On fail‐safe systems under random shocks

In practical situations, systems often suffer shocks from external stressing environments, stressing the system at random. These random shocks may have non‐ignorable effects on the system's reliability. In this paper, we provide sufficient (and necessary) conditions on components' lifetimes and their surviving probabilities from random shocks for comparing the lifetimes of two fail‐safe systems by means of the usual stochastic, hazard rate, and likelihood ratio orderings. Numerical examples are presented to highlight these theoretical results as well.     

Weak Module Amenability for Semigroup Algebras

We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.     

Synthesis of methacrylate derivatives oligomers by dithiobenzoate‐RAFT‐mediated polymerization

Reversible addition fragmentation chain transfer (RAFT) was used to synthesize methacrylic acid oligomers and oligo(methacrylic acid)‐b‐poly(methyl methacrylate) (PMAA‐b‐PMMA) with targeted degree of polymerization ≈ 10. Characterization is by size‐exclusion chromatography (SEC) and electrospray mass‐spectrometry. SEC data are presented as hydrodynamic volume distributions (HVDs), the only proper means to present comparative and meaningful SEC data when there is no unique relationship between size and molecular weight. The RAFT agent, (4‐cyanopentanoic acid)‐4‐dithiobenzoate (CPADB), produced dithiobenzoic acid as a side product during the polymerization of methacrylate derivatives. Precipitation in diethyl ether proved to be an easy way to remove this impurity from the PMAA‐RAFT oligomers. Both unpurified and purified macro‐RAFT agent were used to prepare amphiphilic PMAA‐b‐PMMA copolymers. Diblock copolymer prepared from the purified PMAA homopolymer had a narrower HVD in comparison to those obtained from the equivalent unpurified macro‐RAFT agent. This work shows that while cyanoisopropyl‐dithiobenzoate or CPADB are good RAFT agents for methacrylate derivatives, they exhibit some instability under typical polymerization conditions, and thus when oligomers are targeted, optimal control requires checking for the degradation product and appropriate purification steps when necessary (the same effect is present for larger polymers but is unimportant). © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2277–2289, 2008     

Stability analysis of methods employing reducible rules for Volterra integral equations

The concept of (A ₀,S)-stability, for numerical methods approximating solutions of Volterra integral equations, is formally defined. New stability polynomials for the recent multi-lag type methods are obtained. (A ₀, 1)-stability of these and other methods employing reducible quadrature rules are also investigated.     

Band selection of hyperspectral-image based weighted indipendent component analysis

Huge amounts of data in hyperspectral images have been caused to represent approaches for the band selection of these images. In this paper, a new approach based on independent component analysis (ICA) is proposed. The idea of projection pursuit is used to order the bands on the basis of a non-gaussianity distribution. Applying a negentropy function to weight bands is a novel idea that leads to the selection of bands with minimum mutual information (MI) and besides maximum entropy, with respected to the bands selected using other methods.     

Effect of citric acid concentration as emulsifier on perovskite phase formation of nano‐sized SrMnO3 and SrCoO3 samples

In this study the effects of citric acid concentration, used as organic emulsifier, on the perovskite phase formation of the nano strontium manganite or cobaltite samples were studied. Stoichiometric perovskites in the absence and presence of citric acid were prepared by drying a solution containing molar ratio of Sr(NO₃)₂/Mn(NO₃)₂·4H₂O and Sr(NO₃)₂/Co(NO₃)₂·6H₂O = 1 followed by calcination at 900 °C for 5 h. Citric acid concentration, selected to be 0.0, 0.3, 0.6, 1.0, 1.3, 2.5 and 5 times of the total number of moles of the nitrate ions. The results revealed that increase in the citric acid concentration, larger than number of moles of the nitrate ions equivalent, deteriorates the perovskite phase formation. Instead, a new phase of carbonates and metal oxides are appeared. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of fractional calculus on the formation of quantum-mechanical operators

In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed.     

An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations

A modified Levenberg–Marquardt method for solving singular systems of nonlinear equations was proposed by Fan [J Comput Appl Math. 2003;21;625–636]. Using trust region techniques, the global and quadratic convergence of the method were proved. In this paper, to improve this method, we decide to introduce a new Levenberg–Marquardt parameter while also incorporate a new nonmonotone technique to this method. The global and quadratic convergence of the new method is proved under the local error bound condition. Numerical results show the new algorithm is efficient and promising.     

A new numerical method for delay and advanced integro-differential equations

A general formulation is constructed for Jacobi operational matrices of integration, product, and delay on an arbitrary interval. The main purpose of this study is to improve Jacobi operational matrices for solving delay or advanced integro–differential equations. Some theorems are established and utilized to reduce the computational costs. All algorithms can be used for both linear and nonlinear Fredholm and Volterra integro-differential equations with delay. An error estimator is introduced to approximate the absolute error when the exact solution of a given problem is not available. The error of the proposed method is less compared to other common methods such as the Taylor collocation, Chebyshev collocation, hybrid Euler–Taylor matrix, and Boubaker collocation methods. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.     

Some remarks on the Hodge conjecture for abelian varieties

We show how the classical Hodge conjecture for the middle cohomology of an abelian variety is equivalent to the general Hodge conjecture for the middle cohomology of a smooth ample divisor in the abelian variety. This is best suited to abelian varieties with actions of imaginary quadratic fields.