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Physical Sciences and Mathematics Commons™

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Southern Illinois University Carbondale

Series

2001

Articles 1 - 10 of 10

Full-Text Articles in Physical Sciences and Mathematics

How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall Dec 2001

How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall

Miscellaneous (presentations, translations, interviews, etc)

We describe all symmetries of a single-input nonlinear control system, that is not feedback linearizable and whose first order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation, bringing it to the canonical form, is analytic we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries, if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, …

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A Note On Visualizing Response Transformations In Regression, R. Dennis Cook, David J. Olive Nov 2001

A Note On Visualizing Response Transformations In Regression, R. Dennis Cook, David J. Olive

Articles and Preprints

A new graphical method for assessing parametric transformations of the response in linear regression is given. Simply regress the response variable Y on the predictors and find the fitted values. Then dynamically plot the transformed response Y(λ) against those fitted values by varying the transformation parameter λ until the plot is linear. The method can also be used to assess the success of numerical response transformation methods and to discover influential observations. Modifications using robust estimators can be used as well.

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Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed Sep 2001

Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed

Articles and Preprints

In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.

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The Stable Manifold Theorem For Stochastic Differential Equations (Dynamical Systems And Probability Seminar, Loughborough University), Salah-Eldin A. Mohammed Mar 2001

The Stable Manifold Theorem For Stochastic Differential Equations (Dynamical Systems And Probability Seminar, Loughborough University), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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The Stable Manifold Theorem For Stochastic Differential Equations (Analysis And Probability Seminar, University Of Hull), Salah-Eldin A. Mohammed Mar 2001

The Stable Manifold Theorem For Stochastic Differential Equations (Analysis And Probability Seminar, University Of Hull), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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Numerics Of Stochastic Systems With Memory (Applied Mathematics And Numerical Analysis Seminars, University Of Manchester), Salah-Eldin A. Mohammed Mar 2001

Numerics Of Stochastic Systems With Memory (Applied Mathematics And Numerical Analysis Seminars, University Of Manchester), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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Isotropy And Factorization In Reduced Witt Rings, Robert W. Fitzgerald Mar 2001

Isotropy And Factorization In Reduced Witt Rings, Robert W. Fitzgerald

Articles and Preprints

We consider reduced Witt rings of finite chain length. We show there is a bound, in terms of the chain length and maximal signature, on the dimension of anisotropic, totally indefinite forms. From this we get the ascending chain condition on principal ideals and hence factorization of forms into products of irreducible forms.

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Norms Of Sums Of Squares, Robert W. Fitzgerald Mar 2001

Norms Of Sums Of Squares, Robert W. Fitzgerald

Articles and Preprints

For a finite separable extension K/F of fields of characteristic not 2, the norm of a sum of 2n squares in K is a sum of 2n squares in F. We find explicit identities.

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High Breakdown Analogs Of The Trimmed Mean, David J. Olive Jan 2001

High Breakdown Analogs Of The Trimmed Mean, David J. Olive

Articles and Preprints

Two high breakdown estimators that are asymptotically equivalent to a sequence of trimmed means are introduced. They are easy to compute and their asymptotic variance is easier to estimate than the asymptotic variance of standard high breakdown estimators.

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Discrete-Time Approximations Of Stochastic Differential Systems With Memory, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan Jan 2001

Discrete-Time Approximations Of Stochastic Differential Systems With Memory, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop two discrete-time strong approximation schemes for solving stochastic differential systems with memory: strong Euler-Maruyama schemes for stochastic delay differential equations (SDDE's) and stochastic functional differential equations (SFDE's) with continuous memory, and a strong Milstein scheme for SDDE's. The convergence orders of the Euler-Maruyama and Milstein schemes are 0.5 and 1 respectively. In order to establish the Milstein scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use …

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