• 대한수학회보
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• 제24권1호
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• pp.46-46
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• 1987

• 충청수학회지
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• 제5권1호
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• pp.123-141
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• 1992

• 천문학회보
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• 제39권2호
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• pp.89-89
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• 2014

While the current consensus view holds that galaxy mergers are commonplace, it is sometimes speculated that Globular Clusters (GCs) may also have undergone merging events, possibly resulting in massive objects with a strong metallicity spread such as Omega Centauri. Galaxies are mostly far, unresolved systems whose mergers are most likely wet, resulting in observational as well as modeling difficulties, but GCs are resolved into stars that can be used as discrete dynamical tracers, and their mergers might have been dry, therefore easily simulated with an N-body code. It is however difficult to determine the observational parameters best suited to reveal a history of merging based on the positions and kinematics of GC stars, if evidence of merging is at all observable. To overcome this difficulty, we investigate the applicability of supervised and unsupervised machine learning to the automatic reconstruction of the dynamical history of a stellar system. In particular we test whether statistical clustering methods can classify simulated systems into monolithic versus merger products. We run direct N-body simulations of two identical King-model clusters undergoing a head-on collision resulting in a merged system, and other simulations of isolated King models with the same total number of particles as the merged system. After several relaxation times elapse, we extract a sample of snapshots of the sky-projected positions of particles from each simulation at different dynamical times, and we run a variety of clustering and classification algorithms to classify the snapshots into two subsets in a relevant feature space.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.1549-1552
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• 1991

We apply a TDOF ( Two Degrees of Freedom) robust controller to chaotic systems. We show that the TDOF robust controller is effective not only for rejection of chaotic disturbance but also for control of a chaotic plant.

• 대한수학회보
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• 제51권2호
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• pp.457-478
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• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

• 대한수학회지
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• 제52권5호
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• pp.955-964
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• 2015

Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.

• 대한수학회지
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• 제54권1호
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• pp.1-16
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• 2017

In this paper we study a four dimensional tourism-based social-ecological dynamical system. In fact we analyse tourism profitability, compatibility and sustainability by using bifurcation theory in terms of structural properties of attractors of system. For this purpose first we transformed it into a three dimensional system such that the reduced system is the extended and modified model of the previous three dimensional models suggested for tourism with the same dimension. Then we investigate transcritical, pitchfork and saddle-node bifurcation points of system. And numerically by finding some branches of stable equilibria for system show the profitability of tourism industry. Then by determining the Hopf bifurcation points of system we find a family of stable attractors for that by numerical techniques. Finally we conclude the existence of these stable limit cycles implies profitability and compatibility and then the sustainability of tourism.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.721-741
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• 2011

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권6호
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• pp.2504-2526
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• 2016

Wireless sensors are always deployed in brutal environments, but as we know, the nodes are powered only by non-replaceable batteries with limited energy. Sending, receiving and transporting information require the supply of energy. The essential problem of wireless sensor network (WSN) is to save energy consumption and prolong network lifetime. This paper presents a new communication protocol for WSN called Dynamical Threshold Control Algorithm with three-parameter Particle Swarm Optimization and Ant Colony Optimization based on residual energy (DPA). We first use the state of WSN to partition the region adaptively. Moreover, a three-parameter of particle swarm optimization (PSO) algorithm is proposed and a new fitness function is obtained. The optimal path among the CHs and Base Station (BS) is obtained by the ant colony optimization (ACO) algorithm based on residual energy. Dynamical threshold control algorithm (DTCA) is introduced when we re-select the CHs. Compared to the results obtained by using APSO, ANT and I-LEACH protocols, our DPA protocol tremendously prolongs the lifecycle of network. We observe 48.3%, 43.0%, and 24.9% more percentages of rounds respectively performed by DPA over APSO, ANT and I-LEACH.

• 천문학회보
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• 제44권2호
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• pp.37.3-37.3
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• 2019

We study the stellar populations of the brightest group galaxies (BGGs) in groups whose halos have different dynamical states, using observational data from the GAMA survey. The two independent indicators to probe the dynamical state of the halo are the magnitude gap between two most luminous galaxies (∆M12) and offset between BGG and the luminosity center (Doffset) of the group. Such indicators complement each other in identifying relaxed and unrelaxed galaxy groups in our samples. We find that the BGGs of unrelaxed groups have significantly bluer NUV-r colours than in relaxed groups. This is also true at fixed sersic index. We find the bluer colours cannot be explained away by differing dust fraction, suggesting there are real differences in their stellar populations. SFRs derived from SED-fitting tend to be higher in unrelaxed systems. This could be partly because there is a greater fraction of BGGs with non-elliptical morphology, but also because unrelaxed systems are expected to have larger numbers of mergers, some of which may bring fuel for star formation. The SED-fitted stellar metallicities of BGGs in unrelaxed systems also tend to be higher, perhaps because the building blocks of the unrelaxed systems were more massive and had more time to enrich themselves. We find that the ∆M12 parameter is the most important parameter behind the observed differences in the relaxed/unrelaxed groups. We also find that groups selected to be unrelaxed using our criteria tend to have higher velocity offsets between the BGG and their group.