-1+2[(n+1)/2].     

近断层地震加速度设计反应谱

研究了近断层地震的加速度设计反应谱,选择了30次地震,132组近断层地震记录作为统计样本,根据得到的实际地震波的平均弹性加速度反应谱,给出了近断层地震设计弹性加速度反应谱表达式,并在此基础上,给出了近断层地震设计非弹性加速度反应谱计算公式.研究结果表明:提出的近断层地震设计弹性加速度反应谱与实际地震波平均弹性加速度反应谱较为接近,所建议的近断层地震加速度设计反应谱形式较为简单.     

e-x的三次Hermite-Padé逼近多项式的惟一性与微分恒等式

首先证明了一个关于指数函数恒等式的指数不等式;根据这个指数不等式得到了在首项系数为1的条件下,指数函数e-x的三次Hermite-Padé逼近多项式的惟一性;最后根据指数函数e-x的三次Hermite-Padé逼近多项式的惟一性,得到了指数函数e-x的(k,l,m,n)型三次Hermite-Padé逼近多项式与(k-1,l-1,m-1,n-1)型三次Hermite-Padé逼近多项式之间的一组微分恒等式。     

达布多项式和二次系统周期解的存在性

给出了平面高次系统具有不变实不可约达布多项式的充要条件.在此基础上利用代数方法,根据平面二次系统表达式中的二次多项式来判定系统平衡点是否有闭轨线环绕,进而指出闭轨线内部的平衡点必须具备的一些条件.     

构造切触有理插值函数的一种新方法

文章首先将插值节点进行分块,对每块节点作Hermite插值多项式,并利用其剩下的节点作最高次项系数为1的代数多项式;其次对分块Hermite插值多项式及相应的代数多项式,采用线性组合方法得到一般切触有理插值函数的表达式;最后通过引入参数方法,给出设定次数类型的切触有理插值问题有解的条件。实例表明所给方法直观、灵活。     

Statistical survey on the magnetic field in magnetotail current sheets: Cluster observations

The distribution properties of the magnetic field in magnetotail current sheets have been explored statistically with the magnetic measurement data of the Cluster mission from June to November of the years 2001–2005. It is found that, on average, the strength of the magnetic field and its B_z component in the current sheet are weaker in the region close to midnight but stronger near the dawnside and duskside flanks, which implies that, in general, a thinner current sheet occurs near midnight and thicker ones near both flanks. The occurrence of tail current sheet flapping is higher on both flanks than in the midnight region, although it is most frequent in the dawn flank. Current sheets with a negative B_z component or a strong B_y component have a higher probability of occurring at magnetic local times of 21:00–01:00, indicating that magnetic activity, e.g. magnetic reconnection and current disruption occur more frequently there. Statistically, the probability distributions of the B_y component and the tilt angle of magnetic field lines in the current sheet are approximately normal distributions, and the occurrence probability of the flattened current sheet is about one third that of the normal current sheet. The magnetic field and B_z component in the current sheet mainly vary from 1 nT to 10 nT. The B_y component in the tail central current sheet is on average twice the IMF B_y at 1 AU.     

磁层亚暴过程中高速流分布

采用实际的磁尾位型,利用数值模拟方法研究磁层亚暴过程中高速流分布。结果表明垂直磁场的高速流主要分布在电流片内,范围在|Z|<0.25RE;平行磁场高速流分布区域在两个区域较大,一个是距离地球较近的磁场较强的区域,另一个是距离等离子体片较近磁场较强的区域。     

谐波平衡有限元算法的研究

为解决具有饱和铁芯的交变电磁场的计算需要较大的存储量和较长的计算时间的问题,提出了一种适用于交变电磁场谐波问题分析的新的有效算法。谐波平衡有限元算法是有限元算法与谐波平衡方法的结合,其计算过程类似于非线性静态场。该方法适用于任意阶多项式描述的磁化曲线问题的求解。通过对一电抗器的计算,验证了该方法的正确性。     

横向磁场中矩形金属薄板的振动问题

给出了横向磁场中矩形金属薄板的振动方程,并对四边简支矩形板的振动特性进行了分析,最后给出了数值计算结果,表明磁场变化对振动频率及衰减系数的影响。     

超小尺度地磁场泰勒多项式建模方法

根据实测的地磁数据,提出一种基于泰勒多项式在超小尺度下的地磁正常场的模型建立方式,结合数据处理﹑最小二乘拟合法,利用泰勒多项式模型建立超小尺度下的地磁正常场,并绘制相应的局部地磁图.经实验证明,超小尺度下的泰勒多项式地磁模型能够相对精确的描绘地磁正常场的分布.这为建立超小尺度地磁模型提供了参考,也可为小尺度内测量磁异常提供可靠的参考场.     

铁磁构件释放巴克豪森噪讯数学模型的研究

研究了铁磁构件在磁场作用下受力释放的巴克豪森噪讯，依据巴克豪森噪讯释放随磁场和应力变化的物理模型，通过多项式回归分析的数学方法，建立了可以自洽解说的巴克豪森噪讯数学模型和机理模型，给出巴克豪森噪讯释放与磁场、应力及磁场应力耦合的二次关系方程式，理论与实验曲线实现了很好的吻合。该模型的建立为实际工程检测中的定性分析和定量标定奠定了很好的基础。     

各向异性磁介质中无限大载流薄板的磁场

利用各向异性磁介质中毕奥-萨伐尔定律,以及由此定律求出的,在各向异性磁介质中无限长载流直导线的磁场的基础上,进一步求出无限大载流薄板在磁各向异性介质中的任一点的磁场强度,拓展该定律的应用范围．     

Responses of properties in the plasma sheet and at the geosynchronous orbit to interplanetary shock

On July 22, 2004, the WIND spacecraft detected a typical interplanetary shock. There was sustaining weak southward magnetic field in the preshock region and the southward field was suddenly enhanced across the shock front （i.e., southward turning）. When the shock impinged on the magnetosphere, the magnetospheric plasma convection was abruptly enhanced in the central plasma sheet, which was directly observed by both the TC-1 and Cluster spacecraft located in different regions. Simultaneously, the Cluster spacecraft observed that the dawn-to-dusk electric field was abruptly enhanced. The variations of the magnetic field observed by TC-1, Cluster, GOES-10 and GOES-12 that were distributed in different regions in the plasma sheet and at the geosynchronous orbit are obviously distinct. TC-1 observations showed that the magnetic intensity kept almost unchanged and the elevation angle decreased, but the Cluster spacecraft, which was also in the plasma sheet and was further from the equator, observed that the magnetic field was obviously enhanced. Simultaneously, GOES-12 located near the midnight observed that the magnetic intensity sharply increased and the elevation angle decreased, but GOES-10 located in the dawn side observed that the magnetic field was merely compressed with its three components all sharply increasing. Furthermore, the energetic proton and electron fluxes at nearly all channels observed by five LANL satellites located at different magnetic local times （MLTs） all showed impulsive enhancements due to the compression of the shock. The responses of the energetic particles were much evident on the dayside than those on the nightside. Especially the responses near the midnight were rather weak. In this paper, the possible reasonable physical explanation to above observations is also discussed. All the shock-induced responses are the joint effects of the solar wind dynamic pressure pulse and the magnetic field southward turning.     

Responses of the magnetotail plasma sheet to two interplanetary shocks: TC-1 observations

Two interplanetary shocks are examined to determine the responses of the magnetic field and plasma in the plasma sheet upon the shock impacts by using TC-1 observational data.The two shocks are observed by WIND on November 7,2004.Prior to and after the shock,the IMF is either weakly southward or northward.The responses of the plasma sheet to the two shocks are intense and much similar.When the shock interacts with the magnetosphere,the magnetic field impulsively increases 1-2 min after the geomagnetic field...     

Plasma sheet stretching accompanied by field aligned energetic ion fluxes observed by the NUADU instrument aboard TC-2

The NUADU (NeUtral Atom Detector Unit) instrument aboard TC-2 recorded 4л solid angle images of charged particles (E >180 keV) spiraling around the magnetic field lines in the near-Earth plasma sheet (at ~ -7 RE, equatorial dawn-to-night side) during a geomagnetic storm (Dst =-219 nT) on August 24, 2005. Energetic ion beam events characterized by symmetrical, ring-like, solid angle distributions around ambient magnetic field lines were observed during a 34-minute traversal of the plasma sheet by the TC-2 spacecraft. Also, observations during these multiple crossings of the plasma sheet were monitored by the magnetometer experiment (FGM) aboard the same spacecraft. During each crossing, a whistler-mode chorus enhancement was observed in the anisotropic area by the TC-2 low frequency electromagnetic wave detector (LFEW/TC-2) at a frequency just above that of the local lower hybrid wave. A comparison of the ion pitch angle distribution (PAD) map with the ambient magnetic field shows that an enhancement in the field aligned energetic ion flux was accompanied by tailward stretching of the magnetic field lines in the plasma sheet. In contrast, the perpendicular ion-flux enhancement was accompanied by a signature indicating the corresponding shrinkage of the magnetic field lines in the plasma sheet. Since both parallel ion-flux and perpendicular ion-flux enhancements occurred intermittently, the data were interpreted to imply a dynamical, oscillatory process of the magnetic field line (stretching and shrinking) in the near-Earth plasma sheet, which might have acted to help establish an interaction region in this area which would support continuous aurora-substorm triggering during the ongoing magnetic storm. The whistler-mode chorus may have been produced due to ion gyro-resonance during particle pitch angle diffusion after the plasma sheet compression.