• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.51-60
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• 1995

Let $(M,g_M,F)$ be a (p+q)-dimensional connected Riemannian manifold with a foliation $F$ of codimension q and a complete bundle-like metric $g_M$ with respect to $F$. Let $Ric_D$ be the transverse Ricci field of $F$ with respect to the transverse Riemannian connection D which is a torsion-free and $g_Q$-metrical connection on the normal bundle Q of $F$. We consider transverse confomal (or, projective) fields of $F$. It is clear that a tranverse Killing field s of $F$ preserves the transverse Ricci field of $F$, that is, $\Theta(s)Ric_D = 0$, where $\Theta(s)$ denotes the transverse Lie differentiation with respect to s.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.201-208
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• 2010

Mobile Ad Hoc Network(MANET) has highly dynamic topology, hence presents a great challenge on the network performance evaluation and network protocol design. We proposed total path break up time, $\sum_{i}T_i$, as a metric to measure the performance of the total system as well as an individual connection. In this paper, we evaluate and analyze the performance of three mobility models(Random Waypoint, Manhattan, Blocked Manhattan) by applying the total path break up metric, investigate why network parameters such as packet delivery ratio, end-to-end delay, etc. vary by mobility models. We also present analysis result how much AODV Buffer improve packet delivery ratio and increase the end-to-end delay in spite of the path break up.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1003-1016
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• 2023

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M_⊥×_ϕM_T, where M_⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type M_T×_ϕM_⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

• Journal for History of Mathematics
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• v.31 no.1
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• pp.37-51
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• 2018

In this paper, our main concern is the historical development of the Finsler geometry in Debrecen, Hungary initiated by L. Berwald. First we look into the research trend in Berwald's days affected by the $G{\ddot{o}}ttingen$ mathematicians from C. Gauss and downward. Then we study how he was motivated to concentrate on the then completely new research area, Finsler geometry. Finally we examine the course of establishing Hungarian Debrecen school of Finsler geometry via the scholars including O. Varga, A. $Rapcs{\acute{a}}k$, L. $Tam{\acute{a}}ssy$ all deeply affected by Berwald after his settlement in Debrecen, Hungary.

• Journal of Digital Convergence
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• v.12 no.8
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• pp.295-302
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• 2014

Essential to the establishment of such 3D spatial information are the laser scanning technology to obtain high-precision 3D point group data and the photography-metric camera to obtain high-resolution multispectral image information. The photography-metric camera, however, lacks in usability for its broad scope of utilization due to the high purchase price, difficult purchase channel, and low applicability. This study thus set out to investigate a technique to establish multi-dimensional ortho-image data with a single lens reflex digital camera of high speed and easy accessibility for general users. That is, the study remodeled a single lens reflex digital camera and calibrated the remodeled camera to establish 3D multispectral image information, which is the essential data of 3D spatial information. Multi-dimensional ortho-image data were collected by surveying the reference points for stereo photos, taking multispectral shots of the objects, and converting them into ortho-images.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.11A
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• pp.912-923
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• 2011

In this paper, we propose a routing protocol for WMNs to provide passengers in public transportation vehicles (e.g., bus and tram) with Internet access service. In order to support end users with a reliable Internet connection despite the mobility of vehicles, we assume that mesh router, called mobile mesh router (MMR), is installed in a vehicle and manages a route to Internet Gateway (IGW). We therefore propose an efficient routing protocol and its routing metric, called ETT-TR, considering trajectory information of vehicle as well as link quality in order to find a route between them. Using NS-2 simulations, we observe that our proposed routing protocol reduces the end-to-end delay and improves throughput performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9C
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• pp.891-897
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• 2003

Partial response maxim likelihood (PRML) is a powerful and indispensable detection scheme for perpendicular magnetic recording channels. The performance of PRML can be improved by incorporating a noise prediction scheme into branch metric computations of Viterbi algorithm (VA). However, the systems constructed by VA have shortcomings in the form of high complexity and cost. In this connection, a new simple detection scheme is proposed by exploiting the minimum run-length parameter d=1 of RLL code. The proposed detection scheme have a slicer instead of Viterbi detector and a noise predictor as a feedback filter. Therefore, to improve BER performance, the proposed detection scheme is extended to dual detection scheme for improving the BER performance. Simulation results show that the proposed scheme has a comparable performance to noise-predictive maximum likelihood (NPML) detector with less complexity when the partial response (PR) target is (1,2,1).

• Journal of the Korea Institute of Information Security & Cryptology
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• v.34 no.1
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• pp.53-60
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• 2024

Security assessment is an indispensable process for a secure network, and appropriate performance indicators must be present to manage risks. The most widely used quantitative indicator is CVSS. CVSS has a problem that it cannot consider context in terms of subjectivity, complexity of interpretation, and security risks. To compensate for these problems, we propose indicators that itemize and quantify four things: attackers, threats, responses, and assets, taking into account the security context of ISO/IEC 15408 documents. Vulnerabilities discovered through network scanning can be mapped to MITREATT&CK's technology by the connection between weaknesses and attack patterns (CAPEC). We use MITREATT&CK's Groups, Tactic, and Mitigations to produce consistent and intuitive scores. Accordingly, it is expected that security evaluation managers will have a positive impact on strengthening security such as corporate networks by expanding the range of choices among security indicators from various perspectives.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1535-1547
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• 2015

A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.107-117
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• 2004

A new algorithm for planning a collision-free path based on an algebraic curve as well as the concept of path space is developed. Robot path planning has so far been concerned with generating a single collision-free path connecting two specified points in a given robot workspace with appropriate constraints. In this paper, a novel concept of path space (PS) is introduced. A PS is a set of points that represent a connection between two points in Euclidean metric space. A geometry mapping (GM) for the systematic construction of path space is also developed. A GM based on the 2$^{nd}$ order base curve, specifically Bezier curve of order two is investigated for the construction of PS and for collision-free path planning. The Bezier curve of order two consists of three vertices that are the start, S, the goal, G, and the middle vertex. The middle vertex is used to control the shape of the curve, and the origin of the local coordinate (p, $\theta$) is set at the centre of S and G. The extreme locus of the base curve should cover the entire area of actual workspace (AWS). The area defined by the extreme locus of the path is defined as quadratic workspace (QWS). The interference of the path with obstacles creates images in the PS. The clear areas of the PS that are not mapped by obstacle images identify collision-free paths. Hence, the PS approach converts path planning in Euclidean space into a point selection problem in path space. This also makes it possible to impose additional constraints such as determining the shortest path or the safest path in the search of the collision-free path. The QWS GM algorithm is implemented on various computer systems. Simulations are carried out to measure performance of the algorithm and show the execution time in the range of 0.0008 ~ 0.0014 sec.