Riemann–Hilbert problem for the defocusing Lakshmanan–Porsezian–Daniel equation with fully asymmetric nonzero boundary conditions

The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.

Learning-based control for discrete-time constrained nonzero-sum games

A generalized policy-iteration-based solution to a class of discrete-time multi-player nonzero-sum games concerning the control constraints was proposed.Based on initial admissible control policies,the iterative value function of each player converges to the optimum approximately,which is structured by the iterative control policies satisfying the Nash equilibrium.Afterwards,the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player.Meanwhile,neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints.Finally,two numerical simulations of the discrete-time two-player non-zero-sum games for linear and non-linear systems are shown to illustrate the effectiveness of the proposed scheme.

Dark and multi-dark solitons in the three-component nonlinear Schrodinger equations on the general nonzero background

We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrodinger systems, and require more in-depth studies in the future.

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact(VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope(SAEE) is adopted to seek the stationary probability density functions(PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo(MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.

Self-consistent diverted tokamak equilibria with nonzero edge current

The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria （Bingren Shi, Plasma Phys. Control Fusion 50 （2008） 085006, 51 （2009） 105008, Nucl. Fusion 51 （2011） 023004）, is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch Schliiter（PS） cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.

Nonzero Solutions of Generalized Variational Inequalities

The existence of nonzero solutions for a class of generalized variational inequalities is studied by ?xed point index approach for multivalued mappings in ?nite dimensional spaces and re?exive Banach spaces. Some new existence theorems of nonzero solutions for this class of generalized variational inequalities are established.

Application of the Two Nonzero Component Lemma in Resource Allocation

In this paper we will generalize the author's two nonzero component lemma to general self-reducing functions and utilize it to find closed from answers for some resource allocation problems.

The Case of Nonzero Initial Conditions in the Evolution of the Charge Density Distribution Function for a Spherically Symmetric System

We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.

Behavior Prediction of Untrusted Relays Based on Nonzero-Sum Game

To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor into account. A nonzero-sum game is established to capture the interaction among URs and detection strategies. Secrecy capacity is investigated as game payoff to indicate the untrusted behaviors of the relays. The maximum probabilities of the behaviors of relay and the optimal system detection strategy can be obtained by using the proposed algorithm.

Proving and Extending Greub-Reinboldt Inequality Using the Two Nonzero Component Lemma

We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.

Riemann-Hilbert approach and soliton solutions for the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions

We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.

判定广义严格对角占优矩阵的新条件

仅利用矩阵自身的元素,得到了广义严格对角占优矩阵的几个新的判定条件,扩大了判别范围.给出了数值算例.

实对称矩阵正交特征向量的一种新解法

为克服“只在给定向量组的条件下,才能求得正交向量组”的局限性,利用特征向量和正交的定义及齐次线性方程组的非零解求解方法,给出实对称矩阵对应于重特征值的正交特征向量的一种新的求解方法。研究表明,该方法可以有效地减少计算量,并可以直接写出实对称矩阵对应于重特征值的正交特征向量。

非奇异H-矩阵的新细分迭代判定

利用广义α-对角占优矩阵、不可约α-对角占优矩阵和具有非零元素链α-对角占优矩阵的概念和性质,通过对矩阵非对角占优行的指标集进行细分,构造递进迭代系数,得到一组实用的非奇异H-矩阵判定的细分迭代新准则,通过数值例子说明新准则的有效性。

非奇异H-矩阵的一组新判据

基于广义严格α-对角占优矩阵及其相关概念和性质,通过对矩阵指标集进行划分并构造与之对应的正对角因子及设定新参数的方法,给出一组实用的非奇异H-矩阵新判据,拓广了非奇异H-矩阵的判定范围.最后,通过数值例子说明新判据的有效性.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.

三相电压源型逆变器单传感器相电流重构故障诊断策略

为了解决三相电压源型逆变器采用单电流传感器进行故障诊断的可行性及诊断时间问题,通过调整互补非零矢量补偿零矢量作用时间,确保载波周期内电流采样时间大于最小采样时间,并在一个载波周期内互补非零矢量作用时进行两次电流采样,重构出故障下的三相电流。通过将功率开关管开路故障类型进行区分,分析功率开关管在各类开路故障下的电流流向以及故障后电压矢量的合成机理,构建以电流矢量相角、平均电流矢量模值及相角为判据的故障诊断方法,提出基于单传感器相电流重构的故障诊断策略,实现单传感器相电流重构下的开关管开路故障诊断。实验结果验证了该诊断策略的可行性,并得出当故障诊断时间为0.5 ms,可有效且快速对故障功率开关管定位。

Tunneling magnetoresistance of the double spin-filter junctions at nonzero bias

A recent theoretical estimation indicated that the NM/FI/FI/NM double spin-filter junction (DSFJ, here the NM and FI represent the nonmagnetic electrode and the ferromagnetic insulator (semiconductor) spacer, respectively) could have very high tunneling magnetoresistance (TMR) at zero bias. To meet the requirement in research and application of the magnetoresistance devices, we have calculated the dependences of tunneling magnetoresistance of DSF J on the bias (volt-age), the thicknesses of ferromagnetic insulators (semiconductors) and the average barrier height. Our results show that except its very high value, the TMR of DSFJ does not decrease montonously and rapidly with rising bias, but increase slowly at first and decrease then after having reached a maximum value. This feature is in distinct contrast to the ordinary magnetic tunnel junction FM/NI/FM (FM and NI denote the ferromagnetic electrode and the nonmagnetic insulator (semiconductor) spacer, respectively), and is of benefit to the use of DSFJ as a magnetoresistance device.

非零方阵的一类加法分解

基于矩阵的相关性质,证明了数域上任意非零方阵均可分解为一个幂零阵与一个可逆阵之和,推进了已知相关结论.作为所得结果的应用,给出线性空间上线性变换的加法分解.