• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.155-163
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• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.525-532
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• 2004

For two vertices u and v of an oriented graph D, the set I(u, v) consists of all vertices lying on a u-v geodesic or v-u geodesic in D. If S is a set of vertices of D, then I(S) is the union of all sets 1(u, v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the subsets S of V(D) with I(S) = V(D). In this paper, we give a partial answer for the conjecture by G. Chartrand and P. Zhang and present some results on orient able geodetic number.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.503-509
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• 2014

For a connected graph G, there are orientations of G have different hull numbers, geodetic numbers, and convexity numbers. The lower orientable hull number $h^-(G)$ is defined as the minimum hull number among all the orientations of G and the upper orientable hull number $h^+(G)$ as the maximum hull number among all the orientations of G. The lower and upper orientable geodetic numbers $g^-(G)$ and $g^+(G)$ are defined similarily. In this paper, We investigate characterizations of the orientable numbers and the conditions that the relation $h^-(G){\leq}g^-(G)$ < $h^+(G){\leq}g^+(G)$ holds.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.255-266
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• 2014

For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.

• 한국측량학회지
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• 제29권4호
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• pp.367-380
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• 2011

본 논문에서는 지각판 운동 지진과 같은 급격한 지각변동을 고려한 국가기준점의 상시적 성과 산정 체계 수립에 관한 연구를 수행하였다. 이를 위하여 GPS 기준점의 국내 현황 및 최근 국가기준점의 재정비가 이루어진 국외 사례 조사로부터 시사점을 도출하고 GPS 상시관측점으로 이루어진 위성기준점망과 6,900 여점으로 이루어진 단일 GPS 망으로 단순화된 국가기준점의 계층 구조를 제안하였다. 또한, 초고정밀 다중기선해석과 정규방정식의 누적에 의한 연속조정을 통한 단계별 위성기준점의 성과 산정 절차 및 다중 세션 조정에 의한 단일 GPS 기준망의 성과 산정 방안을 제시하였다. 또한, 시험 조정망을 구성하여 조정계산을 실시하고 결과 분석을 통해 상시적 성과산정의 필요성과 제안한 성과산정 방법 및 절차의 타당성 등을 평가하였다.

• Computers and Concrete
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• 제20권1호
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• pp.23-29
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• 2017

In this study engineered steel fibres used as reinforcement for concrete were characterized by number of key mechanical and spatial parameters, which are easy to measure and quantify. Such commonly used parameters as length, diameter, fibre intrinsic efficiency ratio (FIER), hook geometry, tensile strength and ductility were considered. Effective classification of various fibres was demonstrated using simple multivariate computations involving principal component analysis (PCA). Contrary to univariate data mining approach, the proposed analysis can be efficiently adapted for fast, robust and direct classification of engineered steel fibres. The results have revealed that in case of particular spatial/geometrical conditions of steel fibres investigated the FIER parameter can be efficiently replaced by a simple aspect ratio. There is also a need of finding new parameters describing properties of steel fibre more precisely.

• 한국측량학회지
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• 제27권1호
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• pp.677-682
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• 2009

개정된 측량법에 의해 2010년부터 모든 위치정보좌표는 세계측지계 좌표를 기준으로 하여야 하며 이를 위해 국토지리정보원을 중심으로 세계측지계로의 전환을 위한 기술적 제도적 기반을 마련하였다. 하지만 여러 저해요인으로 인해 현재 지방자치단체별 전환실적이 상대적으로 미흡한 실정이다. 본 연구에서는 세계측지계로의 전환에 필요한 요소 중 좌표변환방법 및 절차에 대한 분석을 통해 보다 유연성 있는 변환방법을 제시하였으며 기존의 좌표변환절차 중 효율적 인 좌표변환을 위한 보완방안을 제공하였다. 이를 위해 국가변환계수를 이용한 기존의 변환방법보다 효율적인 Affine변환의 유용성 여부를 분석하였으며 기준점의 허용오차 분석을 통해 공통점에 존재하는 비상사점의 판별 기준을 제시하였다. 또한 구성과 및 신성과가 혼재하는 지역에서의 효율적인 세계측지계 좌표변환 방법 및 세계측지계 변환에 필요한 공통점의 적절한 수량을 제시하였다.

• Structural Monitoring and Maintenance
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• 제8권4호
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• pp.309-328
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• 2021

The objective of this work was to develop a methodology for geodetic monitoring on onshore wind towers, to ascertain the existence of displacements from object points located in the tower and at the foundation's base. The geodesic auscultation was carried out in the Gravatá 01 and 02 wind towers of the Eólica Gravatá wind farm, located in the Brazilian municipality of Gravatá-PE, using a stable Measurement Reference System. To verify the existence of displacements, pins were implanted, with semi-spherical surfaces, at the bases of the towers being monitored, measured by means of high-precision geometric leveling and around the Gravatá 02 tower, concrete landmarks, iron rods and reflective sheets were implanted, observed using geodetic/topographic methods: GNSS survey, transverse with forced centering, three-dimensional irradiation, edge measurement method and trigonometric leveling of unilateral views. It was found that in the Gravatá 02 tower the average rays of the circular sections of the transverse welds (ST) were 1.8431 m ± 0.0005 m (ST01) and 1.6994 m ± 0.0268 m of ST22, where, 01 and 22 represent the serial number of the transverse welds along the tower. The average calculation of the deflection between the coordinates of the center of the circular section of the ST22 and the vertical reference alignment of the ST1 was 0°2'39.22" ± 2.83" in the Northwest direction and an average linear difference of 0.0878 m ± 0.0078 m. The top deflection angle was 0°8'44.88" and a linear difference of ± 0.2590 m, defined from a non-linear function adjusted by Least Squares Method (LSM).

• 대한수학회논문집
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• 제32권4호
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• pp.805-810
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• 2017

Let $C_n$ be the cycle graph of order n on the vertices $v_0,v_1,{\ldots},v_n$ and $C^k_n$ be the k-th power of $C_n$. In this article we determine the hull-number of $C^k_n$.