• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.491-506
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• 2006

In this paper, we extend the concept of the group ${\varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${\varepsilon}(X,\;A)$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)$ where G is a subgroup of ${\varepsilon}(X,\;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1$ provided the two sets $[X{\wedge}Y,\;X{\times}Y]$ and [X, Y] are trivial.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.289-296
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• 2023

When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤ_q, n+ 2) ∨ M(ℤ_q, n+ 1) ∨ M(ℤ_q, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [M_j , M_k] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔^dim_#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.93-98
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• 1991

An improved and flexible matrix algorithm for solving interlinked separation problems which is based on the homotopy continuation method has been developed. A flexible model of the interlinked stream in standardized matrix form and JACOBIAN generation I algorithm for homotopy continuation are suggested. Also DOF analysis is performed for easy-understanding of equation based simulation of complex column systems. The Algorithm is tested on several problems of interlinked separation processes and some of results are documented.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.55-60
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• 2011

The aim of the paper is to apply Homotopy Perturbation Method (HPM) for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Homotopy perturbation method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.107-112
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• 1997

For a ring R with 1, the higher K-theory of Quillen is defined by the higher homotopy groups of the plus construction of the general linear group of R. On the other hand, the Volodin K-theory is defined by the higher homotopy groups of the Volodin space. In this paper we show that these two K-theories are equivalent. We show that the Volodin space is a homotopy fiber of the acyclic map from BGL(R) to its plus construction.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.349-355
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• 2000

In this paper we generalize the Whitehead theorem which says that a homology equivalence implies a homotopy equivalence for nilpotent spaces. We make some theorems on a homotopy equivalence of non-nilpotent spaces, e.g., the solvable space or space satisfying the condition (T**) or space X with $\pi$1(X) Engel, or locally nilpotent space with some properties. Furthermore we find some conditions that the Wall invariant will be trivial.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.623-644
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• 2019

We investigate the homotopy category ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ of N-complexes of injectives in a Grothendieck abelian category ${\mathfrak{A}}$ not necessarily locally noetherian, and prove that the inclusion ${\mathcal{K}}_N(Inj{\mathfrak{A}}){\rightarrow}{\mathcal{K}}({\mathfrak{A}})$ has a left adjoint and ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ is well generated. We also show that the homotopy category ${\mathcal{K}}_N(PrjR)$ of N-complexes of projectives is compactly generated whenever R is right coherent.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.689-700
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• 2005

In this paper we shall introduce the general idea, historical background and the reasons why we use it about the homotopy method for solving a system of nonlinear systems.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.649-654
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• 1999

We consider the forgetful map from the group of equivariant self equivalences to the group of non-equivariant self equivalences. A sufficient condition for this forgetful map being a monomorphism is obtained. Several examples are given.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.