Dielectric properties and study of AC electrical conduction mechanisms by non-overlapping small polaron tunneling model in Bis(4-acetylanilinium) tetrachlorocuprate(II) compound

In the present work, the synthesis and characterization of the Bis(4-acetylanilinium) tetrachlorocuprate(II) compound are presented. The structure of this compound is analyzed by X-ray diffraction which confirms the formation of single phase and is in good agreement the literature. Indeed, the Thermo gravimetric Analysis (TGA) shows that the decomposition of the compound is observed in the range of 420–520 K. However, the differential thermal analysis (DTA) indicates the presence of a phase transition at T=363 k. Furthermore, the dielectric properties and AC conductivity were studied over a temperature range (338–413 K) and frequency range (200 Hz–5 MHz) using complex impedance spectroscopy. Dielectric measurements confirmed such thermal analyses by exhibiting the presence of an anomaly in the temperature range of 358–373 K. The complex impedance plots are analyzed by an electrical equivalent circuit consisting of resistance, constant phase element (CPE) and capacitance. The activation energy values of two distinct regions are obtained from log σT vs 1000/T plot and are found to be E=1.27 eV (T<363 K) and E=1.09 eV (363 K<T).The frequency dependence of ac conductivity, σ_ac, has been analyzed by Jonscher's universal power law σ(ω)=σ_dc+Aω^s. The value of s is to be temperature-dependent, which has a tendency to increase with temperature and the non-overlapping small polaron tunneling (NSPT) model is the most applicable conduction mechanism in the title compound.     

A concise quantum mechanical treatment of the forced damped harmonic oscillator

By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator \(\hat X\) in x representation. The evolution of \(\left\langle {\hat x} \right\rangle \) is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.     

Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant matrices

In this paper, some improvements on Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128–133] are presented for bounds of the spectral radius of _lω,r$l_{\omega ,r}$, which is the iterative matrix of the generalized AOR (GAOR) method. Subsequently, some new sufficient conditions for convergence of GAOR method will be given, which improve some results of Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128–133].     

利用|x〉导出λ■+μ■的本征矢

利用坐标本征矢|x〉在Fock空间的展开式,导出了算符λ■+μ■在Fock空间的本征矢|ψ〉,并证明了其正交完备性.结果表明,得到的|ψ〉既是完备的,又是正交的,完全可以作为一个表象使用.当λ和μ分别取1和0时,|ψ〉约化为坐标本征态|x〉,而当λ和μ分别取0和1时,|ψ〉约化为动量本征态|p〉.因此,|ψ〉所构成的表象是介于坐标表象和动量表象之间的中介表象.     

保等价部分变换半群的变种半群上的正则元

在现有的保等价部分变换半群的基础上,引入了一个新的运算,得出保等价部分变换半群的变种半群的概念,利用格林关系及幂等元的正则性,讨论了这类半群中元素的正则性,给出了保等价部分变换半群的变种半群中一个元是正则元的充要条件     

粘合、倾斜同调维数与高维Auslander-Reiten理论

本文主要研究阿贝尔范畴粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中$\mathscr{A}$, $\mathscr{B}$与$\mathscr{C}$之间的倾斜同调维数关系. 特别地,对遗传的阿贝尔范畴$\mathscr{B}$,给出了粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中的范畴之间的$n$-几乎可裂序列间的联系.     

Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory

This paper aims to present, in a unified manner, algebraic techniques for least squares problem in quaternionic and split quaternionic mechanics. This paper, by means of a complex representation and a real representation of a generalized quaternion matrix, studies generalized quaternion least squares (GQLS) problem, and derives two algebraic methods for solving the GQLS problem. This paper gives not only algebraic techniques for least squares problem over generalized quaternion algebras, but also a unification of algebraic techniques for least squares problem in quaternionic and split quaternionic theory.     

GENERALIZED DAHLQUIST CONSTANT WITH APPLICATIONS IN SYNCHRONIZATION ANALYSIS EXCITED BY PARAMETER WHITE-NOISE OF TYPICAL NEURAL NETWORKS

In this paper,a novel and effective approach to impulsive synchronization analysis excited by parameter white-noise of neural networks is investigated using the nonlinear operator named the generalized Dahlquist constant.The proposed approach offers a design procedure for impulsive synchronization of a large class of neural networks.Numerical simulations,where the theoretical results are applied to typical neural networks with and without delayed item,demonstrate the effectiveness and feasibility of the proposed technique.     

Operator Realization of Radial- and Azimuthal- Differentiations Obtained by Using the Entangled State Representation

We find Bose operator realization of radial- and azimuthal-differential operations in polar coordinate system by virtue of the entangled state |η〉 representation, which indicates that |η〉 representation just fits to describe the polar coordinate operators in quantum mechanics. The Bose operator corresponding to the Laplacian operation $\frac{\partial^{2}}{\partial r^{2} }+\frac{1}{r}\frac{\partial}{\partial r}+\frac{1}{r^{2}}\frac{\partial^{2} }{\partial\varphi^{2}}$ for 2-dimensional system and its eigenvector are also obtained. Their new applications are partly presented.