• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.467-481
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• 2015

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the $Poincar\acute{e}$ polynomial $P_{M(G)}(z)$, which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

• International Journal of Computer Science & Network Security
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• v.21 no.4
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• pp.289-300
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• 2021

Non-abelian group based Cryptography is a field which has become a latest trend in research due to increasing vulnerabilities associated with the abelian group based cryptosystems which are in use at present and the interesting algebraic properties associated that can be thought to provide higher security. When developing cryptographic primitives based on non-abelian groups, the researchers have tried to extend the similar layouts associated with the traditional underlying mathematical problems and assumptions by almost mimicking their operations which is fascinating even to observe. This survey contributes in highlighting the different analogous extensions of traditional assumptions presented by various authors and a set of open problems. Further, suggestions to apply the Hamiltonian Cycle/Path Problem in a similar direction is presented.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.86-94
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• 2004

In this paper, we show that $ G(2^m, 4), m{\geq}3$with at most m-2 faulty elements has a fault-free cycle of length 1 for every ${\leq}1{\leq}2^m-f_v$ is the number of faulty vertices. To achieve our purpose, we define a graph G to be k-fault hypohamiltonian-connected if for any set F of faulty elements, G- F has a fault-free path joining every pair of fault-free vertices whose length is shorter than a hamiltonian path by one, and then show that$ G(2^m, 4), m{\geq}3$ is m-3-fault hypohamiltonian-connected.

• Journal of IKEEE
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• v.24 no.1
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• pp.326-332
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• 2020

This paper presents the design of a routing metric for energy-efficient and low-delay path selection and a new routing protocol utilizing the metric in duty-cycyled wireless sensor networks. The new routing metric based on duty cycle, EDW, can reduce the energy and delay of transmission paths, which represents total waiting time from source to destination due to duty cycle. Therefore, in this paper, we propose a new multipath routing protocol based on cross-layer information utilizing the new routing metric, and simulation results show that the proposed protocol shows better performance of end-to-end delay and energy consumption.

• Journal of the Korean Society of Propulsion Engineers
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• v.4 no.1
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• pp.93-101
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• 2000

In a gas-turbine engine, fan blades in flow path are confronted with many kinds of loading. The study of the excited force by the wake of struts has proposed and the possibility of fatigue failure about rotating fan blades by the excited force at the steady state is evaluated. Equations of the excited force of wakes has been derived at the steady state and the maximum pressure distributions measured at the transient state are proposed. Dynamic characteristics and the fatigue strength of fan blades by experimental test were obtained. To evaluate HCF(High Cycle Fatigue) damage of fan blades, FEM analysis was performed with a steady state harmonic response, which was followed by high cycle fatigue damage factor from goodman diagram.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.2
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• pp.102-108
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• 1988

In this paper, a channel routing algorithm which considers cycle problem is proposed. The requirements of routing is given by pin numbers which imply interconnections between a upper block and lower block of the channel. Output is represented by interconnections among equipotential pins. When input is given, the algorithm constructs a channel representation graph and makes weight of each net. And then it checks cycle and finidhes the routing. If the cycle is detected, it finds path with maze routing. This algorithm have coded in C language on IBM-PC /AT. If cycle is not detected, the results are near optimal values. If it is detected, routing is possible as well.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.335-343
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• 2022

We show that valleys, high peaks, and modular ascents are statistics of Fuss-Catalan paths having a distribution given by the Fuss-Narayana number. We prove the results using the Cycle Lemma and provide bijections among them. We also show that relative peaks are independent of the base path. In particular, valleys and high peaks can be obtained from relative peaks by fixing the base path in certain ways.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.848-851
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• 1996

Based on the minimum cutting time criteria, the tool path generation algorithm of a pocket machining is developed as a form of a built-in cycle for the WOP(workshop oriented programming) of a CNC controller. Based on the given CAD database and tool information, an optimal cutting depth and geometric properties can be generated, then six different tool paths will be generated internally and automatically. Finally, the G code which commands tool movements is generated for CNC machining.

• Journal of Korea Multimedia Society
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• v.21 no.6
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• pp.667-677
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• 2018

Since sensor networks consist of sensor nodes with limited energy resources, so efficient energy use of sensor nodes is very important in the design of sensor networks. Sensor nodes consume a lot of energy for data transmission. Clustering technique is used to efficiently use energy in data transmission. Recently, mobile sink techniques have been proposed to reduce the energy load concentrated on the cluster header near a sink node. The CMS(Cluster-based Mobile sink) technique minimizes the generation of control messages by creating a data transmission path while creating clusters, and supports the inter-cluster one-hop transmission. But, there is a case where there is no connectivity between neighbor clusters, it causes a problem of having a long hop data transmission path regardless of local distance. In this paper, we propose a SCBC(Strong connection balancing cluster) to support the path of the minimum number of hops. The proposed scheme minimizes the number of hops in the data transmission path and supports efficient use of energy in the cluster header. This also minimizes a number of hops in data transmission paths even when the sink moves and establishes a new path, and it supports the effect of extending the life cycle of the entire sensor network.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.10
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• pp.2658-2681
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• 2023

In edge computing scenarios, IoT end devices play a crucial role in relaying and forwarding data to significantly improve IoT network performance. However, traditional routing mechanisms are not applicable to this scenario due to differences in network size and environment. Therefore, it becomes crucial to establish an effective and reliable data transmission path to ensure secure communication between devices. In this paper, we propose a trusted path selection strategy that comprehensively considers multiple attributes, such as link stability and edge cooperation, and selects a stable and secure data transmission path based on the link life cycle, energy level, trust level, and authentication status. In addition, we propose the Stability-based On-demand Multipath Distance Vector (STAOMDV) protocol based on the Ad hoc AOMDV protocol. The STAOMDV protocol implements the collection and updating of link stability attributes during the route discovery and maintenance process. By integrating the STAOMDV protocol with the proposed path selection strategy, a dependable and efficient routing mechanism is established for IoT networks in edge computing scenarios. Simulation results validate that the proposed STAOMDV model achieves a balance in network energy consumption and extends the overall network lifespan.