Elucidation of the accelerated sulfur vulcanization of bio oil-extended natural rubber compounds

The elucidation of the role of bio-oils on the accelerated sulfur vulcanization of natural rubber (NR) compounds is discussed in this study. Two types of bio-oil, palm oil and soybean oil, were studied in direct comparison with a distillate aromatic extract oil (DAE) as a reference. The scorch and cure times of the bio-oil-extended NR compounds were shorter than those containing DAE. The use of bio-oils gave a higher cure reaction rate constant along with a lower activation energy than the use of DAE. The attenuated total reflectance-Fourier transform infrared spectroscopy analysis revealed that the fatty acid segment of the bio-oils can react with zinc oxide to give zinc carboxylate, which is then involved in and promotes the vulcanization reaction. The use of bio-oils to increase the rate of vulcanization strongly influenced the crosslink density of the obtained NR vulcanizates, yielding NR vulcanizates with a lower crosslinking density. It is proposed here that the bio-oils might consume the curing agent via the reaction between their own unsaturated fatty acid and sulfur. This was supported by the increased viscosity of the oils after exposure to sulfur at a high temperature. The tensile strength and elongation at break of the bio-oil-extended NR compounds were lower and higher, respectively, than the NR extended with DAE oil due to the lower crosslink density of the bio oil-extended NR vulcanizates.     

Data analysis for accelerated life tests via Weibull-gamma frailty regression models

In this article, we study data analysis methods for accelerated life test (ALT) with blocking. Unlike the previous assumption of normal distribution for random block effects, we advocate the use of Weibull regression model with gamma random effects for making statistical inference of ALT data. To estimate the unknown parameters in the proposed model, maximum likelihood estimation and Bayesian estimation methods are provided. We illustrate the proposed methods using real data examples and simulation examples. Numerical results suggest that distribution of random effects has minimal impact on the estimation of fixed effects in the Weibull regression models. Furthermore, to demonstrate the advantage of our proposed model, we also provide methods to compare ALT plans and thus identify the optimal ALT plans.     

A stochastic approximation algorithm with multiplicative step size modification

An algorithm of searching a zero of an unknown function ϕ: ℝ → ℝ is considered: x _t = x _t−1 − γ _t−1 y _t , t = 1, 2, ..., where y _t = ϕ(x _t−1) + ξ _t is the value of ϕ measured at x _t−1 and ξ _t is the measurement error. The step sizes γ _t > 0 are modified in the course of the algorithm according to the rule: γ _t = min{uγ _t−1, } if y _t−1 y _t > 0, and γ _t = dγ _t−1, otherwise, where 0 < d < 1 < u, > 0. That is, at each iteration γ _t is multiplied either by u or by d, provided that the resulting value does not exceed the predetermined value . The function ϕ may have one or several zeros; the random values ξ _t are independent and identically distributed, with zero mean and finite variance. Under some additional assumptions on ϕ, ξ _t , and , the conditions on u and d guaranteeing a.s. convergence of the sequence {x _t }, as well as a.s. divergence, are determined. In particular, if P(ξ ₁ > 0) = P (ξ ₁ < 0) = 1/2 and P(ξ ₁ = x) = 0 for any x ∈ ℝ, one has convergence for ud < 1 and divergence for ud > 1. Due to the multiplicative updating rule for γ _t , the sequence {x _t } converges rapidly: like a geometric progression (if convergence takes place), but the limit value may not coincide with, but instead, approximate one of the zeros of ϕ. By adjusting the parameters u and d, one can reach arbitrarily high precision of the approximation; higher accuracy is obtained at the expense of lower convergence rate.      

Statistical analysis of progressive stress accelerated life test for the product of two-parameter Laplace BS fatigue life distribution under inverse power law model

Based on the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution, its failure distribution mode is theoretically derived under the progressive stress accelerated life test with inverse power law model, and then three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution is introduced. The basic properties of three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution are analyzed, and the image characteristics of its density function, failure rate function and average failure rate function are investigated. Meanwhile, the point estimate method is given for three parameters, and then the point estimates of parameters are obtained for the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution under the progressive stress accelerated life test with inverse power law model. In addition, the practical example and simulation examples are illustrated to show the feasibility of the proposed method.     

对数正态分布基于恒加试验的参数估计

讨论对数正态分布场合有非常数尺度参数恒加试验的参数估计,由最小均方误差准则导出基于完全样本恒加试验的点估计和近似区间估计.     

单参数指数分布产品截尾样本场合简单步进应力加速寿命试验损伤失效率模型下的统计分析

本文给出单参数指数分布产品截尾样本场合简单步进应力加速寿命试验损伤失效率模型下参数的极大似然估计和拟矩估计。     

On the Vector Process Obtained by Iterated Integration of the Telegraph Signal

We analyse the vector process (X ₀(t), X ₁(t),...,X _n(t), t > 0) where , and X ₀(t) is the o two-valued telegraph process.In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed.Special care is given to the case of the process (X ₀(t), X ₁(t), X ₂(t), t > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.     

Letter: Adiabatic Decaying Vacuum Model for the Universe

We study a model that the entropy per particle in the universe is constant. The sources for the entropy are the particle creation and a decaying term. We find exact solutions for the Einstein field equations and show the compatibility of the model with respect to the age and the acceleration of the universe.     

Radiation from Bodies with Extreme Acceleration II: Kinematics

When applied to a dipole source subjected to acceleration which is violent and long lasting (extreme acceleration), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount. The physical assumptions behind this result are made possible by the kinematics of a system of geometrical clocks whose tickings are controlled by cavities which are expanding inertially. For the purpose of measuring the radiation from such a source we take advantage of the physical validity of a spacetime coordinate framework (inertially expanding frame) based on such clocks. They are compatible and commensurable with the accelerated clocks of the accelerated source. By contrast, a common Lorentz frame with its mutually static clocks won't do: It lacks that commensurability. Inertially expanding clocks give a physicist a window into the frame of a source with extreme acceleration, and thus can locate that source and measure radiation from it without being subjected to such acceleration himself. The conclusion is that inertially expanding reference frames reveal qualitatively distinct aspects of nature which would not be accessible if inertial frames were the only admissible frames.     

Statistical evaluation of potash-lime-silica glass weathering

Two potash-lime-silica model glasses with compositions similar to those of medieval stained glass were exposed at 26 test sites all over Europe and in North America for 3–6 years. The objectives of this large-scale field exposure programme were: (a) a qualitative analysis of the weathering products formed on the surface of the samples in the (environmental) scanning electron microscope in combination with energy dispersive X-ray microanalysis (ESEM/EDX or SEM/EDX, respectively); (b) a statistical evaluation of the weathering phenomena by applying a multiple linear regression (MLR) analysis to find correlations between the degree of weathering, which was measured in terms of surface coverage with reaction products, and environmental parameters such as the concentration (c) of the acidifying gases SO₂, NO₂ and O₃, the temperature (T) and the relative humidity (RH); and (c) the calculation of a time-dependence function of the weathering process of these glasses. Mainly sulfates of calcium and potassium such as gypsum (CaSO₄·2 H₂O), arcanite (K₂SO₄) and syngenite (CaSO₄·K₂SO₄·H₂O) could be identified in the SEM and ESEM. Carbonates, nitrates and many particles deposited on the glass surface were found as well. MLR calculations exhibit significant dependencies of the degree of weathering on T, RH, c(NO_x), c(SO₂) and c(O₃). Applying a time-dependence function of the general form y=a·t^b (t=time) results in a value of approximately 0.42 for the exponent b, which comes close to values expected from various studies in the literature.