On existence and asymptotic stability of solutions of a nonlinear integral equation

We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question.     

Ultrasonic investigation of amorphous carbon in various frequencies at low temperatures from 2.1 to 300 K

Using pulse echo overlap measurement, the elastic behavior of amorphous carbon has been studied at ambient and low temperatures. The smaller ratio B/G of the bulk modulus to shear modulus and smaller Poisson's ratio σ at room temperature indicate that there is an intrinsic stiffening of transverse acoustic phonons in the amorphous carbon. The acoustic velocity and attenuation for longitudinal modes have been measured between 2.1 and 300 K at three frequencies of 7, 21 and 35 MHz, respectively. Their frequency and temperature dependence are observed. The elastic constant C₁₁ increases with decreasing temperature and show enhanced stiffening at low temperatures. In the 130-220 K region, the abnormal change and effect of longitudinal velocity and attenuation with temperature and frequency, and a phase transition associated with structure relaxations are discussed.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Nucleon Compton Scattering in the Perturbative Limit

The paper presents results of perturbative calculations for nucleon Compton scattering. The results are given for the real incoming photon and for the virtual incoming photon.     

实二次函数域基本单位的范

作为Ｈ．Ｆ．Ｔｒｏｔｔｅｒ［３］中一个结果的模拟，本文给出实二次函数域Ｋ中基本单位ε的范为Ｎ（ε）＝ｇ的一些充分必要条件，其中ｇ为Ｋ的常数域Ｆｑ的非零乘法群Ｆｑ＾＊的生成元（２├ｑ）。利用图论的语言，本文还给出了Ｎ（ε）＝ｇ的一些充分条件，这些条件对于数域也同样地适用，从而推广了Ｔｒｏｔｔｅｒ［３］和前人工作中关于充分条件的结果。     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

Dimensional Properties of Fractional Brownian Motion

Let B^α = {B^α（t）,t E R^N} be an （N,d）-fractional Brownian motion with Hurst index α∈ （0, 1）. By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion.     

聚丙烯微孔膜的等离子体接枝聚合改性

利用拉伸时的晶型转变致孔特性,从β晶相聚丙烯经单向或双向拉伸制得了新型聚丙烯微孔膜、用等离子体接枝聚合技术接上了亲水性聚合物如聚丙烯酸、聚丙烯腈等。研究了等离子体处理时间、单体性质对得到的亲水膜的亲水性、离子/溶质渗透性的影响。发现接枝聚丙烯酸的双向拉伸膜对Na~+、Mg~(++),尿素有较大的渗透性,并具有优良的形状稳定性。