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We analyze the critical connectivity of systems of penetrable d-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers, and edges are for ...
Lattices abound in nature—from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic proto ...
Which spaces look like an n-sphere through the eyes of the n-th Postnikov section functor and the n-connected cover functor? The answer is what we call the Postnikov genus of the n-sphere. We define in fact the notion of localization genus for any homotopi ...
We construct blow-up solutions of the energy critical wave map equation on R2+1→N with polynomial blow-up rate (t−1−ν for blow-up at t=0) in the case when N is a surface of revolution. Here we extend the blow-u ...
Let L be a lattice in . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in . The first method is based on the observation that if the sphere is sufficiently small then the la ...
Packings of granular materials are complex systems consisting of large sets of particles interacting via contact forces. Their internal structure is interesting for several theoretical and practical reasons, especially when the model system consists in a l ...
We study time and space equivariant wave maps from M×R→S2, where M is dieomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metric on M can be written as $dr^2+f^2(r)d\theta ...
The last quarter of a century has seen a dramatic rise of interest in the spatial constraints on multisensory integration. However, until recently, the majority of this research has investigated integration in the space directly in front of the observer. T ...
We propose a new, general, method for spatial filtering by beam-forming. The desired filter, specified analytically on an n-dimensional sphere, is extended to n+1-dimensional Euclidean space. A continuous beamforming function is then obtained by the n+1-di ...
Connections between quantum anomalies and transformations of pseudomeasures of the type of Feynman pseudomeasures are studied. Mathematical objects related to the notion of the volume element in an infinite-dimensional space considered in the physics liter ...
