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.     

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.     

Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals

Let M₁,…,M_n be right modules over a ring R. Suppose that the endomorphism ring of each module M_i has at most two maximal right ideals. Is it true that every direct summand of M₁⊕?⊕M_n is a direct sum of modules whose endomorphism rings also have at most two maximal right ideals? We show that the answer is negative in general, but affirmative under further hypotheses. The endomorphism ring of uniserial modules, that is, the modules whose lattice of submodules is linearly ordered under inclusion, always has at most two maximal right ideals, and Pavel P?íhoda showed in 2004 that the answer to our question is affirmative for direct sums of finitely many uniserial modules.     

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.     

Renewable-surface sol-gel derived carbon ceramic electrode fabricated by [Ru(bpy)(tpy)Cl]PF6 and its application as an amperometric sensor for sulfide and sulfur oxoanions

A highly sensitive and fast responding sensor for the determination of thiosulfate, sulfite, sulfide and dithionite is described. It consists of a chemically modified carbon ceramic composite electrode (CCE) containing [Ru(bpy)(tpy)Cl]PF6 complex that was constructed by the sol-gel technique. A reversible redox couple of Ru(II)/Ru(III) was observed as a solute in acetonitrile solution and as a component of carbon based conducting composite electrode. Electrochemical behavior and stability of modified CCE were investigated by cyclic voltametry, the apparent electron transfer rate constant (kappa(S)) and transfer coefficient (a) were determined by cyclic voltametry which were about 28 s(-1) and 0.43 respectively. Electrocatalytic oxidation of S(2-), SO3(2-), S2O4(2-) and S2O3(2-) were effective at the modified electrode at significantly reduced overpotentials and in the pH range 1-11. Optimum pH values for amperometric detection of thiosulfate, dithionite, sulfide and sulfite are 7, 9, 2 and 2. Under the optimized conditions the calibration curves are linear in the concentration ranges 1-500, 3-80, 2-90 and 1-100 microM for S2O3(2-), SO3(2-), S2- and S2O4(2-) determination. The detection limit (signal to noise is 3) and sensitivity are 0.5 and 12, 2.8 and 6, 1.6 and 8, and 0.65 microM and 80 nA microM(-1) for thiosulfate, sulfite, sulfide and dithionite detection. The modified carbon ceramic electrode doped with Ru-complex shows good reproducibility, a short response time (t < 2 s), remarkable long term stability (> 6 month) and especially good surface renewability by simple mechanical polishing (RSD for eight successive polishing is 2%). The advantages of this sulfur compound amperometric detector based on ruthenium doped CCE are high sensitivity, inherent stability at a broader pH range, excellent catalytic activity, less expense and simplicity of preparation in comparison with recently published papers. This sensor can be used as a chromatographic detector for analysis of sulfur derivatives.     

A tetra-coordinate nickel(II) complex as neutral carrier for nitrate-selective PVC membrane electrode

The potentiometric response properties and applications of a tetra-coordinate nickel(II) complex with relatively high selectivity toward nitrate ion are described. The nickel(II) complex of 5,7,12,14-tetramethyl-1,4,8,11-tetraazacyclotetradeca-4,6,11,13-tetraene was used as a neutral carrier into plasticized poly(vinyl chloride) (PVC) membrane. The influence of several variables was investigated in order to optimize the potentiometric response and selectivity of the electrode. The resulting membrane electrode incorporating 31.0% PVC, 61.0% dioctyl phthalate (DOP) as plasticizer, 3% methyltrioctylammonium chloride (MTOAC) as a cationic additive and 5% carrier (all w/w) demonstrates a Nernstian response slope of −59.6 mV per decade over the concentration range of 5×10⁻⁶-1×10⁻¹ M NO₃⁻. The electrode exhibits a fast response time (≤10 s), a detection limit of 2.5×10⁻⁶ M, and can be used over a wide pH range of 4-12. The electrode shows improved selectivity in comparison to most of the previously reported nitrate-selective electrodes. It was successfully applied to the determination of nitrate ion in natural water samples.