• 대한수학회보
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• 제43권2호
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• pp.419-424
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• 2006

In this paper we extend the study of ascend and descend of factorization properties (for atomic domains, domains satisfying ACCP, bounded factorization domains, half-factorial domains, pre-Schreier and semirigid domains) to the finite factorization domains and idf-domains for domain extension $A\;{\subseteq}\;B$.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.779-784
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• 2008

We show that $\mathbb{Z}[\sqrt{-p}]$ is not a unique factorization domain (UFD) but a factorization domain (FD) with a condition $1\;+\;a^2p\;=\;qr$, where a and p are positive integers and q and r are positive primes in $\mathbb{Z}$ with q < p. Using this result, we also construct several specific non-unique factorization domains which are factorization domains. Furthermore, we prove that an integral domain $\mathbb{Z}[\sqrt{-p}]$ is not a UFD but a FD for some positive integer p.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.97-107
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• 2024

Let A ⊆ B be an extension of integral domains with characteristic zero. Let H(A, B) and h(A, B) be rings of composite Hurwitz series and composite Hurwitz polynomials, respectively. We simply call H(A, B) and h(A, B) composite Hurwitz rings of A and B. In this paper, we study when H(A, B) and h(A, B) are unique factorization domains (resp., GCD-domains, finite factorization domains, bounded factorization domains).

• 대한수학회지
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• 제60권2호
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• pp.407-464
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• 2023

Let R be a commutative ring with identity. The structure theorem says that R is a PIR (resp., UFR, general ZPI-ring, π-ring) if and only if R is a finite direct product of PIDs (resp., UFDs, Dedekind domains, π-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations v or t as follows: An integral domain R is a Krull domain if and only if every nonzero proper principal ideal of R can be written as a finite v- or t-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation u on R, so that R is a general Krull ring if and only if every proper principal ideal of R can be written as a finite u-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.

• 대한수학회보
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• 제55권3호
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• pp.809-818
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• 2018

We study those integral domains in which every proper ideal can be written as an invertible ideal multiplied by a nonempty product of proper radical ideals.

• 인터넷정보학회논문지
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• 제12권3호
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• pp.131-137
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• 2011

GPGPU는 원래 그래픽 계산을 위한 프로세서인 GPU를 일반 계산에 활용하여 저전력으로 고성능의 효율을 보이는 신개념의 계산 장치이다. 본 논문에서는 GPGPU에서 계산을 하기 위한 병렬 LU 분해법의 알고리즘을 제안하였다. Nvidia GPGPU에서 프로그램을 실행하기 위한 CUDA 계산 환경에서는 계산하고자 하는 데이터 도메인을 블록으로 나누고 각 블록을 쓰레드들이 동시에 계산을 하는데, 이 때 블록들의 계산 순서는 무작위로 진행이 되기 때문에 블록간의 데이터 의존성을 가지는 LU 분해 프로그램에서는 결과가 정확하지 않게 된다. 본 논문에서는 병렬 LU 분해법에서 블록간의 계산 순서를 인위적으로 정하는 구현 방식을 제안하며 아울러 LU 분해법의 부분 피벗팅을 계산하기 위한 병렬 reduction 알고리즘도 제안한다. 또한 구현된 병렬프로그램의 성능 분석을 통하여 GPGPU의 멀티 쓰레드 기반으로 고성능으로 계산할 수 있는 병렬프로그램의 효율성을 보인다.

• International Journal of Internet, Broadcasting and Communication
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• 제13권3호
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• pp.63-72
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• 2021

Mobile crowd-sensing (MCS) is a promising sensing paradigm that leverages mobile users with smart devices to perform large-scale sensing tasks in order to provide services to specific applications in various domains. However, MCS sensing tasks may not always be successfully completed or timely completed for various reasons, such as accidentally leaving the tasks incomplete by the users, asynchronous transmission, or connection errors. This results in missing sensing data at specific locations and times, which can degrade the performance of the applications and lead to serious casualties. Therefore, in this paper, we propose a missing data inference approach, called missing data approximation with probabilistic tensor factorization (MDI-PTF), to approximate the missing values as closely as possible to the actual values while taking asynchronous data transmission time and different sensing locations of the mobile users into account. The proposed method first normalizes the data to limit the range of the possible values. Next, a probabilistic model of tensor factorization is formulated, and finally, the data are approximated using the gradient descent method. The performance of the proposed algorithm is verified by conducting simulations under various situations using different datasets.