Estimation of the Reliability of a Stress–Strength System from Poisson Half Logistic Distribution

This paper discussed the estimation of stress-strength reliability parameter R=P(Y<X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student’s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis–Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.     

基于串并联电阻法的半偏思想测量电表内阻

利用中学物理实验中半偏法测量电表内阻的思想,通过给电表并联和串联电阻,调节串并联电阻的阻值使电表指针达到满偏和半偏的方法测量电表内阻,拓展了测量电表内阻的方法。     

Synthesis and characterization of chiral poly(alkyl isocyanates) by coordination polymerization using a chiral half‐titanocene complex

A new chiral half‐titanocene complex, [CpTiCl₂(O‐(S)?2‐Bu)], is synthesized and characterized by ¹H and ¹³C NMR spectroscopy. This complex is employed for the coordination polymerization of n‐butyl and n‐hexyl‐ isocyanate leading to chiral polymers, as revealed by their CD spectra. Only the left‐handed helix is produced, due to the chiral (S)?2‐butoxy group, which is bound to the polymer chain end. The polymerization of 3‐(triethoxysilyl)propyl isocyanate produces less soluble polymers. On the other hand, phenyl isocyanate reacts slowly with the complex leading quantitatively and selectively to triphenyl isocyanurate. 2‐Ethylhexyl isocyanate is slowly and selectively cyclotrimerized in the presence of the half‐titanocene complex. However, a statistical copolymer of 2‐ethylhexyl isocyanate and hexyl isocyanate is produced. The reaction of benzyl isocyanate with the complex leads to a mixture of low molecular weight polymer and cyclotrimer. The polymers are characterized using SEC, NMR, and CD spectroscopy and their thermal properties are investigated by TGA/DSC analysis. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2141–2151     

Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

Critical comparison of radiometric and mass spectrometric methods for the determination of radionuclides in environmental, biological and nuclear waste samples

The radiometric methods, alpha (α)-, beta (β)-, gamma (γ)-spectrometry, and mass spectrometric methods, inductively coupled plasma mass spectrometry, accelerator mass spectrometry, thermal ionization mass spectrometry, resonance ionization mass spectrometry, secondary ion mass spectrometry, and glow discharge mass spectrometry are reviewed for the determination of radionuclides. These methods are critically compared for the determination of long-lived radionuclides important for radiation protection, decommissioning of nuclear facilities, repository of nuclear waste, tracer application in the environmental and biological researches, these radionuclides include ³H, ¹⁴C, ³⁶Cl, ⁴¹Ca, ^59,63Ni, ^89,90Sr, ⁹⁹Tc, ¹²⁹I, ^135,137Cs, ²¹⁰Pb, ^226,228Ra, ²³⁷Np, ²⁴¹Am, and isotopes of thorium, uranium and plutonium. The application of on-line methods (flow injection/sequential injection) for separation of radionuclides and automated determination of radionuclides is also discussed.     

铜线拉丝模具的优化设计

针对当前铜线拉拔过程中,铜线拉丝速度提高,模具磨损加重的问题,通过对铜线拉丝模具的几何尺寸和金属丝塑性变形的数学分析,基于经典的上界定理,建立数学模型,求解在铜线拉拔过程中,具有最小功率下铜线拉丝模具压缩区的最佳锥角,并估计其误差。采用拼合的凹模模拟铜杆拉拔过程,测得拉拔因子,同时就模具的材质、润滑条件和拉拔力对最佳锥角的影响进行了讨论。研究表明,当铜线截面压缩率为20％～25％之间时,铜线拉丝模具压缩区的锥角2α控制在17°～20°的范围中为最优,此时铜线拉拔过程可有效减少模具磨损,延长了模具寿命。     

一种求解半定规划的邻近外梯度算法

本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.     

Heat kernel estimates for the Bessel differential operator in half‐line

In the paper we consider the Bessel differential operator in half‐line , , and its Dirichlet heat kernel . For , by combining analytical and probabilistic methods, we provide sharp two‐sided estimates of the heat kernel for the whole range of the space parameters and every , which complements the recent results given in 1 , where the case was considered.     

Synthesis of molecular motors incorporating para-phenylene-conjugated or bicyclo[2.2.2]octane-insulated electroactive groups

The insulating role of the bicyclo[2.2.2]octane fragment has been theoretically evaluated by comparing the electronic coupling parameter (V(ab)) in 1,4-bis(ferrocenyl)benzene (1) and 1,4-bis(ferrocenyl)bicyclo[2.2.2]octane (2). The geometries were optimized by DFT and an extended Hückel calculation was performed to evaluate V(ab) by the dimer splitting method. The calculations showed a 12-fold decrease of the electronic coupling from 60 meV for 1 to 5 meV for 2. The second part describes the synthesis of two potential molecular motors with one incorporating the insulating bicyclo[2.2.2]octane fragment. These molecules are based on a ruthenium complex bearing a tripodal stator functionalized to be anchored onto surfaces. The ferrocenyl electroactive groups and the cyclopentadienyl (Cp) rotor are connected through a p-phenylene spacer (5) or through a spacer incorporating an insulating bicyclo[2.2.2]octane moiety (6).