Inequalities Involving Integrals of Polar-Conjugate Concave Functions.
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.
Realization and nonrealization of Poincaré duality quotients of 𝔽₂[x,y] as topological spaces
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...
Stripping and conjugation in the mod p Steenrod algebra and its dual.
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