in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

y In this paper we calculate the 2-primary v 1-periodic homotopy groups of the sym-plectic groups Sp(n). The proof utilizes new methods of calculating the unstable Novikov spectral sequence. One corollary is that some homotopy group of Sp(n) contains an element of order 2 2n?1. 1 Main theorem In this paper we calculate the 2-primary v 1-periodic homotopy groups of the sym-plectic groups Sp(n). ...

Although homotopy-based methods, namely homotopy analysis method and homotopy perturbation method, have largely been used to solve functional equations, there are still serious questions on the convergence issue of these methods. Some authors have tried to prove convergence of these methods, but the researchers in this article indicate that some of those discussions are faulty. Here, after crit...

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coh...

A fundamental construction in the study of stable homotopy is the free infinite loop space generated by a space X. This is the colimit QX = lim −→ ΩΣX. The i homotopy group of QX is canonically isomorphic to the i stable homotopy group of X. Thus, one may obtain stable information about X by obtaining topological results about QX. One such result is the Kahn-Priddy theorem [7]. In another direc...

In this paper we define new homotopy groups for topological spaces. These groups generalize the homotopy groups of Hurewicz. By the use of these groups and by improved methods we obtain new results about the ordinary homotopy groups, and also easier proofs of known results. Among other things, we can show that 76(S3) is non-trivial. 1. One of the principal problems of modern topology is to devi...

We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...

We investigate the following problems. Given a spherical fibration, does the Whitehead square of its homotopy Thom class vanish? If so, is the homotopy Thorn class a cyclic homotopy class?

Homotopy classes of trajectories, arising due to the presence of obstacles, are defined by the set of trajectories joining same start and end points which can be smoothly deformed into one another by gradual bending and stretching without colliding with obstacles. Despite being mostly an uncharted research area, homotopy class constraints often appear in path planning problems. For example, in ...