We consider a skew product with the interval [0,a] as a fiber space and maps in fibers that are concave and fix 0. If the map in the base is an irrational rotation of a circle, then it has been known that under some additional conditions there exists a Strange Nonchaotic Attractor (SNA) for the system. The proofs involved Lyapunov exponents and Birkhoff Ergodic Theorem. We show that the existen...

In the context of Cosmic Microwave Background data analysis, we study solution to equation that transforms scanning into a map. As originally suggested in "messenger" methods for solving linear systems, split noise covariance uniform and non-uniform parts adjust their relative weights during iterative solution. With simulations, mock instrumental with different properties, find this "cooling" o...

New Zealand’s Defence Technology Agency (DTA) has developed a model to explore new methodologies for modelling warfare. The model, Map-Aware Non-Uniform Automata (MANA), is based on the ideas of complexity science, and is intended to capture at least some of the non-linear dynamics inherent in actual combat. It does so by treating the many “intangible” aspects of combatant behaviour in terms of...

For second harmonic generation in two-dimensional wave-guiding structures composed of segments that are invariant in the longitudinal direction, we develop an efficient numerical method based on the Dirichlet-to-Neumann (DtN) maps of the segments and a marching scheme using two operators and two functions. A Chebyshev collocation method is used to discretize the longitudinal variable for comput...

We provide a Laakso construction to prove that the property of having an equivalent norm with the property (β) of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the other hand, we show that the (β)-modulus is not quantitatively preserved via such a map by exhibiting two uniformly homeomorphic Banach spaces that do not have (β)-mo...

Water-fat separation in magnetic resonance imaging (MRI) is of great clinical importance, and the key to uniform water-fat separation lies in field map estimation. This work deals with three-point field map estimation, in which water and fat are modelled as two single-peak spectral lines, and field inhomogeneities shift the spectrum by an unknown amount. Due to the simplified spectrum modelling...

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

We establish the sharp rate of continuity extensions ℝm-valued 1-Lipschitz maps from a subset A ℝn to on ℝn. consider several cases when there exists extension with preserved uniform distance given map. prove that if m > 1, then map is and affine only such preserving for any defined This shows striking difference case = where function has property. Another example we it possible find an same Li...

Following a similar result of Uspenskij on the unitary group of a separable Hilbert space we show that with respect to the lower (or Roelcke) uniform structure the Polish group G = Aut(μ), of automorphisms of an atomless standard Borel probability space (X,μ), is precompact. We identify the corresponding compactification as the space of Markov operators on L2(μ) and deduce that the algebra of r...

In this thesis, we survey the current research into self-complementary hypergraphs, and present several new results. We characterize the cycle type of the permutations on n elements with order equal to a power of 2 which are k-complementing. The k-complementing permutations map the edges of a k-uniform hypergraph to the edges of its complement. This yields a test to determine whether a finite p...