• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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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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• v.26 no.3_4
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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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• v.32 no.1
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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).

• Journal of the Korean Mathematical Society
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• v.60 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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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.

• Journal of Internet Computing and Services
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• v.12 no.3
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• pp.131-137
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• 2011

GPUs were originally designed for graphic processing, and GPGPUs are general-purpose GPUs for numerical computation with high performance and low electric power. In this paper, we implemented the parallel LU factorization program for GPGPUs. In CUDA, which is computational environment for Nvidia GPGPUs, domains are divided into blocks, and multi-threads compute each sub-blocks Simultaneously. In LU factorization program, computation order should be artificially decided due to the data dependence. To resolve the data dependancy, we suggested a parallel LU program for GPGPUs, and also explained parallel reduction algorithm for partial pivoting of LU factorization. We finally present performance analysis to show efficiency of the parallel LU factorization program based on multi-threads on GPGPUs.

• International Journal of Internet, Broadcasting and Communication
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• v.13 no.3
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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.