here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to catalog the higher homotopical information required to restore constructibility (or more precisely, functoriality) in such “up to homotopy” settings. The firs...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

Homotopy type theory is a recent research area connecting type theory with homotopy theory by interpreting types as spaces. In particular, one can prove and mechanize type-theoretic analogues of homotopy-theoretic theorems, yielding “synthetic homotopy theory”. Here we consider the Seifert–van Kampen theorem, which characterizes the loop structure of spaces obtained by gluing. This is useful in...

We calculate the homotopy groups of K(S) in terms of the homotopy groups of K(Z), the homotopy groups of CP∞ −1, and the homotopy groups of S. This completes the program begun by Waldhausen, who computed the rational homotopy groups (building on work of Quillen and Borel), and continued by Rognes, who calculated the groups at regular primes in terms of the homotopy groups of CP∞ −1, and the hom...

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this me...

What is a homotopy theory T? – Examples of homotopy theories (Tpair presentation) – The homotopy category Ho(T) – Examples of homotopy categories – Model category: (C, E) with extras – Examples of model categories (C, E) – Dividends from a model category structure on (C, E) – Equivalences between homotopy theories – T(C, E) ∼ T(C′, E ′) for model categories – Examples of equivalences between ho...