Fixed Point Theorems for Weakly Contractive Mappings in Ordered Metric Spaces with an Application

In this paper, we prove fixed point theorem for weakly contractive mappings using locally $T$-transitivity of binary relation and presenting an analogous version of Harjani and Sadarangani theorem involving more general relation theoretic metrical notions. Our fixed point results under universal relation reduces to Harjani and Sadarangani [Nonlinear Anal., 71 (2009), 3403–3410] fixed point theorems. In this way we also generalize some of the recent fixed point theorems for weak contraction in the existing literature.     

Heisenberg's uncertainty relation of position and momentum in experiments without mutual disturbance

Arranging target atoms in a plane monolayer, one may produce by atomic or nuclear reaction an ensemble of particles with small initial position spread without disturbing their momentum spread. This would either allow a violation of Heisenberg's uncertainty relation, by creating a situation not described by quantum mechanics hence rendering quantum mechanics incomplete, or, if the uncertainty relation should hold also in this non-disturbative situation, it would mean a permanent violation of energy conservation. Thus an uncertainty relation for position and momentum and energy conservation appear to be mutually exclusive.1. Recently also Croca [5] proposed another way of determining a x without interfering with p_X.2. To forbid even speaking of an initial position spread smaller than that indicated by the wave function [6] would amount to circular reasoning and the denial of a falsification of quantum mechanics.     

Shear rheometry of polydimethylsiloxanes. Master curves and testing of Gleissle and Yamamoto relations

This study concerns the shear rheometry of a series of nine silicone fluids, all linear or branched polydimethylsiloxanes (PDMS), with varying mass distributions.The use of a rotative rheometer enabled characterization of these products in a dynamic regime for about five decades of pulsation . In addition, because of the use of rotative rheometers together with a capillary rheometer with controlled piston speed, the behavior of these products could be determined for about six orders of magnitude of shear rate , notably for the permanent regime viscosity coefficient .On the other hand, to obtain the variations of the first normal stress difference coefficient ₁, over a significant range of shear rate , it was necessary to complete the experimental measurements by using empirical relations. Particularly, after having defined the application conditions, the Gleissle and Yamamoto relations were tested for these products.Finally, all the results obtained in dynamic and in transitory regimes by using the rheometers and empirical relations mentioned above were combined in dimensionless form. Indeed, the existence of master curves for the linear and branched PDMS was demonstrated. Our study therefore enables the validity of the master curve method, initially established for a series of linear monodisperse polystyrenes, to be extended to the case of a family of linear or branched PDMS of wide mass distribution.     

在镍系钙钛矿(ABO_3)型催化剂上的氨氧化 Ⅲ.焙烧温度对催化剂结构和活性的影响

本文探讨了焙烧温度对催化剂结构及氨氧化活性的影响。得出:La_(0.9)Sr_(0.1)NiO_(3-λ)在1223K后分解,生成具有K_2NiF_4结构的La_2NiO_4相,NiO相和LaNiO_3相。催化活性相主要是具有钙钛矿结构的组分。最佳活性相在1273K形成。     

On the fractional Newton and wave equation in one space dimension

We consider the new mathematical scenarios in the framework of the Fractional Calculus. In this context, we study the generalized fractional virial theorem as well as the fractional plane wave solutions and the fractional dispersion relations for the fractional wave equation.     

On the moments of order statistics coming from the Topp–Leone distribution

We present recurrence relations for the moments of order statistics from the Topp–Leone distribution without any restriction for the shape parameter. Several relations are also derived when the shape parameter is an integer. An application of the results is provided.     

Composite of discotic liquid crystal and gold nanoparticles: A comperative band gap study

Nanocomposites of discotic liquid crystal namely 2, 3, 6, 7, 10, 11-hexabutyloxytryphenylene (HAT4) in existence of variable concentration of gold nanoparticles (GNPs) have been studied at room temperature and zero pressure. The absorption spectra of nanocomposites are captured by a Shimadzu UV–VIS Spectrophotometer, model UV-1800, in the wavelength range 900–200?nm. In this paper using the Tauc’s relation, the absorption spectra fitting method was applied to estimate the optical band gap. Nanocomposites are prepared by mixing of GNPs with four concentrations in pure HAT4 viz. 0.2, 0.6, 1.2 and 3?wt%. From the investigation of absorption spectra, it has been observed that with the enhance of GNPs concentration in pure HAT4 band gap has decreased for lower concentrations but for higher concentration (3?wt%) it increases.     

基于模糊关系矩阵的可生存系统认知参考模型分析

提出了一种可生存系统认知参考模型的分析方法.基于四维可扩展的可生存系统认知参考模型,确立可生存系统的认知、自律、生存3个基本属性;基于模糊关系矩阵对可生存系统认知参考模型进行分析,计算得出3个基本属性在可生存系统中的贡献率及关联度;仿真实验对可生存系统实施DDOS攻击,导致3个基本属性及其子属性的贡献率发生变化,仿真结果判断出在该时刻可生存系统中哪些属性及其子属性处于主导地位.     

Alternative model for computing intensity patterns through apertured ABCD systems

We propose an alternative model based on mode conversion for computing axial and transverse intensity field distributions of apertured systems. We then develop a new method for the integration of oscillating functions that derive from the model. The integration technique we developed is efficient, very fast and would be useful in many other fields of physics.