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We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas.
We give a full description of the structure under inclusion of all finite level Borel classes of functions, and provide an elementary proof of the well-known fact that not every Borel function can be ...
Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action...
Building on recent work by Rippon and Stallard, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results are expr...
On the structure of ($-\beta$)-integers     structure  math       2010/11/12
The $(-\beta)$-integers are natural generalisations of the $\beta$-integers, and thus of the integers, for negative real bases. When $\beta$ is a $(-\beta)$-number, which is the analogue of a Parry nu...
We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers...
We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.
The theme of the first two sections, is to prepare the framework of how from a "complicated" family of index models I in K_1 we build many and/or complicated structures in a class K_2. The index model...
Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. T...
A result of the author shows that the behavior of Gowers norms on bounded exponent abelian groups is connected to finite nilspaces. Motivated by this, we investigate the structure of finite nilspaces...
We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in...
We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated to the operation of increment of su...
This article describes in detail a new method via the extension predictable algorithm of the matter-element model of parallel structure tuning the parameters of the extension PID controller. In compar...
In this paper, we give a new description for the structure of the $p$-adic period subring $A_{cris}$ using formal groups.
We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.

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