两类微分方程组的特解表达式

利用线性代数工具和复数性质给出两类常系数非齐次线性微分方程组的特解表达式,以简化计算.

含两个未知元的微分方程组的特解

为了简化计算,利用积分因子法和消元法给出含两个未知元的常系数非齐线性微分方程组的特解表达式.

一类二阶时变系数线性微分方程的积分解

对一类二阶时变系数线性齐次微分方程和非齐次微分方程引入了特征方程的概念,给出了由其特征根确定通解和特解的积分表达式,推广了经典的二阶常系数线性微分方程和Euler方程的解法.

Physical Layer Security in MIMO Wiretap Channels with Antenna Correlation

To investigate the impact of antenna correlation on secrecy performance in MIMO wiretap channels with Nakagami-m fading, the expressions of secrecy outage probability and positive secrecy probability were derived. Diversity order and array gain were also achieved for further insight. The study was based on the information theory that physical layer security can be guaranteed when the quality of the main channel is higher than that of the eavesdropper's channel. Monte Carlo simulations well validated the numerical results of analytic expressions. It was shown that antenna correlation is detrimental to secrecy performance when average SNR of the main channel is at medium and high level. Interestingly, when average SNR of the main channel reduces to low level, the effect of antenna correlation becomes benefi cial to secrecy performance.

A special solution to transmission capacity of ad hoc networks

This paper presents an approximate expression to transmission capacity of ad hoc networks by using stochastic geometry. For there is no general close-form expression to the transmission capacity of ad hoc networks, by using Taylor series, we obtain the exact series expression to transmission capacity first, then we take partial summation to yield an n-th order approximate expression. Further- more, compared with the exact expression under a special case, the accuracy of the n-th order ap- proximation has been studied. The numerical results show that the accuracy of the approximation is mainly determined by the order n, and a high accuracy can be obtained when the node density or the outage constraint is close to zero .

Generalised Closed-Form Symbol Error Rate Analysis for Orthogonal Space-Time Block Coded OFDM System

In this paper,the Symbol Error Rate(SER)performance for Orthogonal Space-Time Block Coded(OSTBC)Orthogonal Frequency Division Multiplexing(OFDM)systems over Nakagami-m fading channels is analysed.A novel closed-form SER expression is proposed,which incorporates the Gauss hypergeometric function and Appell hypergeometric function into the conventional Probability Density Function(PDF)approach.The proposed exact closed-form SER expression is a generalised solution since it perfectly captures OSTBCOFDM systems’performances when having different antenna configurations that employ various modulation schemes and which experience various fading conditions.Finally,Monte Carlo simulation results are provided to demonstrate the exact match between the simulation results and the proposed analytical expressions.

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of PercusYevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

Nonlocality of Two-Qubit and Three-Qubit Schmidt-Correlated States

We investigate the nonlocality of Schmidt-correlated （SC） states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser-Horne-Shimony-Holt （CHSH） inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequaJity is only a sumcient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.

Solutions of the Schrdinger Equation for PT-Symmetric Coupled Quintic Potentials in Two Dimensions

This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.

A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

We present a high-resolution relaxation scheme for a multi-class Lighthill-Whitham-Richards (MCLWR) traffic flow model. This scheme is based on high-order reconstruction for spatial discretization and an implicit-explicit Runge-Kutta method for time integration. The resulting method retains the simplicity of the relaxation schemes. There is no need to involve Riemann solvers and characteristic decomposition. Even the computation of the eigenvalues is not required. This makes the scheme particularly well suited for the MCLWR model in which the analytical expressions of the eigenvalues are difficult to obtain for more than four classes of road users. The numerical results illustrate the effectiveness of the presented method.

Theoretical analysis of the harmonic characteristics of modular multilevel converters

To understand the operation principle of the modular multilevel converter(MMC)deeply,it is necessary to study the harmonic characteristics of the MMC theoretically.Besides,the analytical harmonic formulas of the MMC are useful in designing the main circuit,reducing the losses and improving the waveform quality.Based on the average switching function and the Fourier series harmonic analysis,this paper deduces the analytical expressions for such electrical quantities as the arm voltage,the arm current,the capacitor voltage,the capacitor current and the circulating current of the MMC.Finally,a digital model of a 21-level MMC-HVDC system is realized in PSCAD/EMTDC.The results of the analytical expressions coincide with the simulation results,which verify the effectiveness and feasibility of the proposed analytical expressions.

Fidelity and fidelity susceptibility based on Hilbert-Schmidt inner product

We reinvestigate the fidelity based on Hilbert-Schmidt inner product and give a simplified form.The geometric meaning of the fidelity is clarified.We then give the analytic expression of the fidelity susceptibility in both Hilbert and Liouville space.By using the reconstruction of symmetric logarithmic derivative in Liouville space,we present the time derivative of fidelity susceptibility with the normalized density vector representation.

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.