In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the ...

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...

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...

In this paper, an efficient modification of homotopy perturbation method, namely optimal homotopy perturbation method, is introduced for solving linear and nonlinear partial differential equations with large solution domain based on a new homotopy perturbation method and Padé approximation method. We compare the performance of the method with those of new homotopy perturbation and optimal varia...

Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] 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 cross...

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the h...

s− and p−wave Λ single–particle energies are obtained for a variety of Λ hyper-nuclei from the relevant self–energy constructed within the framework of a pertur-bative many–body approach. Results are presented for present realistic hyperon– nucleon interactions such as Jülich B and Nijmegen SC models. Effects of the non–locality and energy–dependence of the self–energy on the bound states are i...

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...

Two of these homotopy types are known 2ï-spaces; namely, SU(3)XS and 5 £7(4). The other two are the new ü-spaces of the title, and a word is in order as to in what sense they are new. If one seeks differentiable manifolds which are H-spaces not homeomorphic to known iT-spaces, then recent work of Belfi [ l ] and Morgan [4] furnish a big supply. For example, there are infinitely many nonhomeomor...

A new class of homotopy continuation methods is developed suitable for globalizing quasiNewton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and ...