非线性奇异边值问题的正解

利用锥映射的不动点指数定量，研究了一类非线性奇异边值问题多个正解的存在性问题。在构造的解的存在条件之下，证明了奇异边值问题至少有两个正解的存在性定理。     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Radiation of a charge moving over the diffraction grating

The states of a charged particle with a finite free path are determined in the field of a resonant electromagnetic wave. The exact resonance conditions, the modulation and beam instability mechanisms, the charge and current densities (Ohm's law) are obtained for the collisionless beam of resonance particles. Quantum theory of radiation is developed for the resonant adiabatic interaction between a particle and a wave taking into account the interaction with a constant magnetic field induced at the grating surface by the charge and nonresonant waves. The radiation power, the spectrum, and the range of generated frequencies are determined. The results obtained can be used in the plasma and solid-state theories and in electronics.     

Lu2Si2O7：Ce晶体的闪烁性能

用提拉法生长了Lu2Si2O7：Ce晶体，对该晶体的闪烁性能进行了研究。透射光谱表明，Lu2Si2O7：Ce晶体的吸收边比Lu2SiO5：Ce晶体向短波方向移动了25nm，使透光范围进一步拓宽。X射线发射光谱和UV激发发射光谱均具有典型的双峰特征，主峰在378nm。UV激发发射谱具有温度效应，即375K以上时，发光效率迅速降低；425K以上时，发光主峰位明显红移。衰减曲线符合单指数式衰减规律，常温下经UV激发后的衰减时间约为34ns。从曲线形态看，375K以下的衰减谱与室温下的几乎完全相同，拟合的结果在32．8～34ns之间；衰减时间的温度效应从375K开始显现，即随温度的升高，衰减时间有加速变短的趋势，到500K时缩短为6．72ns。热释光谱在488，553K处有两个热释光峰，但室温附近几乎观察不到热释光峰。     

有界变量线性规划的基线算法

本文对有界变量线性规划的算法进行了研究，得到了一种解此问题的新算法。文中根据基线算法的算法原理，通过对BL表的旋转，在各变量满足界约束的条件下，使目标函数值不断增大，直至得到有界硬上界，从而得到问题的最优解。文中给出了有界变量线性规划基线算法的计算步骤，并给出了一个例子。与单纯形法相比，采用基线算法解有界变量线性规划操作更简单。迭代次数少，解题速度更快。     

Infinite paths in planar graphs III, 1‐way infinite paths

An infinite graph is 2‐indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4‐connected, 2‐indivisible, infinite, plane graph. It is known that G contains a spanning 1‐way infinite path. In this paper, we prove a stronger result by showing that, for any vertex x and any edge e on a facial cycle of G, there is a spanning 1‐way infinite path in G from x and through e. Results will be used in two forthcoming papers to establish a conjecture of Nash‐Williams. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Balancing a Rotor with Two Coupled Perfectly Rigid Bodies

The steady motions of a vertical rotor balanced by two coupled perfectly rigid bodies (PRBs) are analyzed for stability. The rotor executes plane-parallel motions. The PRBs can rotate together about the rotor axis and about its transverse axes through equal angles but in opposite directions. It is established that when the mass of the PRBs is much less than that of the rotor and the rotor spins with a superresonant speed, only the basic steady motions, which are those of the best-balanced rotor, are asymptotically stable.     

Forward-angle yields of 2≤Z≤11 isotopes in the reaction of 18O(35A MeV) with 9Be

A systematic investigation of the forward-angle inclusive yields of 2≤Z≤11 isotopes produced in collisions of ¹⁸O projectile nuclei with a ⁹Be target in the Fermi energy region (35A MeV) is performed. The measurements were based on the use of the COMBAS double achromatic kinematical separator in the spectrometry mode at the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research, FLNR (JINR, Dubna). The velocity, isotopic, and element distributions are presented. There is no unique mechanism that would explain the total set of results obtained in this experiment. A dominant role of low-energy reaction mechanisms is observed. The intensity of secondary beams of halolike nuclei ¹¹Li, ¹²Be, and ¹⁴Be is determined.     

Quantum discreteness effects and flicker fluctuations in tunneling conductivity

An analysis of events in the tunneling junction shows that the interaction of one-electron processes in a many-electron system may be a source of scale-invariant low-frequency fluctuations of conductivity (the interaction consists in that the quantum probability of an electron transition depends on fast random changes in the environment in the course of the transition, including the changes caused by analogous transitions). The theory relates flicker fluctuations in the tunneling conductivity to the discrete character of the spectrum of electron states and explains the nonlinearity of the noise-current characteristic observed in nanocomposites.     

Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates

The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination.