On convergence of a new secant-like method for solving nonlinear equations

In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence.     

Conformational Analysis of 3,3,4-Trimethylhexane and 2,2,5-Trimethylhexane

Infrared and Raman spectra were obtained for 3,3,4-trimethylhexane and 2,2,5-trimethylhexane and were interpreted with the aid of normal coordinate calculations. It was shown that each compound exists as a mixture of two molecular conformations.     

Transformation formulae for continuous semimartingales and certain non-regular real functions on the sequence space i p

Transformation formulae for continuous semimartingales and twice continuously partially differentiable real functions on the sequence spaces l^p, 1<p<oo, are proved. Also mappings f are treated for which the derivatives do not exist at the zeroes of f, but which fulfil some boundedness conditions. Furthermore, an approximative formula for the function x^x, x>1/2, is obtained. As an application a representation for the p-norm of a semimartingale is given.     

Applications of Floquet–Magnus expansion,average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

This work presents the possibility of applying the Floquet–Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.     

低场核磁共振仪器振铃抑制新方法及其电路实现

加快天线残余能量释放以减弱天线振铃信号有利于缩短低场核磁共振仪器的回波间隔（TE）,从而提高快弛豫组分的测量分辨率和信噪比（SNR）．而天线Q值对能量的发射效率和泄放速度起着相反的作用．为此,我们首先设计了一种新型Q转换电路,在保证发射效率的同时,可以大大缩短能量泄放时间．在此基础上,应用了一种优化的脉冲序列以弥补传统相位交替对脉冲序列（PAPs）不能消除90°脉冲振铃的缺陷,通过相位循环的方法进一步提高了信噪比．最后,在2 MHz岩心分析仪上测试了新型Q转换电路,当天线Q值降为发射期间的约1/5时,天线恢复时间由280.0 μs降为18.2 μs;而且,使用新型Q转换电路和优化的脉冲序列后,TE=60 μs时,可以有效获得快弛豫组分的T₂信号．     

On a problem of Mariusz Meszka

We consider a problem due to Mariusz Meszka similar to the well-known conjecture of Marco Buratti. Does there exist a near-1-factor in the complete graph on _Zp$Z_p$, p$p$ is an odd prime, whose set of edge-lengths equals a given multiset L$L$? We establish several sufficient conditions for the answer to be yes.     

D-T2二维核磁共振脉冲序列及反演方法改进设计

面对日益复杂的勘探对象, D-T₂二维核磁共振技术在实际应用中面临无法兼顾扩散系数测量范围和横向弛豫分辨率的困境. 脉冲序列作为D-T₂二维核磁共振数据采集的核心技术, 其性能优劣直接影响应用效果, 在综合对比PFG, STE-PFG, BP-PFG、改良式CPMG, 扩散编程, 多回波间隔CPMG脉冲序列性能的基础上, 有效融合脉冲梯度场、恒定梯度场D-T₂脉冲序列的优点, 本文提出一种基于脉冲梯度场的双变量、两窗口D-T₂脉冲序列改进设计. 针对两个窗口的D-T₂二维核磁共振数据反演, 为突破现有反演方法无法兼顾反演精度和解谱效率的瓶颈, 本着第二个窗口回波信号为主、第一个窗口回波信号为辅的原则, 本文提出一种同时使用两个窗口数据参与解谱的联合TSVD反演方法. 气水、油水、稠油、油气水模型不同信噪比条件下的数值模拟结果表明, 本文提供的D-T₂改进脉冲序列达到了平衡扩散系数测量范围和横向弛豫分辨率的设计要求, 本文提供的联合TSVD反演方法也有效平衡了反演精度要求和解谱效率. 文中的D-T₂改进脉冲序列及联合TSVD反演方法在复杂油气藏流体识别和产能预测中具有广泛的应用前景, 可为促进国内D-T₂二维核磁共振岩心分析技术的发展提供有利条件.     

交替寻优生成元素幅值结合混沌随机相位构造循环测量矩阵

循环矩阵由于其对应离散卷积且具有快速算法被广泛应用于压缩测量矩阵. 本文从循环测量矩阵生成元素的幅值和相位两个方面探索循环测量矩阵的优化构造, 提出交替寻优生成元素的幅值并结合混沌随机相位实现循环测量矩阵的最优构造. 由一维和二维信号循环测量矩阵的不同表示形式出发, 将等价字典列向量之间互相干系数的Welch界作为逼近目标, 推导出了一维和二维信号循环测量矩阵生成元素幅值优化的统一数学模型, 提出采用交替寻优方法求解生成元素幅值的最优解. 利用混沌序列构造循环测量矩阵生成元素的随机相位. 与已有的典型循环测量矩阵相比, 本文优化构造的循环测量矩阵所对应的等价字典列向量之间具有更低的互相干性, 这正是所构造的循环测量矩阵优越性的本质所在.     

机载光电平台目标交会定位

根据直线交会测量原理,构建了机载光电平台目标定位数学模型。首先建立5个坐标系,确定了坐标系之间的变换关系,在地心直角坐标系下,根据光电平台观测目标的方位和俯仰角度参数,结合飞机的位置和姿态测量参数,通过坐标变换确定从光电平台到目标之间的观测直线方程。选择一组目标观测直线建立目标交会测量目标函数,根据最小二乘原理,建立关于直线交会点坐标的线性方程组。解出直线交会点的三维坐标并根据从地心直角坐标系到大地地理坐标系的变换关系,计算目标的大地经纬度和高程坐标,通过样本数据进行交会定位精度实验。实验结果表明,本文方法定位结果和实际测量数据接近,经度误差为0.65",纬度误差为0.82",高程误差为5 m,验证了本文方法的准确性。本文方法有效可行,对机载光电平台目标定位具有实用价值。     

Sequence‐Controlled Polymers via Simultaneous Living Anionic Copolymerization of Competing Monomers

Natural macromolecules, i.e., sequence‐controlled polymers, build the basis for life. In synthetic macromolecular chemistry, reliable tools for the formation of sequence‐controlled macromolecules are rare. A robust and efficient chain‐growth approach based on the simultaneous living anionic polymerization of sulfonamide‐activated aziridines for sequence control of up to five competing monomers resulting in gradient copolymers is presented. The simultaneous azaanionic copolymerization is monitored by real‐time ¹H NMR spectroscopy for each monomer at any time during the reaction. The monomer sequence can be adjusted by the monomer reactivity, depending on the electron‐withdrawing effect by the sulfonamide (nosyl‐, brosyl‐, tosyl‐, mesyl‐, busyl) groups. This method offers unique opportunities for sequence control by competing copolymerization: a step forward to well‐engineered synthetic polymers with defined microstructures.