Conjugate addition of pyrroles to α,β-unsaturated ketones using copper bromide as a catalyst

Copper bromide was used as a catalyst for the addition of pyrroles to enones. When both the reactants were used in equimolar amounts, mono and dialkylated products were obtained. However, the use of excess enone furnished only dialkylated products. Thus, copper bromide was shown to be an efficient catalyst for the dialkylation of pyrroles.     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit Entangled State

Based on A.K. Pati‘s original idea [Phys. Rev. A 61 (2000) 022308] on single-qubit-state-assisted clone, very recently Zhan has proposed two assisted quantum cloning protocols of a special class of unknown two-qubit entangled states [Phys. Lett. A 336 (2005) 317]. In this paper we further generalize Zhan‘s protocols such that an arbitrary unknown two-qubit entangled state can be treated.     

A triangular map with homoclinic orbits and no infinite ω-limit set containing periodic points

Recently, Forti, Paganoni and Smítal constructed an example of a triangular map of the unite square, F(x,y)=(f(x),g(x,y)), possessing periodic orbits of all periods and such that no infinite ω-limit set of F contains a periodic point. In this note we show that the above quoted map F has a homoclinic orbit. As a consequence, we answer in the negative the problem presented by A.N. Sharkovsky in the eighties whether, for a triangular map of the square, existence of a homoclinic orbit implies the existence of an infinite ω-limit set containing a periodic point. It is well known that, for a continuous map of the interval, the answer is positive.     

Ground-state properties of LiV2O4 and Li1-xZnx(V1-yTiy)2O4

We present susceptibility, microwave resistivity, NMR and heat-capacity results for Li_1-xZn_x(V_1-yTi_y)₂O₄ with 0 ? x ? 0.3 and 0 ? y ? 0.3. For all doping levels the susceptibility curves can be fitted with a Curie-Weiss law. The paramagnetic Curie-Weiss temperatures remain negative with an average value close to that of the pure compound Θ≈ - 36 K. Spin-glass anomalies are observed in the susceptibility, heat-capacity and NMR measurements for both type of dopants. From the temperature dependence of the spin-lattice relaxation rate we found critical-dynamic behavior in the Zn doped compounds at the freezing temperatures. For the Ti-doped samples two successive freezing transitions into disordered low-temperature states can be detected. The temperature dependence of the heat capacity for Zn-doped compounds does not resemble that of canonical spin glasses and only a small fraction of the total vanadium entropy is frozen at the spin-glass transitions. For pure LiV₂O₄ the spin-glass transition is completely suppressed. The temperature dependence of the heat capacity for LiV₂O₄ can be described using a nuclear Schottky contribution and the non-Fermi liquid model, appropriate for a system close to a spin-glass quantum critical point. Finally an ( x / y , T )-phase diagram for the low-doping regime is presented. Received 16 March 2001 and Received in final form 30 October 2001     

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.     

光纤的能量传输特性及应用

着重分析了影响光纤传输能量以及光纤传输中造成能量损耗的因素。这些因素主要包括光纤材料、构造、光纤的折射率分布、光纤的长度和芯径、光纤的数值孔径和热效应以及耦合等。同时 ,结合激光二极管点火的实例 ,分析探讨了其背景和应用价值。结论是 :为了尽可能减少能量损耗、提高光纤输出的激光功率和激光功率密度 ,应当选取合适的激光工作波长、较小的光纤长度、较小的芯径和较小的数值孔径 ,应采用渐变折射率分布光纤 ,应减少弯曲与耦合     

High energy asymptotics of the scattering amplitude for the Schrödinger equation

We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables. This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday.     

粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

不同入射角度下强流脉冲电子束能量沉积剖面和束流传输系数模拟计算

 强流脉冲电子束在材料中的能量沉积剖面、能量沉积系数和束流传输系数受其入射角的影响很大，理论计算了0.5~2.0MeV的电子束以不同的入射角在Al材料中的能量沉积剖面和能量沉积系数，并且还计算了0.4~1.4MeV电子束以不同入射角穿透不同厚度C靶的束流传输系数。计算结果表明，随着入射角的增大，靶材表面层单位质量中沉积的能量增大，电子在靶材料中穿透深度减小，能量沉积系数减小，相应的束流传输系数也减小；能量为0.5~2.0MeV的电子束当入射角在60°~70°时在材料表面层单位质量中沉积的能量较大。