Postnikov homotopy decomposition

1977 ◽  
pp. 293-323
Author(s):  
Hans J. Baues
Keyword(s):  
Homotopy Decomposition

Homotopy Decompositions Involving the Loops of Coassociative Co-H Spaces

2003 ◽  
Vol 55 (1) ◽  
pp. 181-203 ◽  
Author(s):  
Stephen D. Theriault
Keyword(s):  
Homotopy Decomposition

AbstractJames gave an integral homotopy decomposition of ∑Ω∑X, Hilton-Milnor one for Ω(∑X ∨ ∑Y), and Cohen-Wu gave p-local decompositions of Ω∑X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.

scholarly journals Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kılıçman
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Biharmonic Equations ◽  
Poisson Equations ◽  
Physical Problems ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
2D And 3D ◽  
Corrected Function

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.

scholarly journals Homotopy decomposition of a suspended real toric space

2016 ◽  
Vol 23 (1) ◽  
pp. 153-161 ◽  
Author(s):  
Suyoung Choi ◽  
Shizuo Kaji ◽  
Stephen Theriault
Keyword(s):  
Homotopy Decomposition

scholarly journals The Time-Fractional Coupled-Korteweg-de-Vries Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aydin Secer
Keyword(s):  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
De Vries ◽  
Homotopy Analysis

We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).

Self-closeness number and weak homotopy decomposition.

2021 ◽  
Author(s):  
Ho Won Choi ◽  
Kee Young Lee
Keyword(s):  
Homotopy Decomposition ◽  
Weak Homotopy

scholarly journals Two-Dimension Hydrodynamic Dispersion Equation with Seepage Velocity and Dispersion Coefficient as Function of Space and Time

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Abdon Atangana ◽  
S. C. Oukouomi Noutchie
Keyword(s):  
Dispersion Equation ◽  
Dispersion Coefficient ◽  
Analytical Techniques ◽  
Hydrodynamic Dispersion ◽  
Seepage Velocity ◽  
Transform Method ◽  
Space And Time ◽  
Advection Dispersion ◽  
Homotopy Decomposition ◽  
Geological Formation

The contamination through the geological formation cannot move and disperse with the same speed and dispersion coefficient, respectively, due to the variability of the geological formation. This paper is therefore first devoted to the description of the hydrodynamic advection dispersion equation with the seepage velocity and dispersion coefficient as function of space and time. Secondly the equation is solved via two analytical techniques: the homotopy decomposition method and the differential transform method. The numerical simulations of the approximated solutions are presented.

scholarly journals Homotopy decomposition of classifying spaces via elementary Abelian subgroups

Topology ◽  
1992 ◽  
Vol 31 (1) ◽  
pp. 113-132 ◽  
Author(s):  
Stefan Jackowski ◽  
James McClure
Keyword(s):  
Classifying Spaces ◽  
Homotopy Decomposition ◽  
Abelian Subgroups
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