Almansi-Type Decomposition Theorem for Bi-k-regular Functions in the Clifford Algebra Cl_(2n+2,0)(R)

Almansi-type decomposition theorem for bi-k-regular functions defined in a star-like domainΩ⊆R^(n+1)×R^(n+1)centered at the origin with values in the Clifford algebra Cl_(2n+2,0)(R)is proved.As a corollary,Almansi-type decomposition theorem for biharmonic functions of degree k is given.

Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Random noise attenuation by f–x spatial projection-based complex empirical mode decomposition predictive filtering

The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.

Synthesis, Characterization, Thermal Decomposition Mechanism and Non-Isothermal Kinetics of Salicylaldehyde Salicylhydrazone and Its Complex of Erbium(Ⅲ)

The salicylaldehyde salicylhydrazone and its complex of Er(Ⅲ) were synthesized. The formulae K·4H_2O(HL=[C_(14)H_(10)N_2O_3]^(2-), the bivalent form of the salicylaldehyde salicylhydrazone) were determined by elemental analysis and EDTA volumetric analysis. Molar conductance, IR, UV and X-ray power diffraction were carried out for the characterizations of the complex and the ligand. There are two stable five-numbered and six-numbered circles in the complex. The thermal decompositions of the ligand and the complex with the kinetic study are carried out by non-isothermal thermogravimetry. The stages of the decompositions were identified by TG-DTG curve. The non-isothermal kinetic data were analyzed by means of integral and differential methods. The possible reaction mechanism and the kinetic equation were investigated by the corresponding kinetic parameters.The activation energy value of the main step decomposition are also calculated by Kissinger′s method and Ozawa′s method.

3D analysis of functionally graded material plates with complex shapes and various holes

In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.

Method for Functional Design of Axiomatic Design Based on Connections

Axiomatic design（AD） is a popular design method,and satisfying the independence axiom is the basis of AD.However,AD doesn＇t provide methods to decompose functions then keep them independent and to handle coupled design.A few of ways of handling coupled design are mainly passive resolutions when coupled design exists,but not efficient to each product design.Hence,this paper presents an innovative approach to design and decompose functions of complex products based on functional connections,aiming at actively avoiding functional coupling.By contrasting with component networks,four kinds of relations among functions are identified,including spatial,energy,material,and information connection.Then the definitions of these relations and the dominant connection are given.Based on the definitions,the principles of functional decomposition and design are developed,in which each non-leaf function is broken into sub functions centered on its dominant connection with avoidance of functional cross and coupling,and sequentially satisfies the independence axiom.Then the operational flow of the proposed approach is constructed.Determining the dominant connection of a function,decomposing the function into sub functions in terms of the dominant connection and reverse examination and optimization are planed as the core steps in each zigzagging.Input process output（IPO） analysis is introduced to obtain the dominant connection of a function,some rules for examining and optimizing the decomposition results reversely according to oriented object theory are presented as well.An illustrative example about the pouring function of squeeze casting equipments presented demonstrates how to use the proposed approach,and indicates its effectiveness.The proposed approach expands the principles of AD,constructs a guidance policy for independent functional design of complex products based on AD,and can help decrease or actively avoid coupled design and improve design efficiency.

ON APPROXIMATELY(p,q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES

We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.

Re ned rigorous perturbation bounds for the SR decomposition

In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.

基于暂态关键特征逻辑推理的复杂电网响应驱动暂态稳定性判别

暂态稳定实时性判别是响应式稳定控制的核心,新能源和直流输电并网下电网的结构、运行和响应特征复杂程度骤增,现有实时性判别方法的准确性和泛化性面临挑战。该文针对含新能源和直流输电的复杂电网暂态稳定性,提出了一种基于可量测暂态能量特征的自适应逻辑推理判稳方法,实现无电网模型依赖且具有可解释性的实时性稳定性判别。首先,基于发电机转子运动的能量关系,结合特勒根定理构建了面向复杂电网响应信息的能量函数并论证了其守恒性;然后,根据系统动能-势能能量转换特征定义了稳定预判因数,并结合最大功角差构成了判稳关键特征量,提出了基于自适应模糊推理神经网络(ANFIS)的关键特征量与稳定状态之间的映射模型,实现了暂态稳定性实时推理评估;最后,在简单系统中量化分析了关键特征量与系统稳定性间的关系,并在修改后含新能源与直流输电的IEEE10机39节点系统中验证了该文所提方法的有效性与泛化性。

DECOMPOSITION OF A CLASS OF FUNCTIONALS AND THE PREDICTABLE REPRESENTATION THEOREM ON BANACH SPACES

Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).

“复变函数论”中研究型教学模式的探索与实践

近些年,以培养学生创新能力为导向的研究型教学模式受到了广泛关注。在高校,科研是重点,教学是基础,教学和科研的有效结合正是研究型教学的出发点。笔者基于复变函数论中的幂级数展开定理(Taylor定理和Laurent定理),探索研究型教学的有效性,并在教学内容、教学方法和教学反馈方面进行了具体实践。结果表明:研究型教学有利于提升学生学习的主观能动性,尤其在培养学生的创新能力方面有明显的优势,是一种值得借鉴的教学模式。

2-氯-6-氟苯甲酸钆配合物的晶体结构及热分解反应动力学和热力学研究

采用超声法合成了钆的三元配合物[Gd(2-Cl-6-FBA)_(3)(4-OH-terpy)(CH_(3)CH_(2)O)]·0.75CH_(3)CH_(2)OH(BA=苯甲酸,terpy=2,2′:6′,2″-三联吡啶).通过元素分析、红外光谱(IR)、拉曼光谱(R)、单晶X射线衍射(SXRD)以及X射线粉末衍射(PXRD)等手段对配合物进行了表征.晶体结构分析表明,该配合物为单核分子,属于单斜晶系,P2_(1)/c空间群,中心金属离子配位数为9.研究了配合物在不同升温速率下的热分解反应机理,并采用非线性等转化率积分(NL-INT)法和迭代Ozawa法分别求得了配合物在第1步热分解过程中的活化能,2者结果基本一致.采用差示扫描量热(DSC)技术测定了配合物的摩尔热容,利用最小二乘法将平均摩尔热容与折合温度进行拟合得到多项式方程,通过多项式方程和热力学方程计算得到配合物的舒平摩尔热容和热力学函数值.

THE CAUCHY-KOVALEVSKAYA THEOREM-OLD AND NEW

The paper surveys interactions between complex and functional-analytic methods in the CauchyKovalevskaya theory. For instance, the behaviour of the derivative of a bounded holomorphic function led to abstract versions of the Cauchy-Kovalevskaya Theorem.Recent trends in the Cauchy-Kovalevskaya theory are based on the concept of associated differential operators. Since an evolution operator may posses several associated operators, initial data may be decomposed into components belonging to different associated spaces.This technique makes it also possible to solve ill-posed initial value problems.

COMPLEX INTERPOLATION OF L_(p)(C,H)SPACES WITH RESPECT TO CULLEN-REGULAR

The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).

Decomposition of Al_(13) promoted by salicylic acid under acidic condition: Mechanism study by differential mass spectrometry method and DFT calculation

Decomposition of the polycation Al_(13)O_(4)(OH)_(2)4(H_(2)O)_(12)^(7+)(Al_(13)) promoted by ligand is a vital subject to advance our understanding of natural and artificial occurrence and evolution of aluminum ions,especially in the case of acidic condition that dissolved Al^(3+)species can be released from the Al-bearing substances.However,the microscopic pathway of synchronous proton-promoted and ligand-promoted decomposition process for Al_(13)is still in the status of ambiguity.Herein,we applied differential mass spectrometry method and DFT calculation to study the initial detailed process of Al_(13)decomposition under the presence of proton and salicylic acid (H_(2)Sal).Mass results showed that the mononuclear Al^(3+)-H_(2)Sal complexes dominated the resulting Al species,whereas the monodentate complex Al_(13)HSal6+was not observed in the spectra.The difference of decomposition levels between the ligand/Al ratio 0.2 and 0.5 cases revealed that proton and ligand performed synergistic effect in initial Al_(13)decomposition process,and the proton transfer determined the ring closure efficiency.The ring closure reaction is the prerequisite for the collapse of Al_(13)structure and detachment of the mononuclear complex.DFT calculations reveal that hydrogen bond plays an important role in inducing the formation of chelated complex accompanying proton transfer.Attachment of protons at the bridging OH^(-)can elongate and weaken the critical bond between targeted Al^(3+)and μ4-O_(2)-resulting from delocalization of electron pairs in the oxygen atom.These results demonstrate the detailed mechanism of Al_(13)composition promoted by ligand and proton,and provide significant understanding for further application and control of Al_(13).

Synthesis, Characterization, Thermal Decomposition Mechanism and Non-Isothermal Kinetics of the Pyruvic Acid-Salicylhydrazone and Its Complex of Praseodymium(III)

The pyruvic acid salicylhydrazone and its new complex of Pr(III) were synthesized. The formulae C 10 H 10 N 2O 4 (mark as H 3L) and [Pr 2(L) 2(H 2O) 2]·3H 2O (L=the triad form of the pyruvic acid salicylhydrazone [C 10 H 7N 2O 4] 3- ) were determined by elemental and EDTA volumetric analysis. Molar conductance, IR, UV, X ray and 1H NMR were carried out for the characterizations of the complex and the ligand. The thermal decompositions of the ligand and the complex with the kinetic study were carried out by non isothermal thermogravimetry. The Kissinger's method and Ozawa's method are used to calculate the activation energy value of the main step decomposition. The stages of the decompositions were identified by TG DTG DSC curve. The non isothermal kinetic data were analyzed by means of integral and differential methods. The possible reaction mechanism and the kinetic equation were investigated by comparing the kinetic parameters.

基于留数定理的VSC锁相环频率估计算法研究

在柔性直流输电系统中,锁相环对控制电压源型换流器(VSC)的电压和功率稳定具有重要作用。针对连接弱交流系统下VSC锁相环性能恶化和稳定性差的缺点,提出了一种基于留数定理的VSC锁相环频率估计算法,该算法利用留数定理,将交流电压信号由时域转换为复变域,通过求解电压复变函数的闭合路径积分对频率进行估计,实现了三相平衡和不平衡情况下交流电网频率的精确估计和快速追踪,具有良好的暂态特性和稳定性。以一个单端VSC系统为例,仿真结果验证了该算法的有效性和正确性。

设计过程复杂性理论与TRIZ理论集成复杂机电系统功能分解过程模型

传统的功能分解是将产品的总功能分解到功能元,以每个功能元有确定的原理解作为功能分解结束的标志,传统的功能分解方法强调总功能可以分解为若干个功能元,若干个功能元组成一个总功能,体现了总功能和功能元之间的线性关系和还原性。传统的功能分解无法体现复杂机电系统非线性、时变特性、开放性和功能耦合等重要特征,因此急需一种适合于复杂机电系统的功能分解过程模型。将设计过程复杂性理论(Design-centric complexity,DCC)和TRIZ集成,对初步进行功能分解的结果,按照TRIZ理论中有效完整功能和非有效完整功能集对功能进行分类;应用提出的功能实现概率均值法和功能实现概率极值法,将TRIZ理论的有效完整功能和非有效完整功能,与DCC理论中重复功能集和组合集建立联系;经过TRIZ理论对问题功能进行转化后,以系统的重复功能集、组合集和组合辅助功能集作为复杂机电系统功能分解的结果;形成面向复杂机电系统的DCC与TRIZ集成功能分解过程模型。用一个工程实例验证该设计过程模型。

复局部均值分解全矢包络技术及其在转子故障特征提取中的应用

为更全面提取转子故障特征,将全矢谱和复局部均值分解(Complex local mean decomposition,CLMD)相结合,提出二元的全矢包络技术——CLMD全矢包络技术。采用正交采样技术获取转子同一截面上互相垂直方向上的振动信号,并将其组成一个复数信号;运用CLMD将复数信号按能量从高到低的顺序依次分离出系列复乘积函数(Complex product function,CPF),并解调出CPF的复包络;由于故障特征主要在能量较高的CPF分量中,通过全矢谱技术融合前几阶CPF分量的包络信号,得到相应的全矢包络谱。仿真的调幅-调频信号分析结果表面,较之Hilbert解调,CLMD全矢包络技术可提取隐含的调频信息,而且不存在虚假的低频谱线。转子试验台模拟的基座松动信号、碰摩信号分析结果表明,较之单源信息的包络谱,CLMD全矢包络技术提取的谱线特征更清晰、全面,而且根据全矢包络谱可有效区分基座松动引起的碰摩和单一碰摩故障。

非等温TG- DTG法确定2,2'- 联吡啶- 对甲氧基苯甲酸铕(Ⅲ)热分解反应的机理函数和动力学参数(英文)

采用TG DTG和DTA技术研究了2,2' 联吡啶 对甲氧基苯甲酸铕(Ⅲ)在静态空气中的非等温热分解过程及动力学 ,根据TG曲线确定了热分解过程中的中间产物及最终产物 ,运用微分法与积分法对非等温动力学数据进行分析 ,推断出第一步的动力学方程为dα/dt=Aexp( E/RT)2(1 α)1/2 。