• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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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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• v.7 no.4
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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.

• Journal of the Korea Safety Management & Science
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• v.17 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.2
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• pp.220-225
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• 2007

This paper presents an efficient input variable selection method using both principal component analysis(PCA) and adaptive partition mutual information(AP-MI) estimation. PCA which is based on 2nd order statistics, is applied to prevent a overestimation by quickly removing the dependence between input variables. AP-MI estimation is also applied to estimate an accurate dependence information by equally partitioning the samples of input variable for calculating the probability density function. The proposed method has been applied to 2 problems for selecting the input variables, which are the 7 artificial signals of 500 samples and the 24 environmental pollution signals of 55 samples, respectively. The experimental results show that the proposed methods has a fast and accurate selection performance. The proposed method has also respectively better performance than AP-MI estimation without the PCA and regular partition MI estimation.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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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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• v.42 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.5
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• pp.525-530
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• 2006

This paper presents an efficient input variable selection method using both fixed-point independent component analysis(FP-ICA) and adaptive partition mutual information(AP-MI) estimation. FP-ICA which is based on secant method, is applied to quickly find the independence between input variables. AP-MI estimation is also applied to estimate an accurate dependence information by equally partitioning the samples of input variable for calculating the probability density function(PDF). The proposed method has been applied to 2 problems for selecting the input variables, which are the 7 artificial signals of 500 samples and the 24 environmental pollution signals of 55 samples, respectively The experimental results show that the proposed methods has a fast and accurate selection performance. The proposed method has also respectively better performance than AP-MI estimation without the FP-ICA and regular partition MI estimation.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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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.