The limit cycles of a second-order system of differential equations: The method of small forms

In this paper we investigate the existence of limit cycles of a system of the second-order differential equations with a vector parameter.We propose a method for representing a solution as a sum of forms with respect to the initial value and the parameter; we call this technique the method of small forms. We establish the conditions under which a sufficiently small neighborhood of the equilibrium point contains no limit cycles. We construct a polynomial, whose positive roots of odd multiplicity define the lower bound for the number of cycles, and simple positive roots (other positive roots do not exist) define the number of limit cycles in a sufficiently small neighborhood of the equilibrium point.We prove theorems, whose conditions guarantee that a positive root of odd multiplicity defines a unique limit cycle, but a positive root of even multiplicity defines exactly two limit cycles.We propose a method for defining the type of the stability of limit cycles.     

Identification of unstable metabolites of Lonafarnib using liquid chromatography-quadrupole time-of-flight mass spectrometry, stable isotope incorporation and ion source temperature alteration

Structural characterization of unstable metabolites and other drug-derived entities poses a serious challenge to the analytical chemist using instrumentation such as LC-MS and LC-MS/MS, and may lead to inaccurate identification of metabolite structures. The task of structural elucidation becomes even more difficult when an analyte is unstable in the ion source of the mass spectrometer. However, a judicious selection of the experimental conditions and the advanced features of new generation mass spectrometers can often overcome these difficulties. We describe here the identification of three drug-derived peaks (A, B and C) that were detected from a Schering-Plough developmental compound (Lonafarnib) following incubation with cDNA-expressed human CYP3A4. Definitive characterization was achieved using (1) accurate mass measurement, (2) stable isotope incorporation, (3) reduced ion source temperature, (4) alkali ion attachment and (5) MS/MS fragmentation studies. The protonated ions of compounds A and B fragmented almost completely in the source, yielding ions of the same mass-to-charge ratio (m/z) as that of protonated C (CH+). Fortunately, the presence of Na+ and K+ adducts of A and B provided information crucial to distinguishing AH+ and BH+ from their fragment ions. Metabolite A was shown to be an unstable hydroxylated metabolite of Lonafarnib. The metabolite C was shown to be a dehydrogenated metabolite of Lonafarnib (Lonafarnib-2H), unstable in the presence of protic solvents. Finally, B was artifactually formed most likely from C by the solvolytic addition of methanol during sample preparation. MS/MS fragmentation experiments assisted in identifying the site of metabolism in A and chemical modification in B. A and C readily interconvert through hydration/dehydration, and B and C through addition/elimination of methanol present in the sample-processing solvents. Finally, NMR experiments were performed to confirm the structures of A and C.     

Exact Solutions of Five Complex Nonlinear Schrödinger Equations by Semi-Inverse Variational Principle

In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained.     

热带低层弱涡旋中扰动的快速发展及其向中心传播的特征

台风发生的必要条件是热带低层具有气旋式扰动, 从卫星云图和诊断分析看,许多低层涡旋中存在分立的云团或中尺度系统. 这些涡旋能否发展成为台风,取决于其中的中尺度波动是否发展集合组成密闭云带. 本文利用柱坐标下的两层动力模式,研究了低层弱涡旋中第二类条件不稳定 机 制驱动下的波动的发展和移动问题. 结果表明:热带弱涡旋中的低层基本流垂直切变 可以很大地加强波动的不稳定性; 波动的相速度和群速度都指向涡旋中心, 波动向中心传播,能量向中心频散. 实例和数值研究也都表明,低层涡旋中的中尺度扰动会迅速发展并且向 中心靠近,促使台风形成.     

On stabilization of systems with delay

The optimization of the parameters of a controller of given structure for a controlled unstable scalar system with delay is studied. First, the original system with delay is approximated by a system without delay. To this end, the exponent is approximated by a fractional rational function. Since the structure of the controller is fixed, the quality of the approximation is assessed by comparing the stability domains of the original and approximating systems (in the space of controller coefficients). Next, the coefficients of the controller for the reduced system are optimized. The performance of the controller thus synthesized can be assessed by mathematically modeling the original system (with delay) whose feedback is determined by the controller coefficients found. The approach is exemplified by stabilizing an inverted mathematical pendulum with a PD controller. This example is used to examine the issue of synthesis of a robust controller __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 86–100, October 2008.     

Flow regimes in wet conical spouted beds using glass bead mixtures

Using a high-viscosity Newtonian fluid, glycerol, an experimental investigation was carried out to evaluate the stable spouting regime in conical spouted beds using four particle mixtures: a reference (monoparticles), a binary mixture, two ternary mixtures with flat and Gaussian distributions respectively. The mixtures were selected for particle diameters (dp) ranging from 1.09 to 4.98 mm and particle diameter ratios (dpL/dps) ranging from 1.98 to 4.0. Experimental data show that pressure fluctuation signals of the bed, as indicated by changes in their standard deviations, provide suitable information to identify the range of operational conditions for stable spouting. However, the analysis of skewness of curves of pressure fluctuation as a function of air velocity appears not sufficient to identify a particular flow regime. For glycerol in the spouting regime, the standard deviation is noted to increase with increasing glycerol concentration due to the growth of interparticle forces. The implications of these research findings on the drying of suspensions in conical spouted beds using glass bead mixtures are also discussed.     

不均匀不稳定磁场下高分辨液体核磁共振新技术的研究进展

高分辨核磁共振（Nuclear Magnetic Resonance,NMR）谱的获得通常需要高度稳定且均匀的强静磁场. 阻抗磁体或阻抗－超导混合磁体可获得比超导磁体高得多的磁场, 但它们的磁场的稳定性与均匀性比较差;另一方面, 在活体定域波谱研究中,样品内部组分的磁化率差异,运动或生理活动等作用将不可避免地导致磁场的不均匀不稳定,并且这些不稳定不均匀性无法通过锁场匀场等传统的方法消除. 基于分子间零量子相干的方法、空间编码单扫描快速方法、反卷积技术等日渐成为在不均匀不稳定磁场下获取高分辨率的NMR谱的研究热点.     

Physics with loosely bound nuclei

The essential aspect of contemporary physics is to understand properties of nucleonic matter that constitutes the world around us. Over the years research in nuclear physics has provided strong guidance in understanding the basic principles of nuclear interactions. But, the scenario of nuclear physics changed drastically as the new generation of accelerators started providing more and more rare isotopes, which are away from the line of stability. These weakly bound nuclei are found to exhibit new forms of nuclear matter and unprecedented exotic behaviour. The low breakup thresholds of these rare nuclei are posing new challenges to both theory and experiments. Fortunately, nature has provided a few loosely bound stable nuclei that have been studied thoroughly for decades Attempts are being made to find a consistent picture for the unstable nuclei starting from their stable counterparts. Some significant differences in the structure and reaction mechanisms are found.     

混沌系统延迟反馈控制的理论与实验研究

综述了近年来控制混沌的延迟反馈控制技术------DFC控制的相关进展,总结了延迟反馈控制在不动点和不稳定周期轨道镇定方面的局限性和可控性研究的理论成果,介绍了延迟反馈控制在电子线路和磁弹性梁混沌控制方面的实验,并对延迟反馈控制技术未来的研究方向和发展前景进行了预测和展望。      

Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

Summary. Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation For p>5 , the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. Received March 28, 2000; accepted August 24, 2000 %%Online publication November 15, 2000 Communicated by Thanasis Fokas