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.     

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.     

Synthesis,X‐ray Studies,and Catalytic Efficacy of a Novel Iron Complex Containing an N,O‐Type Bidentate Thiazoline Ligand

The reactions of FeCl₃ · 6H₂O and 2‐(2′‐hydroxyphenyl)‐2‐thiazoline as a bidentate O‐N donor thiazoline ligand (thoz) afford a five‐coordinate Fe^III complex [Fe(thoz)₂Cl] with a distorted square pyramidal configuration. Complex [Fe(thoz)₂Cl] was isolated as air‐stable crystalline solids and fully characterized, including by single‐crystal X‐ray structure analysis. Complex [Fe(thoz)₂Cl] shows very efficient reactivity in the oxidation of sulfides to their corresponding sulfoxides using urea hydrogen peroxide (UHP) as the oxidant at room temperature in air.     

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.     

Coupled B-snake grids and constrained thin-plate splines foranalysis of 2-D tissue deformations from tagged MRI

Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which the authors track with coupled B-snake grids. B-spline bases provide local control of shape, compact representation, and parametric continuity. Efficient spline warps are proposed which warp an area in the plane such that two embedded snake grids obtained from two tagged frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a C¹ continuous vector field is interpolated. The implementation proposed in this paper improves on the authors' previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The methods are validated with a cardiac motion simulator, in addition to in-vivo tagging data sets     

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)     

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.