Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

Finite difference technique for solving obstacle problems

In this paper, we use the variational inequality theory coupled with finite difference technique to obtain an approximate solution for a class of obstacle problems in elasticity, like those describing the equilibrium configuration of an elastic string stretched over an elastic obstacle. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution of the obstacle problems.     

Properties of Standard n-Ideals of a Lattice

An n-ideal of a lattice L is a convex sublattice containing a fixed element n L and it is called standard if it is a standard element of the lattice of n-ideals I_n(L). In this paper we have shown that, for a neutral element n of a lattice L, the principal n-ideal a_n of a lattice L is a standard n-ideal if and only if a n is standard and a n is dual standard. We have also shown that if n is a neutral element and (n] and [n) are relatively complemented, then every homomorphism n-kernels of L is a standard n-ideal and every standard n-ideal is the n-kernel of precisely one congruence relation. Finally, we have shown that, for a relatively complemented lattice L with 0 and 1, C(L) is a Boolean algebra if and only if every standard n-ideal of L is a principal n-ideal.AMS Subject Classification (2000) 06B10 06B99 06C15     

On Dual Invex Ky Fan Inequalities

In this paper, we obtain some new results for the dual invex Ky Fan inequalities in topological vector spaces. These results can be viewed as an extension and refinement of the previously known results of Noor and others.     

Wiener-Hopf equations technique for variational inequalities

In recent years, the theory of Wiener-Hopf equations has emerged as a novel and innovative technique for developing efficient and powerful numerical methods for solving variational inequalities and complementarity problems. In this paper, we provide an account of some of the fundamental aspects of the Wiener-Hopf equations with major emphasis on the formulation, computational algorithms, various generalizations and their applications. We also suggest some open problems for further research with sufficient information and references.     

Modified variational iteration method for solving Helmholtz equations

In this paper, we apply the modified variational iteration method (MVIM) for solving the Helmholtz equations. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.     

Global-local methodologies and their application to nonlinear analysis

An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified.     

Vibration analysis of quasi-symmetric structures

An efficient computational procedure is presented for the free vibration analysis of structures with unsymmetric geometry. The procedure is based on approximating the unsymmetric vibrational response of the structure by a linear combination of a few symmetric and antisymmetric modes (global approximation vectors), each obtained using approximately half the degrees of freedom of the original model. The three key elements of the procedure are: (a) use of mixed finite element models having independent shape functions for the internal forces (stress resultants) and generalized displacements, with the internal forces allowed to be discontinuous at interelement boundaries, (b) operator splitting, or additive decomposition of the different arrays in the governing finite element equations to delineate the contributions to the symmetric and antisymmetric response vectors, and (c) use of a reduction method through successive application of the finite element method and the classical Bubnov-Galerkin technique. The finite element method is first used to generate a few symmetric and antisymmetric global approximation response vectors. Then, the classical Bubnov-Galerkin technique is used to substantially reduce the size of the eigenvalue problem.

An initial set of global approximation vectors is selected to be a few symmetric and antisymmetric eigenvectors, and their various-order derivatives with respect to a tracing parameter identifying all the correction terms to the symmetric (and antisymmetric) eigenvectors. A modified (improved) set of approximation vectors is obtained by using the inverse iteration procedure. The effectiveness of the proposed procedure is demonstrated by means of a numerical example.     

Synthesis,physico-chemical and spectral investigations of novel homo-bimetallic mixed-ligand complexes: 57Fe Mössbauer parameters of [Fe2(imda)2(H2O)3Cl]

The newly prepared homo-bimetallic complexes [M₂(imda)₂(H₂O)₄], [M₂(imda)₂(Bipy)₂] (M = Co, Ni or Cu) and [Fe₂(imda)₂(H₂O)₃Cl] (H₂imda = iminodiacetic acid and Bipy = 2,2′-bipyridine) have been studied employing IR, FAB-mass, ¹H and ¹³C NMR, EPR and ligand field spectra, which indicated a high-spin state of metal ion with hexa-coordinate environment. ⁵⁷Fe Mössbauer data of the homo-bimetallic complex [Fe₂(imda)₂(H₂O)₃Cl] confirm a high-spin configuration with Fe (±3/2 → 1/2) nuclear transitions and the presence of Kramer's double degeneracy. At RT, the spin–spin interactions of the neighbouring nuclei (Fe³⁺–Fe³⁺ = S_5/2–S_5/2) are anti-ferromagnetically coupled. However, at LNT, the complex acquires a mixed-valent [Fe^III–Fe^II] composition corroborated from the X-band EPR data. CV studies indicated the presence of quasi-reversible redox Cu^II/I, Cu^II/III, Fe^III/II, Fe^III/I and Fe^II/I couples.     

Spectral and physico-chemical investigations of novel homo-dinuclear di-μ2-alkoxo bridged Schiff base complexes: 57Fe Mössbauer parameters of the Fe(III) complex

Spectral and molecular model computations on homo-dinuclear complexes [M₂L₂(H₂O)₂Cl₂] [L = 1-(salicylaldeneamino)-3-hydroxypropane, M = Cr³⁺, Mn³⁺, Fe³⁺, Co³⁺, Ni³⁺ or Cu³⁺] are consistent with a distorted hexa-coordinate geometry. X-band EPR spectral data indicated a rhombic distortion around Cu(II) ion. Magnetic moment and ⁵⁷Fe Mössbauer data confirmed a high-spin state electronic configuration (t_2g³e_g², S = 5/2) and asymmetric ligand environment around Fe(III) with nuclear transitions Fe(±3/2 → 1/2) exhibiting Kramer's double degeneracy. The neighboring Fe(III) nuclei in the homo-dinuclear species are antiferromagnetically coupled.