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We study a positive characteristic analog of the nonabelian Hodge structure constructed by Katzarkov, Pantev, and Toen on the homotopy type of a complex algebraic variety. Given a proper smooth scheme X over a perfect field of characteristic p and a Tannakian category C of isocrystals on X, we construct an object XC in a suitable homotopy category of simplicial presheaves whose category of loca...

The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is tak...

We propose a notion of groupoid homotopy for generalized maps. This notion of groupoid homotopy generalizes the notions of natural transformation and strict homotopy for functors. The groupoid homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the orbifold homotopy between orbifold maps induced by the...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

Simplicial formal maps were introduced in the first paper of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a natural generalisation can handle much more general backgrounds. The question of the geometric interpretation of these formal maps is partially answered in terms of combinatorial bun...

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of (n − 1)-connected (n + 1)-types for n ≥ 0. Introduction The computation of homotopy groups of spheres in low degrees in [Tod62] uses heavily secondary ...

La provincia de Vilcashuamán, cuyo significado es “Halcón Sagrado” en idioma quechua, se ubica Ayacucho. Esta presenta grandes posibilidades consolidar un destino turístico orden cultural debido al patrimonio ancestral que posee, desde los tiempos la Confederación Chanca y después como parte del Imperio Incaico, pudiera integrarse a circuito destaque zona central, con producto impulse el desarr...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...