We solve the problem of two-dimensional flow of a viscous fluid over a rectangular approximation of an etched hole. In the absence of inertia, the problem is solved by a technique involving the matching of biorthogonal infinite eigenfunction expansions in different parts of the domain. Truncated versions of these series are used to compute a finite number of unknown coefficients. In this way, the stream function and its derivatives can be determined in any arbitrary point. The accuracy of the results and the influence of the singularities at the mask-edge corners is discussed. The singularities result in a reduced convergence of the eigenfunction expansions on the interfaces of the different regions. However, accurate results can be computed for the interior points without using a lot of computational time and memory. These results can be used as a benchmark for other methods which will have to be used for geometries involving curved boundaries. The effect of hole size on the flow pattern is also discussed. These flow patterns have a strong influence on the etch rate in the different regions.
Abstract. This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.Key WOrds. Nonlinear programming, necessary and sufficient optimality conditions, strong and strict local minimizers, isolated minimizers.
We present some experiences obtained with the definition and preliminary design of a new generation command and control system for military applications. We will concentrate on the transfer of research results to development. During this phase, requirements have to be specified for the new system for which it is still hard to envision in detail the desired tasks that it should support. At the same time, the new technologies that are to enable these new capabilities are not known well enough to completely understand their possibilities. We will outline some approaches that, in our project, helped to be creative at the right time and specific and decisive when needed. These are storyboard, natural language and formal methods. We will indicate for each of them at what moment they can be best applied.
Finally, we indicate why any such approach used within a project does not guarantee widespread acceptance of its results by the remaining R&D population.
We study the continuous, desingularized Newton method for Weierstrass' }-functions. This leads to a family of autonomous differential equations in the plane, which depends on two complex parameters ! 1 and ! 2 . For the associated flows there are, up to conjugacy, precisely three possibilities. These are determined by the form of the parallelogram spanned by ! 1 and ! 2 : square, rectangular but not square, and non-rectangular.
We show that, for fixed dimension n, the approximation of inner and outer j-radii of polytopes in N", endowed with the Euclidean norm, is in P. Our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension.
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