• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.893-904
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• 2022

In this note, we apply a maximum principle related to volume growth of a complete noncompact Riemannian manifold, which was recently obtained by Alías, Caminha and do Nascimento in [4], to establish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.115-126
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• 1998

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

• Management Science and Financial Engineering
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• v.13 no.2
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• pp.99-116
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• 2007

This paper considers the value of location in a linear city model and examines the product differentiation equilibrium of duopoly providing different benefits to consumers. We show that if the value of location is small, symmetric location equilibrium occurs where two firms follow the maximal differentiation principle. However, as the value of location increases, asymmetric location equilibrium occurs where the low-value-location firm moves to the high-value-location firm and thus adjusted maximal differentiation principle holds. We also investigate two different price leadership model and demonstrate the relationship between the value of location and the role of price leadership. In particular, we show that when the location value is high, the price leadership by high-value-location firm will appear as a unique equilibrium.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1067-1076
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• 2010

In this paper we investigate complete spacelike (r - 1)-maximal (i.e., $H_r\;{\equiv}\;0$) hypersurfaces with two distinct principal curvatures in the anti-de Sitter space $\mathbb{H}_1^{n+1}$(-1). We give a characterization of the hyperbolic cylinder.

• Korean Journal of Applied Biomechanics
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• v.25 no.2
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• pp.157-165
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• 2015

Object : The goals of this research were to make Performance Enhanced Model(PE) taken the largest performance index (PI) through artificial variation of principle components calculated by principle component analysis for trial data, and to verify the effect through comparing kinematic factors between trial data (Raw) and PE. Method : Ten subjects (5 men, 5 women) were recruited and 80% of their maximal record was considered. The PI is a regression equation. In order to develop PE, we extracted Principle components from trial position data (by Principle Components Analysis (PCA)). Before PCA, we made 17 position data to 3 row matrix according to components. We calculated 3 eigen value (principle components) through PCA. And except Y (medial-lateral direction) component (because motion of Y component is small), principle components of X (anterior-posterior direction) and Z (vertical direction) components were changed as following. Changed principle components = principle components + principle components ${\times}$ k. After changing the each principle component, we reconstructed position data using the changed principle components and calculated performance index (PI). A Paired t-test was used to compare Raw data and Performance Enhanced Model data. The level of statistical significance was set at $p{\leq}0.05$. Result : The PI was significantly increased about 12.9kg at PE ($101.92{\pm}6.25$) when compared to the Raw data ($91.29{\pm}7.10$). It means that performance can be increased by optimizing 3D positions. The difference of kinematic factors as follows : the movement distance of the bar from start to lock out was significantly larger (about 1cm) for PE, the width of anterior-posterior bar position in full phase was significantly wider (about 1.3cm) for PE and the horizontal displacement toward the weightlifter after beginning of descent from maximal height was significantly greater (about 0.4cm) for PE. Additionally, the minimum knee angle in the 2-pull phase was significantly smaller (approximately 2.7cm) for the PE compared to that of the Raw. PE was decided at proximal position from the Raw (origin point (0,0)) of PC variation). Conclusion : PI was decided at proximal position from the Raw (origin point (0,0)) of PC variation). This means that Performance Enhanced Model was decided by similar motion to the Raw without a great change. Therefore, weightlifters could be accept Performance Enhanced Model easily, comfortably and without large stress. The Performance Enhance Model can provide training direction for athletes to improve their weightlifting records.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.2
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• pp.234-252
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• 2013

Due to the uncertain of connections in Delay Tolerant Networks (DTNs), most routing algorithms in DTNs need nodes to forward the message to others based on the opportunistic contact. The contact is related with the beaconing rate. In particular, nodes have more chances to encounter with each other with bigger beaconing rate, but more energy will be used. On the other hand, if the nodes forward the message to every node all the time, the efficiency of the routing algorithm is better, but it needs more energy, too. This paper tries to exploit the optimal beaconing rate and forwarding rate when the total energy is constraint. First, a theoretical framework is proposed, which can be used to evaluate the performance with different forwarding rate and beaconing rate. Then, this paper formulates a joint optimization problem based on the framework. Through Pontryagin's Maximal Principle, this paper obtains the optimal policy and proves that both the optimal forwarding and beaconing rates conform to threshold form. Simulation results show the accuracy of the theoretical framework. Extensive numerical results show that the optimal policy obtained in this paper is the best.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.707-714
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• 2003

Because of complex aliasing, nonregular designs have traditionally been used for screening only main effects. However, complex aliasing actually may allow some interactions entertained and estimated without making additional runs. According to hierarchical principle, the minimum aberration has been used as an important criterion for selecting regular fractional factorial designs. The criterion is not applicable to nonregular designs. In this paper, we give a criterion for choosing fractional factorial designs based on the fan theory. The criterion is focused on the partial ordering given by set inclusion on estimable sets which is called leaves.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.831-850
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• 2023

Our long-standing Metatheorem in Ordered Fixed Point Theory is applied to some well-known order theoretic fixed point theorems. In the first half of this article, we introduce extended versions of the Zermelo fixed point theorem, Zorn's lemma, and the Caristi fixed point theorem based on the Brøndsted-Jachymski principle and our 2023 Metatheorem. We show some of their applications to other fixed point theorems or theorems on the existence of maximal elements in partially ordered sets. In the second half, we collect and improve order theoretic fixed point theorems in the collection of Howard-Rubin in 1991 and others. In fact, we improve or extend several ordering principles or fixed point theorems due to Brézis-Browder, Brøndsted, Knaster-Tarski, Tarski-Kantorovitch, Turinici, Granas-Horvath, Jachymski, and others.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.835-850
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infected prey and predator system in which both the susceptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to investigate the golbal properties of the system.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.823-834
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• 1999

The present paper deals with the problem of nonselective harvesting in a partly infecte prey and predator system in which both the suseptible prey and the predator follow the law of logistic growth and some preys avoid predation by hiding. The dynamical behaviour of the system has been studied in both the local and global sense. The optimal policy of exploitation has been derived by using Pontraygin's maximal principle. Numerical analysis and computer simulation of the results have been performed to inverstigate the global properties of the system.