Related papers: Higher Order Spreading Models
In the study of asymptotic geometry in Banach spaces, a basic sequence which gives rise to a spreading model has been called a good sequence. It is well known that every normalized basic sequence in a Banach space has a subsequence which is…
We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
For every cube $Q \subset \mathbb{R}^n$ we let $X_Q$ be a quasi-Banach function space over $Q$ such that $\|\chi_Q\|_{X_Q} \simeq 1$, and for $X= \{X_Q\}$ define \begin{align*} \|f\|_{\mathrm{BMO}_X} &:=\sup_Q…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
Motivated by the geometry of certain hyperplane arrangements, Manin and Schechtman defined for each positive integer n a hierarchy of finite partially ordered sets B(n, k), indexed by positive integers k, called the higher Bruhat orders.…
For any non-trivial convex and bounded subset $C$ of a Banach space, we show that outside of a $\sigma$-porous subset of the space of non-expansive mappings $C\to C$, all mappings have the maximal Lipschitz constant one witnessed locally at…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
We provide a new succession rule (i.e. generating tree) associated with Schr\"oder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schr\"oder and Baxter generalizations of…
The Bers embebbing realizes the Teichm\"uller space of a Fuchsian group $G$ as a open, bounded and contractible subset of the complex Banach space of bounded quadratic differentials for $G$. It utilizes the schlicht model of Teichm\"uller…
In this paper, we first show that for a Banach space $X$ there is a fully order reversing mapping $T$ from ${\rm conv}(X)$ (the cone of all extended real-valued lower semicontinuous proper convex functions defined on $X$) onto itself if and…
This paper discusses the dimension of spline spaces with highest order smoothness over hierarchical T-meshes over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space with highest order…
We consider spline functions over simplicial meshes in $\RR^n$. We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of…
For a Banach space $X$, we show that any family of graphs quasi-isometric to levels of a warped cone $\mathcal O_\Gamma Y$ is an expander with respect to $X$ if and only if the induced $\Gamma$-representation on $L^2(Y;X)$ has a spectral…
A projectional skeleton in a Banach space is a sigma-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko…
Using a technique of adjoining an order unit to a normed linear space, we have characterized strictly convex spaces among normed linear spaces and Hilbert spaces among strictly convex Banach spaces respectively. This leads to a…
We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension,…