On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Local minima for indefinite quadratic knapsack problems

We consider the complexity of finding a local minimum for the nonconvex Quadratic Knapsack Problem. Global minimization for this example of quadratic programming is NP-hard. Moré and Vavasis have investigated the complexity of local minimization for the strictly concave case of QKP; here we extend their algorithm to the general indefinite case. Our main result is an algorithm that computes a local minimum in O(n(logn)²) steps. Our approach involves eliminating all but one of the convex variables through parametrization, yielding a nondifferentiable problem. We use a technique from computational geometry to address the nondifferentiable problem.Supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, Department of Energy, under contract W-31-109-Eng-38, in part by a Fannie and John Hertz Foundation graduate fellowship, and in part by Department of Energy grant DE-FG02-86ER25013.A000.     

磁场对非对称量子点中极化子性质的影响

采用线性组合算符和幺正变换方法研究磁场对非对称量子点中弱耦合磁极化子性质的影响.导出了非对称量子点中弱耦合磁极化子的振动频率、基态能量和基态结合能随量子点的横向和纵向有效受限长度、磁场和电子-声子耦合强度的变化关系.数值计算结果表明:非对称量子点中弱耦合磁极化子的基态能量和基态结合能随量子点的横向和纵向有效受限长度的增加而迅速增大.随回旋频率的增加而增大,随电子-声子耦合强度的增加而减小.     

Controlling optical responses through local dielectric resonance in nanometre metallic clusters

Optical responses in dilute composites are controlled through the local dielectric resonance of metallic clusters. We consider two located metallic clusters close to each other with admittances \varepsilon₁ and \varepsilon₂. Through varying the difference admittance ratio \eta [ = (\varepsilon₂- \varepsilon ₀) / (\varepsilon₁- \varepsilon₀)], we find that their optical responses are determined by the local resonance. There is a blueshift of absorption peaks with the increase of \eta. Simultaneously, it is known that the absorption peaks will be redshifted by enlarging the cluster size. By adjusting the nano-metallic cluster geometry, size and admittances, we can control the positions and intensities of absorption peaks effectively. We have also deduced the effective linear optical responses of three-component composites \varepsilon_e= \varepsilon₀ \bigl(1 + \sum_n=1^{n_s} [(\gamma_n2+ \eta \gamma_n2)/({\varepsilon₀(s - s_n))]} \bigr), and the sum rule of cross sections: \sum_n=1^{n_s} {(\gamma_n2+ \eta \gamma_n2 ) = N_h1+ N_h2, where N_h1and N_h2 are the numbers of \varepsilon₁ and \varepsilon₂ bonds along the electric field, respectively. These results may be beneficial to the study of surface plasmon resonances on a nanometre scale.     

非局域暗孤子及其稳定性分析

由于其在通信领域潜在的应用前景, 非局域空间孤子一直是研究热点. 但空间非局域暗孤子由于其边界的特殊性, 对其特别是稳定性方面研究甚少. 提出了非局域暗孤子稳定性分析理论, 并对热非线性体介质中1+1维基态和二阶暗孤子的稳定性进行了数值分析和研究, 得到了稳定性图. 从稳定性分析图可知: 在热非线性体介质中, 1+1维基态暗孤子在其存在区域总是稳定的, 而1+1维二阶暗孤子是震荡不稳定的, 其不稳定区域的宽度与传播常数以及介质的非局域程度有关. 为了验证非局域暗孤子稳定性分析理论的正确性, 对加噪声初始输入的传输进行数值模拟得到了传输图, 传输图表明稳定性分析理论的正确性. 关键词： 非局域 稳定性 暗孤子     

Vibrational spectra of (NH4)3ZnCl5

IR and Raman spectra of (NH₄)₃ZnCl₅ have been recorded. The observed spectra have been analysed on the basis of the vibrations of ZnCl ₄ ²⁻ and NH ₄ ⁺ ions. The appearance of multiple Raman bands indicates the presence of two different types of ammonium ions. The effect of anisotropic crystalline field over the ZnCl₄ and NH₄ tetrahedra is also discussed. The assignment of internal modes has been verified by the potential energy distribution calculations.     

1.5MeV LIA脉冲功率系统

本文简要介绍了1.5MeV LIA脉冲功率系统的结构、组成和设计思想;给出了开关运行参数和确定开关时间抖动指标的方法、闭环系统的总抖动对加速电压相对变化的影响、脉冲功率系统各段输出波形和电压幅度的调制关系;测量结果表明,1.5MeV LIA的运行功率和时间同步满足总体设计要求。     

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration, a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out. Those four types are the linear velocity feedback control, the cubic velocity feedback control, the non-linear saturation controller (NSC) and the positive position feedback (PPF) controller. The suitable type is the PPF controller for suppression the vibrations of the cantilever beam. The approximate solution obtained up to the first approximation by using the multiple scale method. The PPF controller effectiveness is studied on the system. We used frequency-response equations to investigate the stability of a cantilever beam. We notified that, there is a good agreement between the analytical solution and the numerical solution.     

Study of Coulomb collisional effects on the propagation of electromagnetic waves in a turbulent plasma

The presence of Weibel instability in laser-irradiated fuel could be detrimental to the process of ablative implosion, which is necessary for achieving thermonuclear fusion reactions. In this paper, the effect of the Coulomb collisional within the turbulent plasma on the Weibel instability growth rate has been investigated for linear and circular polarization. The results indicate that the Weibel instability growth rate at circular polarization near the ignition centre of the fuel fusion (collisional plasma) is about 10⁵ times higher than the collisional Weibel instability growth rate at linear polarization. The Weibel instability growth rate is observed near the critical density of the fuel fusion (collisionless plasma) at linear polarization and enhancement near the foot of the heat in front of the fuel fusion. By increasing the steps of the density gradient plasma in the low-density corona, electromagnetic instability occurs at a higher stress flow. Therefore, the deposition condition of electron beam energy in circular polarization of turbulent plasma can be shifted to the fuel core for suitable ignition.