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.     

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.     

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 .     

三元复合表面膜反射光谱的计算

将二元的金属－介质非均匀复合物的等效介质理论推广到三元的情况，并由此计算出两种铝阳极氧化着色谱试样的反射谱。与实验结果对比可看出，计算曲线与实验曲线大致相符，表明该计算方法在一定范围和条件下的适用性，从而为多元复合表面材料光特性的理论研究提供了一种可行的方法。     

Surface‐modified hydroxyapatite linked by L‐lactic acid oligomer in the absence of catalyst

A new surface modification method of hydroxyapatite nanoparticles (n‐HA) by surface grafting reaction of L ‐lactic acid oligomer with carboxyl terminal (LAc oligomer) in the absence of any catalyst was developed. The LAc oligomer with a certain molecular weight was directly synthesized by condensation of L ‐lactic acid. Surface‐modified HA nanoparticles (p‐HA) were attested by Fourier transformation infrared spectroscopy, ³¹P MAS‐NMR, and thermal gravimetric analysis (TGA). The results showed that LAc oligomer could be grafted onto the n‐HA surface by forming a Ca carboxylate bond. The grafting amount of LAc oligomer was about 13.3 wt %. The p‐HA/PLLA composites showed good mechanical properties and uniform microstructure. The tensile strength and modulus of the p‐HA/PLLA composite containing 15 wt % of p‐HA were 68.7 MPa and 2.1 GPa, respectively, while those of the n‐HA/PLLA composites were 43 MPa and 1.6 GPa, respectively. The p‐HA/PLLA composites had better thermal stability than n‐HA/PLLA composites and neat PLLA had, as determined by isothermal TGA. The hydrolytic degradation behavior of the composites in phosphate buffered saline (PBS, pH 7.4) was investigated. The p‐HA/PLLA composites lost their mechanical properties more slowly than did n‐HA/PLLA composites in PBS because of their reinforced adhesion between the HA filler and PLLA matrix. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5177–5185, 2005     

THE VALIDITY OF THE MODIFIED MORI-TANAKA METHOD FOR COMPOSITES WITH SLIGHTLY WEAKENED INTERFACE

This paper presents a direct Mori-Tanaka approach to calculate the effective moduli ofparticle-reinforced composites and fiber-reinforced composites with spring like imperfect interfaces.Bya comparison between these results and those obtained from the approximate Mori-Tanaka method de-veloped by Qu for composites with slightly weakened interface,the validity of the Qu's method is re-vealed.