Research Article Modified Noor iterations with errors for nonlinear equations in Banach spaces

We introduce a new three step iterative scheme with errors to approximate the unique common fixed point of a family of three strongly pseudocontractive (accretive) mappings on Banach spaces. Our results are generalizations and improvements of results obtained by several authors in literature. In particular, they generalize and improve the results of Mogbademu and Olaleru [A. A. Mogbademu and J. O. Olaleru, Bull

Banach

Convergence theorems of a general approximation method for common fixed points of a finite family of asymptotically-quasi nonexpansive mappings i

Research Article

Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a partial functional differential equation in Banach space

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

Low-Energy Brane-World Effective Actions and Partial Supersymmetry Breaking

As part of a programme for the general study of the low-energy implications of supersymmetry breaking in brane-world scenarios, we study the nonlinear realization of supersymmetry which occurs when breaking N=2 to N=1 supergravity. We consider three explicit realizations of this supersymmetry breaking pattern, which correspond to breaking by one brane, by one antibrane or by two (or more) parallel branes. We derive the minimal field content, the effective action and supersymmetry transformation rules for the resulting N=1 theory perturbatively in powers of kappa = 1/M_{Planck}. We show that the way the massive gravitino and spin-1 fields assemble into N=1 multiplets implies the existence of direct brane-brane contact interactions at order O(kappa). This result is contrary to the O(kappa^2) predicted by the sequestering scenario but in agreement with recent work of Anisimov et al. Our low-energy approach is model independent and is a first step towards determining the low-energy implications of more realistic brane models which completely break all supersymmetries.Comment: Latex, 29 Page

Quasistatic crack growth based on viscous approximation: a model with branching and kinking.

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking

Deformation Twin Formed By Self-Thickening, Cross-Slip Mechanism In Nanocrystalline Ni

We report the observation of a deformation twin formed by a recently proposed self-thickening, cross-slip twinning mechanism. This observation verifies one more twinning mechanism, in addition to those reported before, in nanocrystalline face-centered-cubic metals. In this mechanism, once the first Shockley partial is emitted from a grain boundary, and cross slips onto another slip plane, a deformation twin could nucleate and grow in both the primary and cross-slip planes without requiring the nucleation of additional Shockley partials from the grain boundary

Non-Fourier effect and inertia effect analysis of a strip with an induced crack under thermal shock loading

In this paper, the transient temperature fields and the dynamic stress intensity factors of a thermo-elastic strip containing an inner crack parallel to the heated surface under thermal shock are studied. The Biot number of the crack gap, hyperbolic heat conduction theory and equation of motion are considered to investigate the behavior of the temperature fields around the crack and the stress intensity factors. Fourier transform and Laplace transform are used to reduce this mixed boundary value problem. Numerical methods are used to solved the singular integrate equations. Finally, the numerical results are presented illustrating the influence of Biot number, non-Fourier effect and inertia effect on temperature field and stress intensity factors. It is found that the Biot number strongly affect the uniformity of the temperature field and the magnitude of the stress intensity factors. The stress intensity factors have higher amplitude and an oscillating feature comparing to those obtained under conventional Fourier thermal conduction condition and quasi-static hypothesis, which can help to better understand the crack behaviors of advanced materials under thermal impact loading. (C) 2016 Elsevier Ltd. All rights reserved

Microstructural evolution and formation of nanocrystalline intermetallic compound during surface mechanical attrition treatment of cobalt

Nanocrystalline intermetallic Co3Fe7 was produced on the surface of cobalt via surface mechanical attrition (SMA). Deformationinduced diffusion entailed the formation of a series of solid solutions. Phase transitions occurred depending on the atomic fraction of Fe in the surface solid solutions: from hexagonal close-packed (11% Fe). Nanoscale compositional probing suggested significantly higher Fe contents at grain boundaries and triple junctions than grain interiors. Short-circuit diffusion along grain boundaries and triple junctions dominate in the nanocrystalline intermetallic compound. Stacking faults contribute significantly to diffusion. Diffusion enhancement due to high-rate deformation in SMA was analyzed by regarding dislocations as solute-pumping channels, and the creation of excess vacancies. Non-equilibrium, atomic level alloying can then be ascribed to deformation-induced intermixing of constituent species. The formation mechanism of nanocrystalline intermetallic grains on the SMA surface can be thought of as a consequence of numerous nucleation events and limited growth. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved