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The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

Highly Degenerate Quadratic Forms Over F2, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

Closed-Neighborhood Anti-Sperner Graphs, John P. Mcsorley, Alison Marr, Thomas D. Porter, Walter D. Wallis

Articles and Preprints

For a simple graph G let N_G[u] denote the closed-neighborhood of vertex u ∈ V (G). Then G is closed-neighborhood anti-Sperner (CNAS) if for every u there is a v ∈ V (G)\{u} with N_G [u] ⊆ N_G [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if N_H[u] ≠ N_H[v] when u ≠ v, for all u and v ∈ V (H).

In this paper we …

Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino

Articles and Preprints

We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.

Explicit Factorizations Of Cyclotomic And Dickson Polynomials Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

We give, over a finite field F_q, explicit factorizations into a product of irreducible polynomials, of the cyclotomic polynomials of order 3·2ⁿ, the Dickson polynomials of the first kind of order 3·2ⁿ and the Dickson polynomials of the second kind of order 3·2ⁿ  − 1.