Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff , the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasi-coherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of preshe...

Abstract In this paper, a novel approach has been followed based on FEM simulation and Topology Optimization tools to locate model the reinforcements inside hull of sailing dinghy. This process assumes that inner volume included between deck is, at beginning simulation, filled with material; then portion is eroded until final free form shape obtained. A key point procedure definition optimizati...

A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization solver; interna...

The aim of this paper is to describe Quillen model category structures on the category CatC of internal categories and functors in a given finitely complete category C. Several non-equivalent notions of internal equivalence exist; to capture these notions, the model structures are defined relative to a given Grothendieck topology on C. Under mild conditions on C, the regular epimorphism topolog...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

Network topology discovery is the basis for any network management application. The problem of estimating internal structure and link-level performance from end-to-end measurements is known as network tomography. This paper proposes a novel approach to discover network characteristics, in particular, tree topology from end-to-end path metrics between OD (Origin – Destination) pairs. The approac...

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS3 with a sevendimensional internal space. In one duality frame the only other nonvanishing fields are the NS three-form and the dilaton. We analyse in detail how these local solutions can be extended to globally well-defined solutions of type IIB string theory, with the int...

Recognition of 3-dimensional objects with complex internal geometries relies more heavily on topology than external shape. We discuss a novel voxelization rescaling algorithm intended to preserve topological structure even at low resolutions, appropriate for artistic reproductions of complex geometries. Introduction: Voxels and Motivations Voxels are the 3-dimensional analog of pixels; a filled...