• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.161-173
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• 2005

In this paper, we will introduce the folding on the connected sum of some types of manifolds which are determined by their fundamental group. Also, the fundamental group of the unfolding of the connected sum will be deduced some types of conditional foldings restricted on the elements of the fundamental groups are deduced. Theorems governing these relations will be achieved. Some applications in manufacturing are presented.

• ETRI Journal
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• v.40 no.5
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• pp.582-591
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• 2018

In this paper, we present a performance analysis of large-scale multi-input multi-output (MIMO) systems for wireless backhaul networks. We focus on fully connected N nodes in a wireless meshed and multi-hop network topology. We also consider a large number of antennas at both the receiver and transmitter. We investigate the transmission schemes to support fully connected N nodes for half-duplex and full-duplex transmission, analyze the achievable ergodic sum rate among N nodes, and propose a closed-form expression of the achievable ergodic sum rate for each scheme. Furthermore, we present numerical evaluation results and compare the resuts with closed-form expressions.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.141-155
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• 2010

In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.819-845
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• 2020

In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.221-225
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• 2016

For a connected graph G = (V, E), its inverse degree is defined as $\sum_{{\upsilon}{\in}{V}}^{}\frac{1}{d(\upsilon)}$. Using an upper bound for the inverse degree of a graph obtained by Cioabă in [4], we in this note present sufficient conditions for some Hamiltonian properties and k-connectivity of a graph.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.763-787
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• 2017

A graph is called 1-planar if it can be drawn in the Euclidean plane ${\mathbb{R}}^2$ such that each edge is crossed by at most one other edge. The weight of an edge is the sum of degrees of two ends. It is known that every planar graph of minimum degree ${\delta}{\geq}3$ has an edge with weight at most 13. In the present paper, we show the existence of edges with weight at most 25 in 3-connected 1-planar graphs.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.189-200
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• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Korean Journal of Computational Design and Engineering
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• v.21 no.1
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• pp.1-8
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• 2016

After 2017 years, BWMS units must be installed in the existing ship as well as the new ship by the ballast water management convention. Software tools that can help automatically searching for BWMS installation space to avoid pipes and equipment in the engine room of the existing ship will be very useful in the BWMS layout design. In this study, voxel representation of scanned data is generated first to search space efficiently. Simplified voxel models of each unit are prepared to be located in the engine room space as well. Distance between connected models is calculated through the arrangement direction and position of each model. Sums of distance between connected models are compared for the optimal configuration. It is assumed that the sum of distance between connected models depicts the pipe usage. The proposed method can save the time needed for BWMS installation design and allows optimal configuration of BWMS units.

• International journal of advanced smart convergence
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• v.10 no.1
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• pp.75-81
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• 2021

As the number of connected smart devices and applications increases explosively, the existing orthogonal multiple access (OMA) techniques have become insufficient to accommodate mobile traffic, such as artificial intelligence (AI) and the internet of things (IoT). Fortunately, non-orthogonal multiple access (NOMA) in the fifth generation (5G) mobile networks has been regarded as a promising solution, owing to increased spectral efficiency and massive connectivity. In this paper, we investigate the achievable data rate for non-orthogonal multiple access (NOMA) with negatively-correlated information sources (CIS). For this, based on the linear transformation of independent random variables (RV), we derive the closed-form expressions for the achievable data rates of NOMA with negatively-CIS. Then it is shown that the achievable data rate of the negatively-CIS NOMA increases for the stronger channel user, whereas the achievable data rate of the negatively-CIS NOMA decreases for the weaker channel user, compared to that of the positively-CIS NOMA for the stronger or weaker channel users, respectively. We also show that the sum rate of the negatively-CIS NOMA is larger than that of the positively-CIS NOMA. As a result, the negatively-CIS could be more efficient than the positively-CIS, when we transmit CIS over 5G NOMA networks.