基于迭代凸优化的导弹探测时间估算方法

为准确估算远程预警雷达对弹道导弹探测的时间窗口,需要联立导弹轨迹与雷达探测范围的数学模型,求解非线性二次方程组。提出了一种非线性二次方程组的求解方法,首先将核问题转化为二次等式的优化问题,引入误差范数约束非凸优化问题,将二次等式进行一阶和二阶泰勒展开,将原问题在局部近似为一个最优化问题并利用迭代凸优化求解,得到雷达探测范围与导弹弹道的交汇点坐标的解析解,实现对雷达探测时间窗口的准确估算。通过场景模拟与求解分析证明了该方法的正确性,并表明该方法具有精度高、通用性强的特点。

Nonlinear static filtering and prediction considering quadratic terms

The parameters are considered as normal random quantities in filtering and prediction, and the observation equations usually are nonlinear ones. The nonlinear equations should be deployed in Taylor抯 formula, adopting to first power of term, by linear static filtering and prediction, and transformed into linear equations, and then the tested estimating values and their variances according to some statistical methods such as maximum tested estimation. The formulas of nonlinear static filtering and prediction, adapting to quadratic and cross terms by Taylor抯 progression formula, and the compu-tation formulas were also deduced that filtering the corresponding function nonlinear sig-nals and predicting the signals with nonlinear function. Meanwhile, it is been testified that the formula of static filtering and prediction is a special case of nonlinear filtering formulas.

Integrable Deformations of Heisenberg Supermagnetic Model

We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.

OSCILLATION CRITERIA FOR NONLINEAR SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.

Peaked Traveling Wave Solutions to a Generalized Novikov Equation with Cubic and Quadratic Nonlinearities

The Camassa-Holm equation, Degasperis–Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.

Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.

BACKWARD LINEAR-QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO-SUM DIFFERENTIAL GAME PROBLEM WITH RANDOM JUMPS

This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).