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991.
Hortensia Soto‐Johnson Michele Iiams Todd Oberg Barbara Boschmans April Hoffmeister 《School science and mathematics》2008,108(8):345-354
In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually. 相似文献
992.
Donocadh P. Lydon David Albesa‐Jové Gemma C. Shearman Judith A. K. Howard Todd B. Marder 《Liquid crystals》2013,40(2):119-132
Despite the prevalence of organised 1,4‐bis(phenylethynyl)benzene derivatives in molecular electronics, the interest in the photophysics of these systems and the common occurrence of phenylethynyl moeties in molecules that exhibit liquid crystalline phases, the phase behaviour of simple alkoxy‐substituted 1,4‐bis(phenylethynyl)benzene derivatives has not yet been described. Two series of 1,4‐bis(phenylethynyl)benzene derivatives, i.e. 1‐[(4′‐alkoxy)phenylethynyl]‐4‐(phenylethynyl)benzenes (5a–5f) and methyl 4‐[(4″‐alkoxy)phenylethynyl‐4′‐(phenylethynyl)] benzoates (18a–18f) [alkoxy = n‐C4H9 (a), n‐C6H13 (b), n‐C9H19 (c), n‐C12H25 (d), n‐C14H29 (e), n‐C16H33 (f)] have been prepared and characterised. Both series have good chemical stability at temperatures up to 210°C, the derivatives featuring the methyl ester head‐group (18a–18f) offering rather higher melting points and generally stabilising a more diverse range of mesophases at higher temperatures than those found for the simpler compounds (5a–5f). Smectic phases are stabilised by the longer alkoxy substituents, whereas for short and intermediate chain lengths of the simpler system (5a–5c) nematic phases dominate. Diffraction analysis was used to identify the SmBhex phase in (5d–5f) that is stable within a temperature range of approximately 120–140°C. The relationships between the organisation of molecules within these moderate temperature liquid crystalline phases and other self‐organised states (e.g. Langmuir‐Blodgett films) remain to be explored. 相似文献
993.
994.
We analyze a single step method for solving second-order parabolic initial-boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with those of Crank-Nicolson, as well as those of more general extrapolated theta-weighted schemes. We provide an example computation that illustrates both the use of step-doubling for adaptive time step control and the application of step-doubling to a nonlinear system.
995.
Todd Munson 《Mathematical Programming》2007,110(3):561-590
Meshes containing elements with bad quality can result in poorly conditioned systems of equations that must be solved when
using a discretization method, such as the finite-element method, for solving a partial differential equation. Moreover, such
meshes can lead to poor accuracy in the approximate solution computed. In this paper, we present a nonlinear fractional program
that relocates the vertex coordinates of a given mesh to optimize the average element shape quality as measured by the inverse
mean-ratio metric. To solve the resulting large-scale optimization problems, we apply an efficient implementation of an inexact
Newton algorithm that uses the conjugate gradient method with a block Jacobi preconditioner to compute the direction. We show
that the block Jacobi preconditioner is positive definite by proving a general theorem concerning the convexity of fractional
functions, applying this result to components of the inverse mean-ratio metric, and showing that each block in the preconditioner
is invertible. Numerical results obtained with this special-purpose code on several test meshes are presented and used to
quantify the impact on solution time and memory requirements of using a modeling language and general-purpose algorithm to
solve these problems. 相似文献
996.
997.
Michael J. Todd 《Mathematical Programming》1983,26(1):1-20
This paper is concerned with linear programming problems in which many of the constraints are handled implicitly by requiring that the vector of decision variables lie in a polyhedronX. It is shown that the simplex method can be implemented using a working basis whose size is the number of explicit constraints as long as the local structure ofX around the current point is known. Various ways of describing this local structure lead to known implementations whenX is defined by generalized or variable upper bounds or flow conservation constraints. In the general case a decomposition principle can be used to generate this local structure. We also show how to update factorizations of the working basis. 相似文献
998.
Michael J Todd 《Journal of Combinatorial Theory, Series B》1985,39(2):105-133
We prove constructively duality theorems of linear and quadratic programming in the combinatorial setting of oriented matroids. One version of our algorithm for linear programing has the interesting feature of maintaining feasibility. The development of the quadratic programming duality result suggests the study of properties of square matrices such as symmetry and positive semi-definiteness in the context of oriented matroids. 相似文献
999.
Syntheses of morpholine-2,3-diones and 2-hydroxymorpholin-3-ones: intermediates in the synthesis of aprepitant 总被引:1,自引:0,他引:1
Todd D. Nelson Jonathan D. Rosen Bridgette Craig James M. McNamara 《Tetrahedron letters》2004,45(48):8917-8920
The preparation of morpholine-2,3-diones and 2-hydroxymorpholin-3-ones from N-substituted β-amino alcohols is reported. These were useful intermediates in the synthesis and development of aprepitant. 相似文献
1000.