Analysis and numerical solution of a functional differential equation

In the present work we investigate the existence, uniqueness and computation of the solutions of an initial value problem for a class of functional differential equations involving autoregulations in the limits of the integration.     

Variable Programming: A Generalized Minimax Problem. Part II: Algorithms

In this part of the two-part series of papers, algorithms for solving some variable programming (VP) problems proposed in Part I are investigated. It is demonstrated that the non-differentiability and the discontinuity of the maximum objective function, as well as the summation objective function in the VP problems constitute difficulty in finding their solutions. Based on the principle of statistical mechanics, we derive smooth functions to approximate these non-smooth objective functions with specific activated feasible sets. By transforming the minimax problem and the corresponding variable programming problems into their smooth versions we can solve the resulting problems by some efficient algorithms for smooth functions. Relevant theoretical underpinnings about the smoothing techniques are established. The algorithms, in which the minimization of the smooth functions is carried out by the standard quasi-Newton method with BFGS formula, are tested on some standard minimax and variable programming problems. The numerical results show that the smoothing techniques yield accurate optimal solutions and that the algorithms proposed are feasible and efficient.This work was supported by the RGC grant CUHK 152/96H of the Hong Kong Research Grant Council.     

衰减器对螺旋线慢波结构高频特性影响的理论研究

以加载衰减器的螺旋线慢波结构作为研究对象，采用螺旋导电面模型，用真空层模拟螺旋带的厚度，用均匀介质层等效分立的介质夹持杆，并考虑到各横向区域横向传播常数的不同，得到了任意次模式的色散方程和耦合阻抗的表达式. 在此基础之上，分析了衰减器对主模和-1次模式的衰减常数、相位常数和耦合阻抗的影响.所得结果对设计衰减器具有理论指导意义，为螺旋线慢波系统高频特性的改善以及反射振荡和返波振荡的抑制提供了理论依据. 关键词： 螺旋线 行波管 衰减 色散     

利用宇宙线对BESⅢ量能器CsI(Tl)晶体探测器单元的测量

利用宇宙射线进行探测器模型的性能测试是高能物理普遍采用的方法, 其中最重要的步骤之一就是确定宇宙线入射的准确位置和径迹. 多数采用丝室探测器来进行宇宙线的精确定位, 需要很高的造价和复杂的电子学系统. 本文介绍一种简单的定位方法, 采用塑料闪烁体条加波移剂光纤编码读出的方式, 可以实现精度为1cm的定位. 据此建立了一套实验装置, 对BESⅢ电磁量能器CsI(Tl)晶体探测器单元的光输出强度和不均匀性进行了测量.     

Chaotic rotations of a liquid-filled solid

The disturbed Hamiltonian equations of a solid filled with a rotating ellipsoidal mass of a liquid and subjected to small-applied moments are revisited using Deprit's variables. We investigate the chaotic dynamics of the orbiting liquid-filled solid and of the liquid-filled solid sliding and rolling on a perfectly smooth plane, in either energy-conservative or energy-dissipative conditions, when appropriately perturbed. Criteria for the judgment of potential chaotic rotations of the perturbed system are formulated by means of Melnikov-Holmes-Marsden (MHM) integrals. Strategies for the solution of heteroclinic orbits of the symmetrical liquid-filled solid under torque-free conditions are outlined theoretically. Physical parameters that will probably trigger the onset of chaotic motions can be determined accordingly. Results from MHM algorithms are crosschecked with Poincare sections together with Lyapunov characteristic exponents.     

Large negative Goos-Hanchen shift at metal surfaces

It has been previously established that for p-polarized light incident onto a semi-infinite absorbing medium, large negative Goos-Hanchen (GH) shifts can be expected in the case of weak absorption at incidence close to the Brewster angle. The effect has been demonstrated for certain semiconducting media at optical frequencies. Here we point out that similar phenomenon can take place for strongly reflecting and attenuating medium such as metal at IR frequencies, with large incident angles close to grazing incidence. Moreover, unlike the previously-studied case with semiconductors, the Brewster angle in the present case with metals plays an insignificant role in the possible hindrance of the observation of such large negative shifts.     

Synthesis and structural characterization of 5,6,15,16-tetradehydrobenzo[a]phenanthro[9, 10-e]cyclooctene,C24H12

A benzo-phenanthro-fused planar cyclooctatetraene derivative, namely, 5,6,15,16-tetradehydrobenzo[a]phenanthro[9, 10-e]cyclooctene (5) was synthesized in two steps from the known benzo[a]phenanthro[9, 10-e]cyclooctene (6). Compound5 crystallizes in space groupPbam witha=9.828(2),b=19.466(4),c=15.901(3) Å, and Z=8. X-Ray analysis (MoK radiation,R=0.060 for 1233 observed data) has shown that both independent molecules have the same planarC _2v configuration with averaged bond lengths of 1.381(7) and 1.208(7) Å for the phenanthrene C_6a–C_14b bond and the acetylenic CC bond, respectively.¹H and¹³C NMR spectral results of 5 and 5,6,15,16-tetrabromo-5,6,15,16-tetrahydrobenzo[a]phenanthro[9, 10-e]cyclooctene (7) are also presented.     

Homogentisic acid γ-lactone suppresses the virulence factors of Pseudomonas aeruginosa by quenching its quorum sensing signal molecules

Homogentisic acid γ-lactone exhibited excellent anti-quorum sensing (QS) and anti-biofilm activities against Pseudomonas aeruginosa. Moreover, it suppressed the QS-dependent virulence factors in P. aeruginosa by quenching its QS signal molecules.     

Total Synthesis and Conformational Study of Callyaerin A: Anti‐Tubercular Cyclic Peptide Bearing a Rare Rigidifying (Z)‐2,3‐ Diaminoacrylamide Moiety

The first synthesis of the anti‐TB cyclic peptide callyaerin A ( 1 ), containing a rare (Z)‐2,3‐diaminoacrylamide bridging motif, is reported. Fmoc‐formylglycine‐diethylacetal was used as a masked equivalent of formylglycine in the synthesis of the linear precursor to 1 . Intramolecular cyclization between the formylglycine residue and the N‐terminal amine in the linear peptide precursor afforded the macrocyclic natural product 1 . Synthetic 1 possessed potent anti‐TB activity (MIC₁₀₀=32 μm ) while its all‐amide congener was inactive. Variable‐temperature NMR studies of both the natural product and its all‐amide analogue revealed the extraordinary rigidity imposed by this diaminoacrylamide unit on peptide conformation. The work reported herein pinpoints the intrinsic role that the (Z)‐2,3‐diaminoacrylamide moiety confers on peptide bioactivity.