• 대한수학회지
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• 제38권1호
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• pp.87-99
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• 2001

We prove that the germ of a CR mapping f between real analytic real hypersurfaces has a holomorphic extension and satisfies a complete system of finite order if the source is of finite type in the sense of Bloom-Graham and the target is k-nondegenerate under certain generic assumptions on f.

• 충청수학회지
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• 제33권4호
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• pp.387-394
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• 2020

Matthews introduced the concepts of partial metric spaces and proved the Banach fixed point theorem in complete partial metric spaces. Dukic, Kadelburg, and Radenovic proved fixed point theorems for Geraghty-type mappings in complete partial metric spaces. In this paper, we prove the fixed point theorem for some contractive mapping in a complete partial metric space.

• 대한수학회지
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• 제37권2호
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• pp.225-243
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• 2000

We explain the notion of complete system and how it naturally arises from the equivalence problem of G-structures. Then we construct a complete system of 3rd order for the infinitesimal CR automorphisms of CR manifold of nondegenerate Levi form.

• 대한수학회지
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• 제39권1호
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• pp.91-102
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• 2002

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.665-678
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• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• 대한수학회논문집
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• 제31권3호
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• pp.507-518
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• 2016

The aim of this paper is to prove some strong convergence theorems for the modified Ishikawa iteration process involving a pair of a generalized asymptotically nonexpansive single-valued mapping and a quasi-nonexpansive multi-valued mapping in the framework of $\mathbb{R}$-trees under the gate condition.

• ETRI Journal
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• 제20권4호
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• pp.327-345
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• 1998

This paper deals with the problem of one-to-one mapping of 2$^n$ task modules of a parallel program to an n-dimensional hypercube multicomputer so as to minimize the total communication cost during the execution of the task. The problem of finding an optimal mapping has been proven to be NP-complete. First we show that the mapping problem in a hypercube multicomputer can be transformed into the problem of finding a set of maximum cutsets on a given task graph using a graph modification technique. Then we propose a repeated mapping scheme, using an existing graph bipartitioning algorithm, for the effective mapping of task modules onto the processors of a hypercube multicomputer. The repeated mapping scheme is shown to be highly effective on a number of test task graphs; it increasingly outperforms the greedy and recursive mapping algorithms as the number of processors increases. Our repeated mapping scheme is shown to be very effective for regular graphs, such as hypercube-isomorphic or 'almost' isomorphic graphs and meshes; it finds optimal mappings on almost all the regular task graphs considered.

• 대한수학회논문집
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• 제27권1호
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• 대한수학회지
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• 제57권4호
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• 한국정보처리학회논문지
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• 제5권11호
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• pp.2823-2834
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• 1998

본 논문에서는 병렬 프로그램을 구성하는 $2^n$개의 타스크 모듈들을 n-차원 하이퍼큐브 다중 컴퓨터에 전체 통신 비용이 최소가 되도록 일대일 매핑하는 문제를 다룬다. 하이퍼큐브에서 최적 매핑을 구한 것은 NP-complete문제이다. 본 논문에서는 먼저 하이퍼큐브 다중 컴퓨터에서의 매핑 문제를 그래프 상에서의 최대 컷세트 집합을 구하는 문제로 변환시키는 그래프 변형 기법을 제안한다. 이러한 그래프 변형 기법을 사용하여 기존의 그래프 이분할 방법을 변형된 그래프 상에 반복 적용함으로써 하이퍼큐브에 타스크 모듈들을 효율적으로 일대일 매핑하는 반복 매핑 알고리즘을 제안한다. 여러가지 타스크그래프 상에서의 실험을 통해, 제안된 반복 매핑 알고리즘이 기존의 greedy나 recursive 매핑 알고리즘들 보다 성능이 우수함을 보인다. 특히 제안된 알고리즘은 하이퍼큐브-isomorphic, 메쉬등과 같은 정형 그래프 상에서 성능이 우수하며 거의 모든 정형 그래프에서 최적 매핑을 찾음을 보인다.