Complexity of some cutting plane methods that use analytic centers

We consider cutting plane methods for minimizing a convex (possibly nondifferentiable) function subject to box constraints. At each iteration, accumulated subgradient cuts define a polytope that localizes the minimum. The objective and its subgradient are evaluated at the analytic center of this polytope to produce one or two cuts that improve the localizing set. We give complexity estimates for several variants of such methods. Our analysis is based on the works of Goffin, Luo and Ye. Research supported by the State Committee for Scientific Research under Grant 8S50502206.     

银河系中心超大质量黑洞的探索历程

经过逾半个世纪的探索,天文学家确认在我们银河系的中心存在一个4百万倍太阳质量的致密天体,很可能是爱因斯坦广义相对论所预言的黑洞。文章简要回顾了探索这个大质量致密天体过程中的若干里程碑。     

Radiation-induced color centers in the near-surface layer of lithium fluoride crystals

For radiation-induced intrinsic color centers, we show that the concentrations of identical centers and the concentration ratios of different centers are quite different in the near-surface layer and within the interior volume of a lithium fluoride crystal. We have established that these differences also depend on the sign of the difference between the temperature at which the crystal was irradiated with γ photons and the vacancy mobility temperature. We provide an interpretation for the results obtained, based on the structural features of the near-surface layer and the concentration ratio of vacancies and electrons in the layer, serving as the starting components for color center formation. We found that the concentrations of centers change over the course of a few days by tens of percent in the layer “emerging” from the interior onto the surface as a result of cleavage of the crystal. We measured the luminescence lifetimes of F₃ (R2) and F₄ centers: 6.6 nsec and 11.7 nsec. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 6, pp. 775–781, November–December, 2006.     

短波红外平场光谱仪的波长定标

针对自行研制的短波红外平场光谱仪,讨论了波长定标的原理和方法.短波红外平场光谱仪由两个分光探测单元组成,探测单元以平场凹面光栅分光,处于焦平面上的线阵列探测器探测,波长定标分为两个波段进行.为了实现准确的波长定标,针对短波红外平场光谱仪的特点设计了波长定标步骤.双单色仪可以输出光谱仪波长范围内任意波长单色光,选用双单色仪作为光谱定标光源,双单色仪的输出单色光光潜分辨力为1.5 nm,经过光谱仪的分光会聚后成像在线阵列探测器像元上,采用重心法计算出给定波长对应的像元精确位置,通过多项式拟合得出两个探测单元的波长定标系数.定标结果表明,在900～2400 nm波长范围内,定标曲线拟合误差小于0.5 nm,波长定标不确定度优丁0.6 nm.     

Influence of dielectric microcavity on the spontaneous emission rate of atom: a perspective on the closed-orbit theory of photons

The formulas of the quantum electrodynamics have been applied to calculate the spontaneous emission rate of excited atom in dielectric microcavity.The results exhibit damping oscillating Patterns which depend sensitively on the scaling parameter and geometrical structure.Compared with the case that the emitting atom is immersed in dielectric,the spontaneous emission rate is depressed obviously and the center or the mean value of the oscillations is intimately related to the real refractive index of the local position where the atom is.In order to explain this phenomenon,we utilize the closed-orbit theory to deal with the classical trajectories of the emitted photon.and extract the corresponding frequencies of the oscillations by Fourier transform.It is found that the oscillations can be represented in terms of the closed-orbits of the photon motion constrained in dielectric microcavity,thus providing another perspective on the spontaneous emission of atom sandwiched by dielectric slabs.     

Four dimensional regular algebras with point scheme,anonsingular quadric in P3

In [22], a class of four-dimensional, quadratic, Artin-Schelter regular algebras was introduced, whose point scheme is the graph of an automorphism of a nonsingular quadric in P³. These algebras are the first examples of quadratic Artin-Schelter regular algebras whose defining relations are not determined by the point scheme and, hence, not determined by the algebraic data obtained from the point modules. In this paper, we study these algebras via their line modules. In particular, the set of lines in P³ that correspond to left line modules is not the set of lines in P³ that correspond to right line modules. Our analysis focuses on a distinguished member R _λ of this class of algebras, where R _λ is a twist by a twisting system of the other algebras. We prove that R _λ is a finite module over its center and that its central Proj is a smooth quadric inP⁴.     

Effects of indium doping on the superconducting properties of YBa2Cu3Oy sintered compounds and thin films

We investigated the effects of indium doping on the superconducting properties of YBCO sintered samples and thin films. In₂O₃-doped YBCO and YBa₂Cu_3−xIn_xO_y sintered samples showed a gradual decrease in the critical temperature (T_c) with increasing indium content; however, a T_c value above 80 K was maintained even up to 30 vol.% addition and x = 0.4, respectively. Ba₃Cu₃In₄O₁₂ was detected by X-ray diffractometry and energy-dispersive X-ray spectroscopy as a reaction product for both sintered samples. The normalized J_c under a magnetic field of 0.1 T showed a maximum at x = 0.3. Indium-doped YBCO films prepared by pulsed laser deposition showed a similar dependence of T_c on indium content as the sintered samples.