Given a conjugation C on separable complex Hilbert space H, bounded linear operator T H is said to be C-skew symmetric if CTC = -T*. This paper describes the maps, algebra of all operators acting that preserve difference for every H.

Let R = K[x;σ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based ...

We consider polynomial maps of the form f(z,w) = (p(z), q(z,w)) that extend as holomorphic maps of CP. Mattias Jonsson introduces in “Dynamics of polynomial skew products on C2” [Math. Ann., 314(3): 403– 447, 1999] a notion of connectedness for such polynomial skew products that is analogous to connectivity for the Julia set of a polynomial map in one-variable. We prove the following dichotomy:...

EXPLOSION POINTS IN SKEW MAPS Anne Stefanie Costolanski, MS George Mason University, 2007 Thesis Director: Dr. Evelyn Sander This paper describes various chaotic behavior present in skew maps. Some aspects common in the study of dynamical systems are explored: the existence of homoclinic orbits, the behavior of manifolds, chaotic attractors, and period doubling cascades; and for each, the simil...

The Hénon family of planar maps is considered driven by the Arnold family of circle maps. This leads to a five-parameter family of skew product systems on the solid torus. In this paper the dynamics of this skew product family and its perturbations are studied. It is shown that, in certain parameter domains, Hénon-like strange attractors occur. The existence of quasi-periodic Hénon-like attract...

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

Strong starters and skew starters have been widely used in various combinatorial designs. In particular skew balanced starters and symmetric skew balanced starters are crucially used in the construction of completely balanced Howell rotations. Let n = 2mfc + 1 be an odd prime power where m > 2 and k is an odd number. The existence of symmetric skew balanced starters for GF(n) has been proved fo...

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.