• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.59-68
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• 2022

For a finite group G ⊂ GL(n, ℂ), the G-Hilbert scheme is a fine moduli space of G-clusters, which are 0-dimensional G-invariant subschemes Z with H⁰(𝒪_Z ) isomorphic to ℂ[G]. In many cases, the G-Hilbert scheme provides a good resolution of the quotient singularity ℂⁿ/G, but in general it can be very singular. In this note, we prove that for a cyclic group A ⊂ GL(n, ℂ) of type ${\frac{1}{r}}$(1, …, 1, a) with r coprime to a, A-Hilbert Scheme is smooth and irreducible.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.59-72
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• 2024

In the presented paper, the first section contains strong convergence and demiclosedness property of a sequence generated by Karakaya et al. iteration scheme in a Hilbert space for quasi-nonexpansive mappings and also the comparison between the iteration scheme given by Karakaya et al. with well-known iteration schemes for the convergence rate. The second section contains some applications of the fixed point theory in solution of different mathematical problems.

• 정보과학회 논문지
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• 제41권10호
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• pp.792-798
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• 2014

R-tree는 공간 데이터베이스 분야에서 가장 널리 쓰이는 색인 구조이며 다양한 변형된 기법들이 제안되었다. 이 기법들 중 Hilbert R-tree는 공간 채움 곡선인 Hilbert 곡선을 이용해서 대용량의 데이터를 고비용의 분할 과정 없이 R-tree를 구성하는 기법이다. 하지만 기존의 CPU기반의 Hilbert R-tree는 대용량의 데이터를 처리할 때는 순차적인 접근으로 발생되는 고비용의 전처리 비용과 느린 구축시간으로 실제 응용에 적용되기에는 한계가 있다. 본 논문에서는 이러한 문제를 해결하기 위해 GPU를 이용해서 데이터의 Hilbert 매핑을 병렬화 하고 이를 통해서 최종적으로 GPU의 메모리에 Hilbert R-tree의 벌크로딩을 고속화하는 기법을 제안한다. GPU기반의 Hilbert R-tree는 inversed-cell 기법과 트리구조 패킹의 병렬화 기법을 통해서 벌크로딩의 성능을 향상시켰다. 실험 결과에서는 기존의 CPU 기반의 벌크로딩에 비해 최대 45배의 성능향상을 보여주었다.

• 대한수학회논문집
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• 제33권3호
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• pp.767-786
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• 2018

In this paper, we introduce new iterative schemes by using the modified Ishikawa iteration for two hybrid multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. We use CQ and shrinking projection methods with Ishikawa iteration for obtaining strong convergence theorems. Furthermore, we give examples and numerical results for supporting our main results.

• International Journal of Internet, Broadcasting and Communication
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• 제15권2호
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• pp.22-30
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• 2023

The portable mobile devices with high performance and high speed 5G network activate and explode the demands for ubiquitous information services that remove the limitations of time for the communication and places to request for the information. NN (Nearest Neighbor) search is one of the most important types of queries to be processed efficiently in the information services. Various indexes have been proposed to support efficient NN search in the wireless broadcast system. The indexes adopting Hilbert curve, grid partition or Voronoi diagram enable the clients to search for NN quickly in the wireless broadcast channel. It is necessary that an efficient means to evaluate the performances of various indexes. In this paper, we propose an open framework that can adopt a variety of indexing schemes and evaluate and compare the performances of them. The proposed framework is organized with open and flexible structure that can adopt hybrid indexing schemes extensible to Voronoi diagram as well as simple indexing schemes. With the implemented framework, we demonstrate the efficiency and scalability and flexibility of the proposed framework by evaluating various indexing schemes for NN query.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제16권11호
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• pp.1071-1075
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• 2010

무선 센서 네트워크에 활용되는 센서 노드는 제한된 전력, 메모리 동의 한정된 자원을 지니기 때문에, 제한된 에너지를 효율적으로 관리하기 위한 데이터 집계 기법의 연구가 활발히 진행되어 왔다. 한편, 센서 네트워크는 무선통신을 수행하기 때문에 공격자에게 쉽게 데이터 노출될 수 있다. 따라서, 센서 네트워크에서 데이터 집계를 위한 데이터 보호 기법에 관한 연구가 필수적이다. 그러나, 기존 데이터 집계를 위한 데이터 보호 기법은 네트워크 구성 및 데이터 집계 처리 시, 다수의 연산과 데이터 전송이 발생한다. 이러한 문제점을 해결하기 위하여, 본 논문에서는 데이터 집계를 위한 힐버트 커브(hilbert curve) 기반 데이터 보호 기법을 제안한다. 제안하는 기법은 트리 기반의 라우팅을 구성하여 이웃노드와의 통신을 최소화한다. 또한 seed에 기반한 힐버트 커브 기법을 통해 데이터를 암호화함으로써, 센서 노드간의 통신 시 공격자로부터 데이터를 보호할 수 있다. 마지막으로, 제안하는 기법이 메시지 전송량 및 센서노드 평균 수명 측면에서 기존 연구보다 우수함을 보인다.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.469-481
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• 2017

In this paper, we established a general nonconvex split variational inequality problem, this is, an extension of general convex split variational inequality problems in two different Hilbert spaces. By using the concepts of prox-regularity, we proved the convergence of the iterative schemes for the general nonconvex split variational inequality problems. Further, we also discussed the iterative method for the general convex split variational inequality problems.

• 대한수학회지
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• 제34권3호
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• pp.515-531
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• 1997

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.381-403
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• 2022

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

• 한국멀티미디어학회논문지
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• 제17권10호
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• pp.1182-1188
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• 2014

Recently, the research on database outsourcing has been actively done with the popularity of cloud computing. However, because users' data may contain sensitive personal information, such as health, financial and location information, the data encryption methods have attracted much interest. Existing data encryption schemes process a query without decrypting the encrypted databases in order to support user privacy protection. On the other hand, to efficiently handle the large amount of data in cloud computing, it is necessary to study the distributed index structure. However, existing index structure and query processing algorithms have a limitation that they only consider single-column query processing. In this paper, we propose a grid-based multi column indexing scheme and an encrypted query processing algorithm. In order to support multi-column query processing, the multi-dimensional index keys are generated by using a space decomposition method, i.e. grid index. To support encrypted query processing over encrypted data, we adopt the Hilbert curve when generating a index key. Finally, we prove that the proposed scheme is more efficient than existing scheme for processing the exact and range query.