On Selfsimilar Jordan Curves on the Plane

We study the attractors of a finite system of planar contraction similarities S _j (j=1,...,n) satisfying the coupling condition: for a set {x ₀,...,x _n} of points and a binary vector (s ₁,...,s _n ), called the signature, the mapping S _j takes the pair {x ₀,x _n} either into the pair {x _j-1,x _j } (if s _j =0) or into the pair {x _j , x _j-1} (if s _j =1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis.     

Inertial effects of hypoelastic cylindrical bar of grade zero under simple extension of constant velocity

In this paper an analytical solution for finite deformation at the simple extension of a hypoelastic cylindrical bar of grade zero under constant velocity is obtained. It is found that the difference between stress-strain curves at different tensile velocities is only due to the inertial terms in the solution. The axial stress due to inertia increases with the square of ratio of tensile velocities.     

Diverse Imprecise Goal Programming Model Formulations

The goal programming (GP) model is probably the best known in mathematical programming with multiple objectives. Available in various versions, GP is one of the most powerful multiple objective methods which has been applied in much varied fields. It has also been the target of many criticisms among which are those related to the difficulty of determining precisely the goal values as well as those concerning the decision-maker's near absence in this modelling process. In this paper, we will use the concept of indifference thresholds for modelling the imprecision related to the goal values. Many classical imprecise and fuzzy GP model formulations can be considered as a particular case of the proposed formulation.     

Riccati方程与(2+1)维非线性物理模型的分离变量解

对于(2+1)维非线性物理模型,欲获其解并非易事.本文试图在变量分离法中,通过设定的R iccati方程来得到方程的解.同时,以(2+1)维Bo iti-L eon-M anna-P em p inelli方程和Burgers方程为例来说明之.     

Synthesis and characterization of water-soluble carbon nanotubes from mustard soot

Carbon nanotubes (CNT) has been synthesized by pyrolysing mustard oil using an oil lamp. It was made water-soluble (wsCNT) through oxidative treatment by dilute nitric acid and was characterized by SEM, AFM, XRD, Raman and FTIR spectroscopy. The synthesized wsCNT showed the presence of several junctions and defects in it. The presence of curved graphene structure (sp²) with frequent sp³ hybridized carbon is found to be responsible for the observed defects. These defects along with the presence of di- and tri-podal junctions showed interesting magnetic properties of carbon radicals formed by spin frustration. This trapped carbon radical showed ESR signal in aqueous solution and was very stable even under drastic treatment by strong oxidizing or reducing agents. Oxidative acid treatment of CNT introduced several carboxylic acid group functionalities in wsCNT along with the nicking of the CNT at different lengths with varied molecular weight. To evaluate molecular weights of these wsCNTs, an innovative method like gel electrophoresis using high molecular weight DNA as marker was introduced.     

Persistence of regions with high segment density in polyethylene melts

Proton nuclear magnetic resonance (NMR) spin-spin relaxation measurements were made on three commercial-grade polyethylenes in the melt state, free of solvent. All samples exhibit a three-component relaxation behavior, with components being assigned to amorphous low-molecular weight material (non-network fraction), amorphous entangled network fraction, and an ordered or high-segmental-density fraction, in order of decreasing relaxation times. Sample thermal history is shown to have a considerable effect on the overall relaxation behavior, and therefore on the relative amounts of each of the three components in the melt. An adequate thermal treatment of samples produces an equilibrium melt with invariant composition of the three fractions. The effects of thermal history on the relative amount of high-segment-density regions in the melt parallels its effect on the fraction of crystalline material in the solid polymer. These results are evidence for the persistence of ordered regions in polyethylene at temperatures well above the crystalline melting point of the polymer. We further comment on the nature of the two slower relaxing components and present examples of how the components manifest themselves in other polymer characterization techniques. © 1992 John Wiley & Sons, Inc.     

A class of B-(p,r)-invex functions and mathematical programming

Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems.     

The Spectrum of the Two-Dimensional Periodic Schrödinger Operator

The absence of eigenvalues (of infinite multiplicity) for the two-dimensional periodic Schrödinger operator with a variable metric is proved. The method of proof does not use the change of variables reducing the metric to a scalar form.     

关于整系数多项式有理根求法的注记

现行高等代数教材给出了求整系数多项式有理根的经典方法 ,周仲旺近日撰文又给出了一个新方法 ,称其“要比经典的方法有趣简捷”,但没有给出两个方法运算量的定量分析与比较 .本文先对经典方法从数学原理和算法设计两个方面作较详细明确的描述 ;再给出经典算法与周方法运算量的定量分析 ,比较的结果是周方法运算量比经典算法运算量多得多 .     

γ射线辐照石英玻璃吸收光谱的研究

石英玻璃以其低热膨胀系数、高紫外透过率而成为不可缺少的光学材料,但并不是所有的石英玻璃都可以作为光学材料。有些石英玻璃在短波长射线环境运行一段时间后,透过率下降,甚至变黑。哪些石英玻璃能够用于射线环境、哪些不能用?这要求对石英玻璃分类。美国Lawerence Livemore国家实验室提出的LL分类法中隐藏一个理论缺陷,即它暗中假定石英玻璃在γ射线照射下,只感生E′,D_0,B_1,Al等4条吸收带,虽然他们所接触的石英玻璃是这种情况,但缺乏理论依据,没有理由认为任何石英玻璃在γ射线照射下只有这4条感生吸收带,事实上确实有的石英玻璃在γ射线照射下还有其他感生吸收带,LL分类法就无法对这种石英玻璃归类。石英玻璃对γ射线的响应有三类,一是有响应的辐照变色石英玻璃,另一是没有响应的耐辐照石英玻璃,第三类是介于这两类之间的、不产生可见的感生吸收带但产生紫外感生吸收带的过渡类石英玻璃。石英玻璃耐γ射线照射的能力取决于杂质总量和羟基含量的比值;比值越大,耐辐照能力越差;比值大于2为变色石英玻璃,比值小于0.01为耐辐照石英玻璃;比值介于其间为紫外透过下降的石英玻璃,即过渡类石英玻璃。