Mesh shape-quality optimization using the inverse mean-ratio metric

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.     

Large-scale linear programming: Geometry,working bases and factorizations

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.     

Linear and quadratic programming in oriented matroids

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.     

Syntheses of morpholine-2,3-diones and 2-hydroxymorpholin-3-ones: intermediates in the synthesis of aprepitant

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.     

The interaction of Ag with Si(111)

Deposits of Ag on Si(111), at room temperature, have yielded a linear Auger signal-time characteristic to a gradient break point at (7.6 ± 0.9) × 10¹⁴ atoms ofAg cm^?2, which is very close to the Si surface state density of (8–10) × 10¹⁴ cm^?2, and which supports a Stranski-Krastanov growth mechanism. Analysis of the Auger spectra at the monolayer end point revealed a new peak at 82 ± 1 eV. This peak is believed to arise from an Auger process involving an induced Ag-Si interface state. A model is proposed for this state arising from the chemisorption of Ag on Si.     

On the characterization of dihydro-oxazin-6-ones and N-acetylazetidin-2-ones by mass spectrometry

Mass spectrometry has been used in an attempt to resolve the ambiguity in the structures of the isomeric dihydro-oxazin-6-ones and N-acyl-azetidin-2-ones.     

Relative escape depth of Auger and photoelectrons from a solid surface

A new method of determining the escape depth of electrons in the energy range 0–1000 eV is described. Values obtained were 6.1 Å and 6.8 Å at 234 and 266 eV, respectively, in GeO₂.