Physical Sciences and Mathematics Commons^™

Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We show that any symmetry of a smooth strict feedforward system is conjugated to a scaling translation and any 1-parameter family of symmetries to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We deduce, in accordance with our previous work, that a smooth system is feedback equivalent to a strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry whose flow is conjugated to a 1- parameter families of scaling translations and, …

Random Dynamics (Siuc 2006 Outstanding Scholar Public Lecture), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Large Deviations For Stochastic Systems With Memory, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

We establish a large deviations principle for stochastic delay equations driven by small multiplicative white noise. Both upper and lower large deviations estimates are obtained.

Periodic Prime Knots And Toplogically Transitive Flows On 3-Manifolds, William Basener, Michael C. Sullivan

Articles and Preprints

Suppose that φ is a nonsingular (fixed point free) C¹ flow on a smooth closed 3-dimensional manifold M with H₂(M)=0. Suppose that φ has a dense orbit. We show that there exists an open dense set N ⊆ M such that any knotted periodic orbit which intersects N is a nontrivial prime knot.

Bass Series For Small Witt Rings, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao

Articles and Preprints

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2.

In Part 1, we prove general existence and compactness theorems for C^k-cocycles of semilinear see’s and spde’s. Our results cover a large class of semilinear see’s as well as certain semilinear spde’s with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the …

Factoring Positive Braids Via Branched Manifolds, Michael C. Sullivan

Articles and Preprints

We show that a positive braid is composite if and only if the factorization is "visually obvious" by placing the braid k in a specially constructed smooth branched 2- manifold B(k) and studying how a would-be cutting sphere meets B(k). This gives an elementary proof of a theorem due to Peter Cromwell.