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.     

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.     

Reproducing-kernel-based splines for the regularization of the inverse ellipsoidal gravimetric problem

To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not stable. Since the anharmonic part (orthogonal complement) of the density function produces a zero potential, we restrict our attention only to reconstruct the harmonic part of the density function by using the gravitational potential. This spline interpolation method gives the existence and uniqueness of the unknown solution. Moreover, this method represents a regularization, i.e. every spline continuously depends on the given gravitational potential. These splines are also combined with a multiresolution concept, i.e. we get closer and closer to the unknown solution by increasing the scale and adding more and more data at each step.     

Riemann–Roch theory for weighted graphs and tropical curves

We define a divisor theory for graphs and tropical curves endowed with a weight function on the vertices; we prove that the Riemann–Roch theorem holds in both cases. We extend Baker’s Specialization Lemma to weighted graphs.     

Trapped-ion quantum logic gates based on oscillating magnetic fields

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.