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1992
Up to now, all applications of the Dual Reciprocity Method considered is this book were related to the Laplace operator. This means that the governing partial differential equations were initially recast as some kind of Poisson’s equation and the fundamental solution of Laplace’s equation employed to obtain an equivalent integral formulation.
P. W. Partridge +2 more
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Up to now, all applications of the Dual Reciprocity Method considered is this book were related to the Laplace operator. This means that the governing partial differential equations were initially recast as some kind of Poisson’s equation and the fundamental solution of Laplace’s equation employed to obtain an equivalent integral formulation.
P. W. Partridge +2 more
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1993
Abstract We can apply this result in the theory of Diophantine inequalities to the basic plan for classifying Haken manifolds. Remember that the 3-manifold M consists of tetrahedrons—that is, a set of sets of four vertices. Furthermore, any normal surface consists of squares and triangles in the tetrahedrons.
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Abstract We can apply this result in the theory of Diophantine inequalities to the basic plan for classifying Haken manifolds. Remember that the 3-manifold M consists of tetrahedrons—that is, a set of sets of four vertices. Furthermore, any normal surface consists of squares and triangles in the tetrahedrons.
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2003
In Section 3.2, we saw how, using various tricks, solutions in rational x and y of x 2 — dy 2 = 1 could be obtained from two solutions of an equation x 2 - dy 2 = k. Sometimes, the rational numbers turned out to be integers. The chances of this happening would apparently improve with the number of solutions of x 2 - dy 2 = k for a particular k.
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In Section 3.2, we saw how, using various tricks, solutions in rational x and y of x 2 — dy 2 = 1 could be obtained from two solutions of an equation x 2 - dy 2 = k. Sometimes, the rational numbers turned out to be integers. The chances of this happening would apparently improve with the number of solutions of x 2 - dy 2 = k for a particular k.
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Distributions and Fundamental Solutions
2015This chapter is an introduction to distribution theory illustrated by the verification of fundamental solutions of the classical operators \(\Delta _{n}^{k},(\lambda -\Delta _{n})^{k},(\Delta _{n}+\lambda )^{k},\partial _{\bar{z}}, (\partial _{t}^{2} - \Delta _{n})^{k},\partial _{1}\cdots \partial _{k},(\partial _{t} -\lambda \Delta _{n})^{k},(\partial
Norbert Ortner, Peter Wagner
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Examples of Fundamental Solutions
2017When the number \(n \ge 4\) of independent variables is even, the exponent m defined in Eq. ( 17.3.2) is a positive integer and the construction of U in Sect. 17.4 no longer holds, because the whole algorithm (see Eq. ( 17.4.4)) involves division by \((l-m)\), which vanishes when \(l=m\).
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Fundamentals of Solution Growth
1989In order for growth to occur the solute species must move from the bulk solution to the crystal surface, be adsorbed on the crystal surface, move to a step, and finally move to a kink on the step. If ionic species are involved then dehydration and chemical reaction may also be required.
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