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.     

有限宽度楔的反射和衍射实验

通过实验验证了Clay和Kinney提出的楔组合法的时域计算理论,获得了相当一致的结果。     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

Some hydrodynamic aspects of 3-phase inverse fluidized bed

Hydrodynamics of 3-phase inverse fluidized bed is studied experimentally using low density particles for different liquid and gas velocities. The hydrodynamic characteristics studied include pressure drop, minimum liquid and gas fluidization velocities and phase holdups. The minimum liquid fluidization velocity determined using the bed pressure gradient, decreases with increase in gas velocity. The axial profiles of phase holdups shows that the liquid holdup increases along the bed height, whereas the solid holdup decreases down the bed. However, the gas holdup is almost uniform in the bed.     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

学了统计学可以有什么样的作为?(续)──介绍统计学的特点和用处

Ⅲ、统计学家是做什么的? 为了描述统计学家工作的各个领域,最好的方法是给出大量的事例.限于篇幅,这里叙述六个事例.第一个事例描述统计学家的一个新的且很有希望的出路,就是在私人单位里当顾问.许多统计学家例如大学里的那些统计学家,在个人的部分时间从事于这种顾问工作. 经历1 A.B.先生与几个公司和研究所一起工作.几乎每周一次,每次花两到四小时与他的委托人中的每一个人联系,虽然他极少看见他们中的一些人.他与他们中的许多人每天都要通过电话谈话.他经常研究他们的问题,并且为了进行工作他或者重复写他的指示或者根据研究的结果所进…     

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.     

MAURER-CARTAN EQUATION OF A_∞-ALGEBRAS

§ 0　IntroductionA∞ - algebras were first introduced and applied by Stasheff in [12 ,13].Recently,theyappeared in both mathematics and mathematical physics[1 ,5— 8,1 0 ] .An A∞ - algebra is a Z-graded vector space over a fixed field k with a sequence of graded maps mn∶ A n→ A ofdegree n- 2 (n≥ 1) satisfying certain axioms (see [5 ,6 ,12 ,13]) .In this paper,we focusour attentions on,as we call,the minimal A∞ - algebras,which are usual A∞ - algebrasdefined in [5 ,6 ,12 ,13]with m1 =…