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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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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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Fundamental Solutions in Elasticity
2019This chapter is concerned with the fundamental solutions of the systems of equations in the linear theory of elasticity for materials with quadruple porosity.
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