• 대한수학회보
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• 제29권1호
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• 호남수학학술지
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• 제21권1호
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• pp.157-169
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• 1999

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

• 호남수학학술지
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• 제30권4호
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• 대한수학회지
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• 제48권3호
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• pp.627-639
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• 2011

Hopf corings are dened in this work as coring objects in the category of algebras over a commutative ring R. Using the Dieudonn$\'{e}$ equivalences from [7] and [19], one can associate coring structures built from the Hopf algebra $F_p[x_0,x_1,{\ldots}]$, p a prime, with Hopf ring structures with same underlying connected Hopf algebra. We have that $F_p[x_0,x_1,{\ldots}]$ coring structures classify thus Hopf ring structures for a given Hopf algebra. These methods are applied to dene new ring products in the Hopf algebras underlying known Hopf rings that come from connective Morava ${\kappa}$-theory.

• 대한수학회보
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• 제34권1호
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• pp.1-8
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• 1997

Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} \times Z/2$ and $D_{2p} \times Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.105-118
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• 2007

In this paper, we first define a new kind of two-weight-$A_r^{{\lambda}_3}({\lambda}_1,{\lambda}_2,{\Omega})$-weight, and then prove the imbedding inequalities for $\mathcal{A}$-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space $L^p(D,{\bigwedge}^l)$ to the Sobolev space $W^{1,p}(D,{\bigwedge}^{l-1})$, $l=1,2,{\cdots},n$, and to establish the basic weighted $L^p$-estimates for $\mathcal{A}$-harmonic tensors.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.151-158
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• 1999

Let (X, G) be a transformation group and ${\sigma}(X,x_0,G)$ the fundamental group of (X, G). In this paper, we prove that the Reidemeister number $R(f_G)$ for an endomorphism $f_G:(X,G){\rightarrow}(X,G)$ is a homotopy invariant. In particular, when any self-map $f:X{\rightarrow}X$ is homotopic to the identity map, we give some calculation of the lower bound of $R(f_G)$. Finally, we discuss commutativity and product formula for the Reidemeister number $R(f_G)$.

• Nuclear Engineering and Technology
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• 제49권8호
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• pp.1645-1653
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• 2017

This investigation explores the thermally stratified stretchable flow of an Oldroyd-B material bounded by a linear stretched surface. Heat transfer characteristics are addressed through thermal stratification and heat generation/absorption. Formulation is arranged for mixed convection. Application of suitable transformations provides ordinary differential systems through partial differential systems. The homotopy concept is adopted for the solution of nonlinear differential systems. The influence of several arising variables on velocity and temperature is addressed. Besides this, the rate of heat transfer is calculated and presented in tabular form. It is noticed that velocity and Nusselt number increase when the thermal buoyancy parameter is enhanced. Moreover, temperature is found to decrease for larger values of Prandtl number and heat absorption parameter. Comparative analysis for limiting study is performed and excellent agreement is found.