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Max-plus fundamental solution semigroups for a class of difference Riccati equations [PDF]
Automatica, 2015 Recently, a max-plus dual space fundamental solution semigroup for a class of difference Riccati equation (DRE) has been developed. This fundamental solution semigroup is represented in terms of the kernel of a specific max-plus linear operator that ...
Peter M Dower
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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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Preconditioners Based on Fundamental Solutions
BIT Numerical Mathematics, 2005A new type of preconditioner is used in solving systems of linear algebraic equations obtained from the finite difference discretization of partial differential equations. This preconditioner is a discretization of an approximate inverse given by a convolution-like operator with the fundamental solution as a kernel.
Brandén, H., Sundqvist, P.
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2004
Trajectories of a dynamical system, starting from a particular initial state, might evolve towards a steady state of the system. A steady state can be an equilibrium of the system but can also be a (quasi-)periodic motion. The stability of equilibria is (for the hyperbolic case) determined by the eigenvalues of the local linearization of the system ...
Remco I. Leine, Henk Nijmeijer
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Trajectories of a dynamical system, starting from a particular initial state, might evolve towards a steady state of the system. A steady state can be an equilibrium of the system but can also be a (quasi-)periodic motion. The stability of equilibria is (for the hyperbolic case) determined by the eigenvalues of the local linearization of the system ...
Remco I. Leine, Henk Nijmeijer
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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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A Note on fundamental solutions
Communications in Partial Differential Equations, 1999(1999). A Note on fundamental solutions. Communications in Partial Differential Equations: Vol. 24, No. 1-2, pp. 369-376.
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Fundamental solution of a dissipative operator [PDF]
, 1997 Summary: The fundamental solution \(K\) of a third-order operator \(L_\varepsilon\) is explicitly determined and various properties of \(K\) are analyzed. As an example of applications, the explicit solution of the initial-valued problem with arbitrary data is deduced.
D'ACUNTO, BERARDINO +2 more
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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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