| Analytic methods for diophantine equations and diophantine inequalities, 2d ed. |
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| Number theory has been enriched by diophantine analysis since the third century, but it is still a very active study and includes many open questions and conjectures. |
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| In number theory many problems may be posed as diophantine equations to be solved in integers. |
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| He developed Kronecker's polynomial ideals and presented many results on discriminants of forms, elimination theory and Diophantine problems. |
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| He also made contributions to analytic number theory, Diophantine analysis and numerical functions. |
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| His early work was on number theory and he wrote on Diophantine inequalities and the geometry of numbers. |
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| That conjecture offers a new way of expressing Diophantine problems, in effect translating an infinite number of Diophantine equations into a single mathematical statement. |
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| In addition Poinsot worked on number theory and on this topic he studied Diophantine equations, how to express numbers as the difference of two squares and primitive roots. |
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| Then, the controller parameters are derived from general solution of Diophantine equation. |
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| Keywords Diophantine equation, positive integer solutions, elementary method. |
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| The system design approach utilizing the Diophantine equation is not a state-variable system design technique. |
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| The consecutive controller design was performed through the solution of Diophantine equation. |
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| Suitable and efficient tools for description and derivation are algebraic notions as rings, polynomial matrices, and Diophantine equations. |
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| Also it is known that the solution of sets of Diophantine equations is a generator of primes. |
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| Unlike most other Diophantine equations, LDEs can be solved algorithmically. |
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| Further, the controller is derived from general solutions of Diophantine equations in the ring of proper and stable rational functions. |
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| In the algebraic approach the controller is obtained by solving the Diophantine equation corresponding to the 1DOF feedback loop in Fig. |
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| A set of stabilizing controllers are given by a solution of Diophantine equation in this ring. |
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| The book can be used for a graduate course on Diophantine approximation, or as an introduction for non-experts. |
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| The consecutive controller is derived through parameterized solutions of Diophantine equations in the ring of proper and stable rational functions. |
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| Penrose draws upon classes of mathematical problems for which no computational solution exists, including the tiling problem as well as certain Diophantine equations. |
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