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

• Journal of the Korea Computer Graphics Society
• /
• v.13 no.4
• /
• pp.21-27
• /
• 2007

The 3D Delaunay triangulation is the most widely used method for the mesh creation via the triangulation of a 3D point cloud. However, the method involves a heavy computational cost and, hence, in many interactive applications, it is not appropriate for surface triangulation. In this paper, we propose an efficient triangulation method to create a surface mesh from a 3D point cloud. We divide a set of object points into multiple subsets and apply the 2D Delaunay triangulation to each subset. A given 3D point cloud is cut into slices with respect to the OBB(Oriented Bounding Box) of the point set. The 2D Delaunay triangulation is applied to each subset producing a partial triangulation. The sum of the partial triangulations constitutes the global mesh. As a postprocessing process, we eliminate false edges introduced in the split steps of the triangulation and improve the results. The proposed method can be effectively applied to various image-based modeling applications.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.787-811
• /
• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• East Asian mathematical journal
• /
• v.25 no.2
• /
• pp.179-196
• /
• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.1
• /
• pp.15-26
• /
• 2013

This paper proposes a classification method of parallel, vertical parking states and pillars for parking assist system using ultrasonic sensors. Since, in general parking space detection module, the compressed amplitude of ultrasonic data are received, the analysis of them is difficult. To solve these problems, in preprocessing state, symmetric transform and noise removal are performed. In feature extraction process, four features, standard deviation of distance, reconstructed peak, standard deviation of reconstructed signal and sum of width, are proposed. Gaussian fitting model is used to reconstruct saturated peak signal and discriminability of each feature is measured. To find the best combination among these features, multi-class SVM and subset generator are used for more accurate and robust classification. The proposed method shows 92 % classification rate and proves the applicability to parking space detection modules.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.875-883
• /
• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10a
• /
• pp.857-862
• /
• 1987

Given a network with k specified vertices bi called centers, a cardinality constrained cover is a family {Bi} of k subsets covering the vertex set of a network, such that each subset Bi corresponds to and contains center bi, and satisfies a given cardinality constraint. A set of cardinality constrained overlapping territories is a cardinality constrained cover such that the total sum of T(B$_{i}$) for all subsets is minimum among all cardinality constrained covers, where T(B$_{i}$) is the summation of the shortest path lengths from center bi to every vertex in B$_{I}$. This paper considers a problem of finding a set of cardinality constrained overlapping territories. and proposes an algorithm for the Problem which has the time and space complexities are O(k$^{3}$$\mid$V$\mid$$^{2}$) and O(k$\mid$V$\mid$+$\mid$E$\mid$), respectively, where V and E are the sets of vertices and edges of a given network, respectively. The concept of overlapping territories has a possibility to be applied to a job assignment problem.oblem.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.753-762
• /
• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Journal of KIISE:Computer Systems and Theory
• /
• v.29 no.4
• /
• pp.213-219
• /
• 2002

A secret sharing scheme is a kind of cryptographic protocol to maintain secret information by splitting it to many small pieces of shares and sharing between shareholders. In case of shareholders having different authorization to reconstruct the original secret, it is required a new secret sharing scheme to reflect any hierarchical structure between shareholders. In this paper, we propose a new weighted secret sharing scheme, that is, each shareholder has a weight according to the authorization of reconstructing the secret and an access set which is a subset of shareholders can reconstruct the secret if the sum of weights is equal or greater than a predefined threshold.

• Health Policy and Management
• /
• v.13 no.1
• /
• pp.98-115
• /
• 2003

Concerns about growing health insurance expenditures became a national Issue in 2001 when the National Health Insurance went into a deficit. Increases in spending for ambulatory care shared the largest portion of the problem. Methods and systems to control the spending should be developed and a system to measure case mix of providers is one of core components of the control system. The objectives of this article is to examine the feasibility of applying Korean Diagnosis Related Groups (KDRGs) to classify health insurance claims for ambulatory care and to identify problem areas of the classification. A database of 11,586,270 claims for ambulatory care delivered during January 2002 was obtained for the study, and the final number of claims analyzed was 8,319,494 after KDRG numbers were assigned to the data and records with an error KDRG were excluded from the study. The unit of analysis was a claim and resource use was measured by the sum of charges incurred during a month at a department of a hospital of at a clinic. Within group variance was assessed by th coefficient of variation (CV), and the classification accuracy was evaluated by the variance reduction achieved by the KDRG classification. The analyses were performed on both all and non-outlier data, and on a subset of the database to examine the validity of study results. Data were assigned to 787 KDRGs among 1,244 KDRGs defined in the classification system. For non-outlier data, 77.4％ of KDRGs had a CV of charges from tertiary care hospitals less than 100％ and 95.43％ of KDRGs for data from clinics. The variance reduction achieved by the KDRG classification was 40.80％ for non-outlier claims from tertiary care hospitals, 51.98％ for general hospitals, 40.89% for hospitals, and 54.99% for clinics. Similar results were obtained from the analyses performed on a subset of the study database. The study results indicated that KDRGs developed for a classification of inpatient care could be used for ambulatory care, although there were areas where the classification should be refined. Its power to predict tile resource utilization showed a potential for its application to measure case mix of providers for monitoring and managing delivery of ambulatory care. The issue concerning the quality of diagnostic information contained in insurance claims remains to be improved, and significance of future studies for other classification systems based on visits or episodes is guaranteed.