Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

Signal generation and spatial resolution in scanning electron acoustic microscopy

The thermal conduction and Navier-Stokes equations are usedto obtain the stress field generated by a chopped electron beam incident ona disk sample.The piezoelectric equation is then used to obtain the out-put signal of the transducer coupled to the sample.The results lead to aconsideration of the signal generation mechanism and spatial resolution inscanning electron acoustic microscopy(SEAM).It is shown that atime-variant heat source generated both a thermal wave and an acousticwave simultaneously,and thermal-to-acoustic wave mode conversion oc-cured on the boundary surfaces depends on the amplitudes and the gra-dients at boundary surfaces of both heat source and thermal waves.It isargued that the spatial resolution of a imaging system operated in thenear field,such as SEAM and thermal wave microscope,is dependent onthe distance between the heat source and scatterer and,at best,the lateralresolution in SEAM is of the order of the diameter of the focal spot ofthe electron beam.     

高效液相色谱死体积的热力学定义

本文讨论了高效液相色谱死体积的定义和如何以吉布斯热力学理论为基础对其测定。推荐的热力学理论方法能应用于任何一种液相色谱方法,如正相、反相、离子交换、甚至体积排斥色谱。提出了一种能在整个浓度范围内准确计算流动相组分干扰峰死体积的方法。对某些化合物容量因子出现负值也作了解释。     

126Cs的高自旋态能级结构

利用融合蒸发反应¹¹⁶Cd(¹⁴N,4n)¹²⁶Cs布居了¹²⁶Cs的高自旋态.观测到了100多条新的γ跃迁和相应的能级,建立了双奇核¹²⁶Cs由9个转动带构成的能级纲图.尝试性地指定了大部分能级的自旋和宇称以及各转动带的Nilsson单粒子组态.极大地丰富了已有的实验结果.     

APPROXIMATION OF CONTINUOUS FUNCTIONS BY GENERALIZED KARAMATA MEANS

A sufficient condition for the order of approximation of a continuous 2π periodic function with a givenmajorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order isobtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums oftheir Fourier series to be of Jackson order. The error estimate is shown to be the best possible.     

蒙特卡罗哈密顿新方案及其检验

蒙特卡罗哈密顿方法(MCH)是研究量子理论的数值模拟新方法, 其优点是可求出超出基态的能谱和波函数. 旧MCH方案需要自由粒子的信息, 较难推广应用于格点规范理论. 本文提出克服这个困难的新方案. 首先介绍这一方案的思想, 并以1维量子力学模型V(x)=μ²x²+λx⁴(其中μ²< 0,λ>0)为例说明实现这一新方案的具体计算步骤和方法.     

ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF A CERTAIN FOURTH-ORDER DIFFERENTIAL EQUATION

The present paper establishes sufficient conditions for the uniformly bounded of any solution of (1.1) and which tend to zero as t → ∞.     

CRYSTAL STRUCTURE AND MORPHOLOGY OF NASCENT SAMPLES OF SYMMETRIC AROMATIC POLYESTERS——Ⅱ. POLY(p-PHENYLENE 2,6-NAPHTHALATE)

Confined thin film melt polymerization (CTFMP) of naphthalene chloride/hydroquinone (NCMQ, 1/1, molar)mixtures at polymerization temperatures (T_p) below ca. 300℃ resulted in relatively thick, elongated crystals. Polymerizationof NC/HQ above 300℃ between glass yielded well-formed lamellar crystals ca. 100 A thick. Phase Ⅰ and Ⅱ [001] EDpatterns were obtained for all T_p, the relative amount of phase Ⅰ increasing with T_p. Polymerization of naphthalenedicarboxylic acid/hydroquinione diacetate 1/1 mixtures at high T_p also yielded lamellar crystals that "curled up" off of thesubstrate. When the high temperature CTFMP polymerization was conducted between mica, aggregates of lamellae on-edgedeveloped but epitaxial growth did not occur. Epitaxial growth of lamellae between mica could be obtained, however, byconfined thin film solution polymerization, with both of the latter samples yielding apparently related ED patterns from adifferent unit cell than phase Ⅰ or Ⅱ. Fiber patterns, obtained from sheared samples, indicated considerably greater crystaldisorder than in the nascent crystals. Refinement of the phase Ⅰ unit cell parameters, based on the [001] and [01 1] EDpatterns, with modeling based on Cerius~2, suggests a monoclinic phase Ⅰ unit cell with a = 7.76, b = 5.71, c = 14.99 A, α = γ= 90°, β= 99.7°, ρ = 1.47 g/cm~3, space group P12_1/al.     

Generation of high energy and good beam quality pulses with a master oscillator power amplifier

A high efficiency and high peak power laser system with short-pulse and good beam quality has been demonstrated by using a master oscillator power amplifier with two-pass amplification configuration. The master oscillator, end-pumped with a fiber-coupled laser diode array, provides low power but excellent beam quality pulses, and the amplifier boosts the pulse energy by orders without significant beam quality degradation. Short pulses of 8.5 ns with energy up to 130 mJ and approximately diffraction limited beam quality have been demonstrated.     

原子核的单粒子共振态

采用基于相对论平均场的耦合常数解析延拓方法研究球形核的单粒子共振态.具体计算了Zr同位素链中巨晕核的核芯核122Zr阈值附近的中子共振态的能量、宽度和波函数,其结果同相应的散射相移法的结果一致. Using analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory, the energies, widths and wave functions for single-particle resonant states close to the continuum threshold are evaluated. Predictions are also compared with corresponding results obtained by the scattering phase shift method.