Nanoscale manipulation of pyrochlore: new nanocomposite ionic conductors

The ionic conductivity of isometric pyrochlore, ideally A2B2O (7), is extremely sensitive to disordering of A- and B-site cations and oxygen anion vacancies. We report the first use of ion beam irradiation-induced disordering in Gd 2Ti 2O (7) to produce a strain-free, buried, disordered defect-fluorite layer approximately 12 nm thick within an ordered pyrochlore matrix. This approach provides a new means of creating nanoscale, mixed ionic-electronic conductors in pyrochlore ceramics, such as those required for solid-state electrochemical cells.     

The analysis of multigrid algorithms for cell centered finite difference methods

In this paper, we examine multigrid algorithms for cell centered finite difference approximations of second order elliptic boundary value problems. The cell centered application gives rise to one of the simplest non-variational multigrid algorithms. We shall provide an analysis which guarantees that the W-cycle and variable V-cycle multigrid algorithms converge with a rate of iterative convergence which can be bounded independently of the number of multilevel spaces. In contrast, the natural variational multigrid algorithm converges much more slowly.     

A coupled non-linear hyperbolic-sobolev system

Summary A boundary-initial value problem for a quasilinear hyperbolic system in one space variable is coupled to a boundary-initial value problem for a quasilinear equation of Sobolev type in two space variables of the form Mu_t(x, t)+L(t) u (x, t)=f(x, t, u(x, t)) where M and L(t) are second order elliptic spacial operators. The coupling occurs through one of the boundary conditions for the hyperbolic system and the source term in the equation of Sobolev type. Such a coupling can arise in the consideration of oil flowing in a fissured medium and out of that medium via a pipe. Barenblatt, Zheltov, and Kochina[2] have modeled flow in a fissured medium via a special case of the above equation. A local existence and uniqueness theorem is demonstrated. The proof involves the method of characteristics, some applications of results of R. Showalter and the contraction mapping theorem. Entrata in Redazione il 28 luglio 1976.     

Making Mathematical Connections Across the Curriculum: Activities to Help Teachers Begin

Ample evidence is available to support the contention that, for learning to be meaningful, concepts must be connected and integrated within the experiences of the learner. In mathematics, at least three kinds of connections are particularly beneficial: connections within mathematics, across the curriculum, and with real world contexts. The authors' work with preservice and inservice teachers has convinced them that teachers possess both the willingness and the capability to help students make meaningful connections, given encouragement and support. This article focuses on making mathematical connections across the curriculum; activities which help teachers learn how to design their own are shared.     

Parent Beliefs about Technology and Innovative Mathematics Instruction

Parent beliefs about roles of education, teachers, computers, and innovative mathematics instruction were examined through factor analysis. Strong relationships between parent beliefs regarding teacher and computer roles were found. The beliefs of parents about the similar roles of teachers and computers in education may impact the implementation of innovations in mathematics education and the uses of computers in education. Reciprocally, the ways computers are implemented in education may impact the beliefs parents have about the purposes of education.     

Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography

The simulated annealing (SA) algorithm is a well-established optimization technique which has found applications in many research areas. However, the SA algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule. This paper demonstrates that the temperature parallel simulated annealing (TPSA) algorithm, a parallel implementation of the SA algorithm, shows great promise to overcome these limitations when applied to continuous functions. The TPSA algorithm greatly reduces the computational time due to its parallel nature, and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process. The main contributions of this paper are threefold. First, this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature (T_C). Second, this paper presents systematic tests of the TPSA algorithm on various continuous functions, demonstrating comparable performance as well-established sequential SA algorithms. Third, this paper demonstrates the application of the TPSA algorithm on a difficult practical inverse problem, namely the hyperspectral tomography problem. The results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the TPSA algorithm.