• Journal of the Semiconductor & Display Technology
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• v.11 no.3
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• pp.13-18
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• 2012

This paper presents a velocity disturbance estimation system for the stable fine seek control using a genetic algorithm. To estimate accurately the velocity disturbance in spite of the uncertainties of fine actuator, the system utilizes an objective function to minimize the differences of the frequency characteristics between the nominal velocity control loop and the extremal velocity control loops. The objective function is considered by applying a genetic algorithm and the velocity disturbance is estimated by the measurable velocity, the adjusted velocity controller, and the fine actuator model. The proposed velocity disturbance estimation system is applied to the fine seek control system of a DVD recording device and is evaluated through the experimental results.

• Journal of Communications and Networks
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• v.7 no.1
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• pp.87-92
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• 2005

This paper presents basic queueing analysis contributing to teletraffc theory, with commonly accessible mathematical tools. This paper studies queueing systems with bulk arrivals. It is assumed that the number of arrivals and the expected number of arrivals in each bulk are bounded by some constraints B and (equation omitted), respectively. Subject to these constraints, convexity argument is used to show that the bulk-size probability distribution that results in the worst mean queue performance is an extremal distribution with support {1, B} and mean equal to A. Furthermore, from the viewpoint of security against denial-of-service attacks, this distribution remains the worst even if an adversary were allowed to choose the bulk-size distribution at each arrival instant as a function of past queue lengths; that is, the adversary can produce as bad queueing performance with an open-loop strategy as with any closed-loop strategy. These results are proven for an arbitrary arrival process with bulk arrivals and a general service model.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.229-242
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• 2022

In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.391-402
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• 2022

For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V ＼ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power G^k of a graph G with V (G^k) = V (G) for which uv ∈ E(G^k) if and only if 1 ≤ d_G(u, v) ≤ k. Note that G² is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1045-1067
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• 2022

Given a graph G, a {1, 3, …, 2n-1}-factor of G is a spanning subgraph of G, in which each degree of vertices is one of {1, 3, …, 2n-1}, where n is a positive integer. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {1, 3, …, 2n-1}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {1, 3, …, 2n-1}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.741-752
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• 2023

A new variant of vertex edge domination, namely semi total vertex edge domination has been introduced in the present paper. A subset S of the vertex set V of a graph G is said to be a semi total vertex edge dominating set(stved - set), if it is a vertex edge dominating set of G and each vertex in S is within a distance two of another vertex in S. An stved-set of G having minimum cardinality is said to be an γ_stve(G)- set and its cardinality is denoted by γ_stve(G). Bounds for γ_stve(G) - set have been given in terms of various graph theoretic parameters and graphs attaining the bounds have been characterized. In particular, bounds for trees have been obtained and extremal trees have been characterized.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• East Asian mathematical journal
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• v.40 no.1
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• pp.75-83
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• 2024

For a reduced, irreducible and nondegenerate curve C ⊂ ℙ^r of degree d, it was shown that the arithmetic genus g of C has an upper bound π₀(d, r) by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll S(0, 2) ⊂ ℙ³ which attain the maximal arithmetic genus.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.2
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• pp.561-574
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• 2018

In this study, regional variations and factors associated with prevalence of metabolic syndrome were grasped using GWR (geographically weighted regression) and methodologies for the efficient management of metabolic syndrome were then set up to resolve health inequalities. Based on the National Health Screening Statistical Yearbook published by the National Health Insurance Service (NHIS), community health survey (KCDC) and other governmental institutions, indicators of social structural and mediation factors related to the regional prevalence of metabolic syndrome were collected. First, the existence of indicators to measure variations in metabolic syndrome were confirmed with the collected data by calculating the EQ (extremal quotient) and CV (coefficient of variations). The GWR, which is able to take spatial variations into consideration, was then adopted to analyze the factors of regional variations in metabolic syndrome. The GWR analysis revealed that severity and management of the main causes need to be prioritized in accordance with the prevalence of metabolic syndrome. Consequently, the order of priority in management of regional prevalence of metabolic syndrome was established, and plans that can increase the effectiveness of management of metabolic syndrome were confirmed to be feasible.