X-Ray Mapping and Interpretation of Scatter Diagrams

Electron beam induced quantitative X-ray mapping has become a very useful characterisation tool for determining the elemental distribution in materials, whether using energy dispersive spectroscopy or wavelength dispersive spectroscopy. The X-ray intensity distributions of the elements from an X-ray map allow us to generate two dimensional and ternary scatter diagrams thus converting spatial information into concentration dimensions, which is an important tool for displaying the spatial relationships of elements or correlated elements (phases) in materials. To best understand how to use this tool, we need to understand the production and features of the scatter diagram. The type of clustering observed in the scatter diagram, whether oval, linear or spherical, can give the major and trace element distributions within phases as well as qualitative and quantitative phase information. This paper demonstrates the generation of scatter diagrams, properties of scatter diagrams, interpretation of scatter diagrams and the advantages of scatter diagrams through the use of examples.     

On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

A high‐resolution scheme for low Mach number flows

A method for computing low Mach number flows using high‐resolution interpolation and difference formulas, within the framework of the Marker and Cell (MAC) scheme, is presented. This increases the range of wavenumbers that are properly resolved on a given grid so that a sufficiently accurate solution can be obtained without extensive grid refinement. Results using this scheme are presented for three problems. The first is the two‐dimensional Taylor–Green flow which has a closed form solution. The second is the evolution of perturbations to constant‐density, plane channel flow for which linear stability solutions are known. The third is the oscillatory instability of a variable density plane jet. In this case, unless the sharp density gradients are resolved, the calculations would breakdown. Under‐resolved calculations gave solutions containing vortices which grew in place rather than being convected out. With the present scheme, regular oscillations of this instability were obtained and vortices were convected out regularly. Stable computations were possible over a wider range of sensitive parameters such as density ratio and co‐flow velocity ratio. Copyright © 2004 John Wiley Sons, Ltd.     

On Optimality Condition for Vector Optimization Based on Convex Set-Valued Mapping

1.IntroductionTheoptimalityconditionsofmathematicalprogrammingisaveryimportantsubjectbecausetLeyprovideausefulanalyticaltoolforstudingthedualitytheoryandnonlinearprogrammingalgoirthms.Inrecelltyears,someauthorshavebeguntostudytheoptimalityconditionsforvectoroptimizationproblemofset-valuedmapping,suchas[4][51.Inthispaperlwedefinetheconceptofcone--weaklyefficientsubdifferentialofset-valuedmappinginthecaseofgeneralpartiallyorderedlocallyconvextopologicalvectorspaces.Thecone-weaklysubdifferential…     

Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity

We study the solvability and Galerkin approximation of an exterior hyperelastic interface problem arising in plane elasticity. The weak formulation is obtained from an appropriate combination of a mixed finite element approach with a Dirichlet-to-Neumann method. The derivation of our results is based on some tools from nonlinear functional analysis and the Babuska-Brezzi theory for variational problems with constraints.     

映象方程多解问题的某些研究

本文用ｆｐ－同伦方法，在一定的技巧和变换的配合下，在紧性条件支持下，研究了赋范线性空间中一类集值映象方程的多解问题。还给出所得理论结果的一个应用。