For spaces localized at 2, the classical EHP fibrations [1, 13] ΩS S ΩS ΩS play a crucial role for the computations of the homotopy groups of the spheres [16, 25]. The EHP-fibrations for (p− 1)-cell complexes for p > 2 are given in this article. These fibrations can be regarded as the odd prime analogue of the classical EHP-fibrations by considering the spheres as 1-cell complexes for p = 2. So...

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σand Π-types, a...

A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplacemethodwhich is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the prop...

Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested o...

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

The hadroproduction of lepton pairs with mass Q and transverse momentum QT can be described in pertur-bative QCD by the same partonic subprocesses as prompt photon production. We demonstrate that, like prompt photon production, lepton pair production is dominated by quark-gluon scattering in the region QT > Q/2. This leads to sensitivity to the gluon density in kinematical regimes that are acce...

We develop an unambiguous and practical method to calculate one-loop quantum corrections to the energies of classical time-independent field configurations in renormalizable field theories. We show that the standard pertur-bative renormalization procedure suffices here as well. We apply our method to a simplified model where a charged scalar couples to a neutral " Higgs " field, and compare our...

In this paper, a new iterative method for solving the system of nonlinear equations is suggested based on Newton-Raphson method and homotopy analysis method. Comparison of the result obtained by present method with Newton-Raphson method and homotopy perturbation method reveals that the accuracy and fast convergence of the proposed method.

This paper is the extended introduction of a series of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in dihomotopy theory is explained.

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is computed.