• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.331-343
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• 2024

Let ℜ be a *-algebra with unity I and a nontrivial projection P₁. In this paper, we show that under certain restrictions if a map ψ : ℜ → ℜ satisfies $$\Psi(S_1{\diamond}S_2{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n)=\sum_{k=1}^nS_1{\diamond}S_2{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{k-1}{\diamond}{\Psi}(S_k){\diamond}S_{k+1}{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n$$ for all S_n-2, S_n-1, S_n ∈ ℜ and S_i = I for all i ∈ {1, 2, . . . , n - 3}, where n ≥ 3, then ψ is an additive *-derivation.

• Journal of information and communication convergence engineering
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• v.22 no.2
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• pp.98-108
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• 2024

Scrypt is a password-based key derivation function proposed by Colin Percival in 2009 that has a memory-hard structure. Scrypt has been intentionally designed with a memory-intensive structure to make password cracking using ASICs, GPUs, and similar hardware more difficult. However, in this study, we thoroughly analyzed the operation of Scrypt and proposed strategies to maximize computational parallelism in GPU environments. Through these optimizations, we achieved an outstanding performance improvement of 8284.4% compared with traditional CPU-based Scrypt computations. Moreover, the GPU-optimized implementation presented in this paper outperforms the simple GPU-based Scrypt processing by a significant margin, providing a performance improvement of 204.84% in the RTX3090. These results demonstrate the effectiveness of our proposed approach in harnessing the computational power of GPUs and achieving remarkable performance gains in Scrypt calculations. Our proposed implementation is the first GPU implementation of Scrypt, demonstrating the ability to efficiently crack Scrypt.

• Journal of the Korean Institute of Landscape Architecture
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• v.47 no.5
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• pp.28-40
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• 2019

In order to resolve the imbalances in the supply of living SOCs according to socio-economic status, location, and population groups, the discussions on inclusive city policies are expanding. The purpose of this study is to propose an Index of Park Derivation (IPD) as an alternative indicator for the promotion of an inclusive urban park policy that can be applied in the 7 major metropolitan cities to select a region with a relatively high park needs. The main research results are as follows. First, the concept of an inclusive urban park policy is defined as "a policy to supply to manage high-quality park services with priority given to areas with low socio-economic and environmental status, such as a large amount of elderly, children, low-income families, areas vulnerable to disasters, such as heat and fine dust, and population groups." Second, we developed the index of park derivation (IPD), which is a combination of 17 variables including park service level, demographic characteristics, economic and educational level, health level, and environmental vulnerability. The variables that constitute the index of park deprivation (IPD) can be applied to SOC policies outside the parks, such as sports facilities, daycare centers, kindergartens, and public libraries. Third, applying index of park deprivation (IPD) to 1,148 Eup/Myeon/dong areas of the 7 metropolitan cities resulted in areas with relatively high park service needs. This study implies that the central and the local government suggest an alternative index to promote an inclusive urban park policy based on statistical and geographical information and data that can be easily accessed and utilized.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.583-593
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• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.495-504
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• 2010

This paper continues a line investigation in [1]. Let A be a K-algebra and M an A/K-bimodule. In [5] Hamaguchi gave a necessary and sufficient condition for gDer(A, M) to be isomorphic to BDer(A, M). The main aim of this paper is to establish similar relationships for generalized ($\sigma$, $\tau$)-derivations.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.27-38
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• 2014

The notion of generalized (regular) (${\alpha},\;{\beta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${\alpha},\;{\beta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${\alpha},\;{\beta}$)-derivation and ${\alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${\alpha},\;{\beta}$)-derivations are proved.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.65-87
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• 2014

The purpose of this paper is to prove that the noncommutative version of the Singer-Wermer Conjecture is affirmative under certain conditions. Let A be a noncommutative Banach algebra. We show that if there exists a continuous linear Jordan derivation D : A ${\rightarrow}$ A such that [D(x), x]$D(x)^3{\in}$ rad(A) for all $x{\in}A$, then D(A) ${\subseteq}$ rad(A).

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.415-421
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• 2020

In the proof of Theorem 3 on p.253 in [4], both right and left distributivity are assumed simultaneously which makes the proof invalid. We give a corrected proof for this theorem by introducing an extension of Lemma 2.2 in [2].

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.251-258
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• 2017

The aim of the present paper is to establish some results involving generalized ${\ast}$-derivations in ${\ast}$-rings and investigate the commutativity of prime ${\ast}$-rings admitting generalized ${\ast}$-derivations of R satisfying certain identities and some related results have also been discussed.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.469-477
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• 2008

We introduce the notion of two-sided $\Gamma$-$\alpha$-derivation of a $\Gamma$-near-ring and give some generalizations of [1, 2].