• 대한수학회보
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• 제61권1호
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• 대한수학회지
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• 제59권4호
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• pp.685-697
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• 2022

Recently, Gireesh, Shivashankar, and Naika [11] found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the 3^k-regular cubic partitions. We also find new families of congruences.

• International journal of advanced smart convergence
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• 제7권4호
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• pp.10-18
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• 2018

For the information services supporting requests of data items from a great number of mobile clients, wireless data broadcasting is an effective way because it can accommodate any number of clients. In the wireless data broadcasting, various air indexing schemes and data scheduling schemes have been developed in order to enable the clients to access their desired data items efficiently. The broadcasting system needs a method to simulate newly designed air indexing and scheduling schemes of the system, and to evaluate the performance parameters of the schemes. In this paper, we design an expandable and efficient simulation framework for the wireless data broadcasting based on the partition of data ID space. The framework can adopt regular and irregular space partition and evaluate various performance parameters of the broadcasting system. We implement a testbed of the broadcasting system using the framework, that adopts IIP, GDI and EXP as its air indexing schemes. We simulate the system using the testbed and evaluate the performance parameters of the system. Thus, we show the efficiency and expandability of the designed and implemented framework.

• 대한안전경영과학회지
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• 제17권1호
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• pp.53-66
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• 2015

This study classified the study subjects as apartment residents and managers, and conducted the descriptive statistics of research questions related to the effectiveness of the lightweight partition walls and the evacuation space. This study also conducted T-test and Anova to find the different perceptions of the lightweight partition walls and the evacuation space, and the different perceptions of related laws according to the characteristics of the residents and managers. The findings and suggestions were as follows. Firstly, strengthening of the Senior Fire Safety Manager system to prevent the insolvency of fire safety management due to the affiliate. Secondly, implementing enhanced penalties in accordance with not implementing residents education, in order to prevent not smoothly delivering manager trained education to residents. Thirdly, adjusting hands-on training time according to the gender of the managers to supplement women's relatively low perceptions of lightweight partition. Fourthly, mandating evacuation guidance stickers on the evacuation space for residents to remove obstacles in the evacuation space. Finally, establishing regular residents education system in order to improve the awareness of the related laws for residents residing over 16th floors.

• 한국지능시스템학회논문지
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• 제17권2호
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• pp.220-225
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• 2007

본 논문에서는 주요성분분석과 상호정보 추정을 조합한 입력변수선택 기법을 제안하였다. 여기서 주요성분분석은 2차원 통계성에 기반을 둔 기법으로 입력변수 간의 종속성을 빠르게 제거하여 과추정을 방지하기 위함이고, 상호정보의 추정은 적응적 분할을 이용하여 입력변수의 확률밀도함수를 계산함으로써 변수상호간의 종속성을 좀 더 정확하게 측정하기 위함이다. 제안된 기법을 각 500개 샘플의 7개 신호를 가지는 인위적인 문제와 각 55개 샘플의 24개의 신호를 가지는 환경오염신호를 대상으로 각각 실험한 결과, 빠르고 정확한 변수의 선택이 이루어짐을 확인하였다. 또한 주요성분분석을 수행하지 않을 때와 정규분할의 상호정보 추정 때보다 제안된 방법은 각각 우수한 선택성능이 있음을 확인하였다.

• 대한수학회보
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• 제61권3호
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• pp.621-635
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• 2024

An 𝑙-regular overpartition of n is an overpartition of n with no parts divisible by 𝑙. Recently, the authors introduced a partition statistic called r_𝑙-crank of 𝑙-regular overpartitions. Let M_r𝑙(m, n) denote the number of 𝑙-regular overpartitions of n with r_𝑙-crank m. In this paper, we investigate the monotonicity property and the unimodality of M_r3(m, n). We prove that M_r3(m, n) ≥ M_r3(m, n - 1) for any integers m and n ≥ 6 and the sequence {M_r3(m, n)}_|m|≤n is unimodal for all n ≥ 14.

• 대한수학회지
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• 제59권5호
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• pp.945-962
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• 2022

For a positive integer ℓ, $\bar{A}_{\ell}(n)$ denotes the number of over-partitions of n into parts not divisible by ℓ. In this article, we find certain Ramanujan-type congruences for $\bar{A}_{r{\ell}}(n)$, when r ∈ {8, 9} and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\bar{A}_{13}(n)$ by using an algorithm developed by Radu and Sellers [15].

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.969-983
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• 2024

For an integer ℓ ≥ 1, let ${\bar{B}}_{\ell}(n)$ denotes the number of ℓ-regular over partition pairs of n. For certain conditions of ℓ, we study the divisibility of ${\bar{B}}_{\ell}(n)$ and arithmetic properties for ${\bar{B}}_{\ell}(n)$. We further obtain infinite family of congruences modulo 2^t satisfied by ${\bar{B}}_3(n)$ employing a result of Ono and Taguchi (2005) on nilpotency of Hecke operators.

• 한국지능시스템학회논문지
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• 제16권5호
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• pp.525-530
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• 2006

본 논문에서는 고정점 알고리즘의 독립성분분석과 적응분할의 상호정보 추정을 조합한 입력변수선택 기법을 제안하였다. 여기서 고정점 알고리즘의 독립성분분석은 할선법에 기반을 둔 방법으로 입력변수 간의 독립성을 빠르게 찾기 위함이고, 적응분할의 상호정보 추정은 입력변수의 확률밀도함수 계산에서 동일한 량의 샘플분할을 가능하게 하여 변수상호간의 종속성을 좀 더 정확하게 구하기 위함이다. 제안된 기법을 인위적으로 제시된 각 500개의 샘플을 가지는 7개의 신호와 특정지역을 대상으로 측정된 각 55개의 샘플을 가진 24개의 환경오염신호를 대상으로 실험한 결과, 빠르고 정확한 변수의 선택이 이루어짐을 확인하였다. 또한 할선법의 고정점 알고리즘 독립성분분석을 수행하지 않을 때와 정규분할의 상호정보 추정 때보다 각각 우수한 선택성능이 있음을 확인하였다.

• 충청수학회지
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• 제35권3호
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• pp.205-225
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• 2022

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSO_α for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.