富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Co‐syndiospecific Alternating Copolymerization of Functionalized Propylenes and Styrene by Rare‐Earth Catalysts

The precise control of monomer sequence and stereochemistry in copolymerization is of much interest and importance for the synthesis of functional polymers, but studies toward this goal have met with only limited success to date. Now, the co‐syndiospecific alternating copolymerization of methoxyphenyl‐ and N,N‐dimethylaminophenyl‐functionalized propylenes with styrene by half‐sandwich rare‐earth catalysts is reported. This reaction efficiently afforded the corresponding functionalized propylene‐alt‐styrene copolymers with a perfect alternating sequence and excellent co‐syndiotacticity (rrrr >99 %), thus constituting the first example of co‐stereospecific alternating copolymerization of polar and non‐polar olefins.     

基于虚拟中心电流法的 HL-2M快控电源数学模型

针对中国环流器2号M(HL-2M)装置中用于核聚变物理实验等离子体的垂直不稳定性控制的快控电源拓扑结构，充分考虑线圈的自感与互感对输出的影响，构建出数学模型，首次提出并运用虚拟中心电流法，使得控制算法更加简单，采用多输入多输出的控制方法，利用2个参量控制3个变量。本文基于基本供电方案得到多线圈耦合电压，基于快控电源拓扑推导出快控电源电路方程，再将其合并得到最终的线圈电压数学模型，最后进行仿真验证。结果表明数学模型搭建正确，为今后进行进一步计算提供了坚实的基础。     

Zr掺杂对MgB2超导微观结构和超导电性的影响

将Mg粉、Zr粉和B粉按比例混合获得Mg1-xZrxB2(x=5%10%和20%),压制成型后,在流通氩气的条件下于800℃烧结2h.利用X射线衍射仪(XRD)、扫描电子显微镜(SEM)分析烧结后样品的显微结构和化学组成,采用差热分析(DTA)观察Zr掺杂对MgB2分解温度的影响,并用物性测试仪(PPMS)测试样品的超...     

金属氧化物对十氯联苯的降解研究

分别以市售的Fe2O3、MgO和CaO为催化剂,对十氯联苯(CB209)进行了催化降解研究.结果表明,MgO对CB209的降解具有较高的活性.在反应温度为300℃,反应时间为60 min时,MgO对CB209的降解效率达到98.9%.进一步研究表明,MgO催化降解CB209的动力学符合准一级动力学反应.通过GC-MS和GC-ECD,并结合衍生化实验,检测到九氯联苯、五氯苯和四氯苯、五氯苯酚、四氯苯酚和三氯苯酚等降解产物,进而推测出MgO催化降解CB209的过程中存在相互竞争的反应路径:氧化反应、碳碳桥键断裂和加氢脱氯.     

处理噪声问题的泰勒展开交替最小化算法

为了处理图像、计算机视觉和生物信息等领域中广泛存在的稀疏大噪声和高斯噪声问题,提出了一种利用交替方向最小化思想求解主成分追求松弛模型的泰勒展开交替最小化算法(TEAM).采用推广泰勒展开和收缩算子等技术推导出低秩矩阵和稀疏大噪声矩阵的迭代方向矩阵,加入连续技术提高算法的收敛速率,设计出TEAM算法的求解步骤.实验中,将TEAM算法与该领域的顶级算法作分析对比.结果表明,TEAM算法时间优势明显,误差优势略好.     

High-speed deposition of RE123 film with large current capacity by hot-wall type PLD system

We have studied a hot-wall heating system to produce GdBa₂Cu₃O_y (GdBCO) films with large critical currents (I_c) at a high production rate by a pulsed-laser-deposition (PLD) method. GdBCO films fabricated at a production rate of 30 m/h under the optimized conditions, especially a distance of 95 mm between the target and the substrate (T–S), exhibited high critical current densities (J_c) of about 3 MA/cm² and I_c over 300 A at a thickness of 1–2 μm. Furthermore, long GdBCO tapes prepared by repeated depositions at each tape-passing speed of 80 m/h showed uniform I_c distribution along the longitudinal direction, because the hot-wall system enabled to stabilize temperature within a few degrees at 800 °C. A 170 m long tape with I_c over 600 A was successfully fabricated at a production rate of 16 m/h using a laser power of 360 W.     

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two suffcient and necessary conditions for such graphs to be 1- or 2-arc-regular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.     

Spin-dependent transport in a nanopillar non-local spin valve

We investigate the injection of a pure spin current into a non-magnetic Cu wire in a lateral spin valve. We detect the spin accumulation occurring at the interfaces between the magnetic nanopillars and the non-magnetic wire in the non-local geometry. We confirm that the accumulated spins diffuse equally in the Cu wire irrespective of the presence of a charge current. The inversion of the injector and detector magnetic nanopillars does not affect the spin signal, in agreement with analytical predictions for this system.