• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1203-1216
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• 2010

The homotopy analysis method (HAM) has been applied to develop an analytic solution for the coupled radiation-convection dissipative non-gray gas flow in a non-Darcy porous medium. Results are presented for the surface shear and temperature profiles are presented to illustrate the effect of various parameters appearing in the analytical formulation. The accuracy and convergence of the method is also discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.193-198
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• 2009

In the previous work [5] we have determined the group ${{\varepsilon}_{\sharp}}^{dim+r}^{dim+r}(X)$ for $X\;=\;M(Z_q,\;n+1){\vee}M(Z_q,\;n)$ for all integers q > 1. In this paper, we investigate the group ${{\varepsilon}_{\sharp}}^{dim+r}(X)$ for $X\;=\;M(Z{\oplus}Z_q,\;n+1){\vee}M(Z{\oplus}Z_q,\;n)$ for all odd numbers q > 1.

• Coupled systems mechanics
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• 제2권3호
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• pp.255-269
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• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• 충청수학회지
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• 제35권4호
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• pp.297-305
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• 2022

First, we generalize homotopy results of O'Regan [6] for Mönch type multimaps to Chandrabhan type multimaps. Second, we show that the better admissible Chandrabhan type multimaps have fixed point properties whenever their ranges are Klee approximable. Finally, we give examples of essential maps for various class of multimaps including 𝚽-condensing multimaps.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• 대한수학회지
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• 제21권2호
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• pp.227-232
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• 1984

• 대한수학회보
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• 제22권1호
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• pp.64-64
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• 1985

• 한국항공우주학회지
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• 제35권7호
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• pp.647-654
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• 2007

본 논문에서는 일정한 추력을 이용한 지구-달의 연료 최적 궤적해를 이용하여, 가변 추력기를 이용한 지구 탈출 궤적에서의 에너지 및 연료 최적 궤적을 설계하였다. 에너지 최적의 지구 탈출 궤적은 여러 차례 지구를 공전하게 되고, 궤도 천이 시간이 일반적인 궤도 천이 시간 보다 상대적으로 오래 소요되므로 최적화 문제를 해를 구하기가 쉽지 않다. 따라서 에너지 최적 해를 구하기 위하여, 초기 상태변수를 조정하면서 Discrete continuation의 기법을 적용하였다. 최적화 문제의 종말 조건은 일정한 추력기를 이용한 지구 탈출 궤적의 종말 조건을 이용하였고, 구속 시간은 일정한 추력기를 이용한 궤도 천이의 경우보다 큰 값으로 설정하였다. 한편, 연료 최적 궤적은 제어 입력의 형태가 불연속적이기 때문에 해를 구하기가 쉽지 않다. 따라서 연료 최적 궤적은 에너지 최적의 해와 호모토피(Homotopy) 기법을 적용시켜 그 해를 구하였다.

• Structural Engineering and Mechanics
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• 제50권4호
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• pp.487-500
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• 2014

An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton's principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated.

• 호남수학학술지
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• 제26권4호
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• pp.411-421
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• 2004

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.