自旋3/2粉末样品四极核中心跃迁的NMR回波序列

本文提出脉冲序列45_X~°—t_1—90_(±Y)~°—t_2,从理论和实验上证实了它能够有效地会聚粉末样品中I=3/2四极核中心跃迁的磁化矢量,并对该回波序列的激发谱宽作了数值计算。     

A Coulomb-related family of potentials having zero-energy bound states

We propose here a new large class of singular central potentials having zero-energy bound states for many values of angular momenta. The potentials are shown to be closely related to the standard attractive Coulomb interaction. Some of them admit the E≠0$E\ne 0$ bound states as well. A quantum–classical correspondence is also discussed.     

Foucault Pendulum-like problems: A tensorial approach

The paper offers a comprehensive study of the motion in a central force field with respect to a rotating non-inertial reference frame. It is called Foucault Pendulum-like motion and it is a generalization of a classic Theoretical Mechanics problem. A closed form vectorial solution to this famous problem is presented. The vectorial time-explicit solution for the classic Foucault Pendulum problem is obtained as a particular case of the considerations made in the present approach. New interesting conservation laws for the Foucault Pendulum-like motion are deduced by using simple differential and vectorial computations. They help to visualize the shape of the trajectories. Exact vectorial expressions for the law of motion and the velocity are also offered. The case of the driven Foucault Pendulum is also analyzed, and a closed form solution is deduced based on the general considerations. In the end, an new tensorial prime integral for the Foucault Pendulum problem is offered. It helps to reveal in a concise form, within a single entity, all the scalar and vectorial conservation laws for the Foucault Pendulum motion.Two important engineering applications to this approach are presented: the motion of a satellite with respect to a rotating reference frame and the Keplerian relative orbital motion. The latter has a great importance in modeling the problems concerning satellite formation flying, satellite constellations and space terminal rendezvous. The classic problem of the harmonic oscillator in an electromagnetic field is also solved by using the instruments presented in this paper.     

Bifurcation and chaos of a simple walking model driven by a rhythmic signal

The walk of animals is achieved by the interaction between the dynamics of their mechanical system and the central pattern generator (CPG). In this paper, we analyze dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. In particular, we examine the long-term global behavior and the bifurcation of the motion that leads to chaotic motion, depending on the model parameter values. The simple model consists of a hip and two legs connected at the hip through a rotational joint. The joint is driven by a rhythmic signal from an oscillator, which is an open loop. In order to analyze the bifurcation, we first obtained approximate solutions of the walking motion and then constructed discrete dynamics using the Poincaré map. As a result, we found that consecutive period-doubling bifurcations occur as the model parameter values change, and that the walking motion leads to chaotic motion over the critical value of the model parameters. Moreover, we approximately obtained the period-doubling solutions and the critical value by employing a Newton-Raphson method. Our analytical results were verified by the numerical simulations.     

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J-TEXT装置由许多相关子系统组成,其中央控制系统的主要功能和作用是统一调度和协调各个子系统,控制装置的运行状态。J-TEXT中央控制系统是基于Windows和QNX操作系统平台,并采用工业控制计算机结合PCI工业控制卡来实现的。该系统已经完成了相关测试并获得满意结果。在首轮的J-TEXT放电调试中,该系统运行稳定可靠,控制效果良好。     

Sodium-23 MAS NMR study on nuclear quadrupole interaction in NA(1-x)Ag(x)NO2.

Ag-impurity effects on the first- and second-order quadrupole interaction (QI) at ²³Na site in an isomorphic mixed system, Na_1−xAg_xNO₂ (x=0, 0.0084, 0.026, 0.079, 0.094, 0.16), have been investigated by employing ²³Na (I=3/2) magic angle spinning nuclear magnetic resonance (MAS NMR) technique. The central transition (CT) and satellite transition (ST) are simultaneously observed with this system. From the spectral analysis, the quadrupole parameter and its distribution width are obtained as a function of Ag concentration. From the intensity loss of CT MAS centerband and of the envelope function of ST MAS sidebands due to impurities, the range of their influence on the second- and first-order QI is estimated. The estimated ranges contain the second and first neighbouring Na sites from the resonating ²³Na nucleus for the first- and second-order QI, respectively.     

A new smoothing Newton-type method for second-order cone programming problems

A new smoothing function of the well-known Fischer–Burmeister function is given. Based on this new function, a smoothing Newton-type method is proposed for solving second-order cone programming. At each iteration, the proposed algorithm solves only one system of linear equations and performs only one line search. This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Numerical results demonstrate the effectiveness of the algorithm.     

Optimization of Microwave-Assisted Michael Addition Reaction Catalyzed by L-Proline in Ionic Liquid Medium Using Response Surface Methodology

Michael addition reactions of aldehyde to β-nitrostyrene catalyzed by L-proline were investigated by using controlled, monomode microwave-assisted technique in a closed vessel system. Ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([bmim]NTf₂) was used as the reaction medium to replace the commonly used volatile organic solvents and as a good absorbing solvent during Michael reaction under the influence of microwave irradiation. The Michael product is clean and generates good yields in short reaction times with moderate results on enantioselectivity (ee). In this work, optimization of proline-catalyzed Michael reaction was carried out using response surface methodology (RSM) based on a three-factor-three-level central composite design (CCD). Various reaction parameters including catalyst loading (5–30 mol%), reaction time (5–40 min), and substrate (2–5 equivalent ratio) were investigated. A high Michael yield (96.5%) with 36.9 ee% was obtained at the optimum conditions of 10.0 mol% catalyst loading, 5.0 min reaction time, and 2.0 substrate equivalent ratio.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Fundamental groupoids for simplicial objects in Mal'tsev categories

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini).     

Central elements of the elliptic monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the R-matrix are studied. When the crossing parameter w takes a special rational value , where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the “quantum determinant” provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo.