• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.541-551
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• 2009

Generalized processor sharing(GPS) service policy is a scheduling algorithm to allocate the bandwidth of a queueing system with multi-class input traffic. In a queueing system with single-class traffic, the stationary queue length becomes larger stochastically when the bandwidth (i.e. the service rate) of the system decreases. For a given GPS server, we consider the similar problem to this. We define the monotonicity for the head of the line processor sharing(HLPS) servers in which the units in the heads of the queues are served simultaneously and the bandwidth allocated to each queue are determined by the numbers of units in the queues. GPS is a type of monotonic HLPS. We obtain the HLPS server whose queue length of a class stochastically bounds upper that of corresponding class in the given monotonic HLPS server for all classes. The queue lengths process of all classes in the obtained HLPS server has the stationary distribution of product form. When the given monotonic HLPS server is GPS server, we obtain the explicit form of the stationary queue lengths distribution of the bounding HLPS server. Numerical result shows how tight the stochastic bound is.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.2
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• pp.142-150
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• 2002

This paper presents a systematic method of the zigzag gait planning for quadruped walking robots. When a robot walks with a zigzag gait, its body is allowed to move from side to side, while the body movement is restricted along a moving direction in conventional continuous gaits. The zigzag movement of the body is effective to improve the gait stability margin. To plan a zigzag gait in a systematic way, the relationship between the center of gravity(COG) and the stability margin is firstly investigated. Then, new geometrical method is introduced to plan a sequence of the body movement which guarantees a maximum stability margin as well as monotonicity along a moving direction. Finally, an optimal swing-leg sequence is chosen for a given arbitrary configuration of the robot. To verify the proposed method, computer simulations have been performed for both cases of a periodic gait and a non-periodic gait.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.483-491
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• 2000

In this paper, we use the auxiliary principle technique to suggest and analyze a class of predictor-corrector methods for solving noncoercive mixed variational inequalities. The convergence of the proposed method requires only the partially relaxed strongly monotonicity. which is even weaker than the co-coercivity. As special cases, we obtain a number of new and known results for classical variational inequalities.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-107
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• 2004

In this paper, we consider fuzzy number-valued functions and fuzzy number-valued Choquet integrals. And we also discuss positively homogeneous and monotonicity of Choquet integrals of fuzzy number-valued functions(simply, fuzzy number-valued Choquet integrals). Furthermore, we prove convergence theorems for fuzzy number-valued Choquet integrals.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.657-659
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• 2006

This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.117-126
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• 1991

When {X(t), t ${\geq}$ 0} is a Markov process representing time-varying system states, we develop efficient bounding methods for some time-dependent performance measures. We use the discretization technique for stochastically monotone Markov processes and a combination of discretization and uniformization for Markov processes with the stochastic convexity(concavity) property. Sufficient conditions for stochastic monotonocity and stochastic convexity of a Markov process are also mentioned. A simple example is given to demonstrate the validity of the bounding methods.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.329-334
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• 1996

The notion of approximate derivative was introduced by Denjoy in 1916 [3]. Khintchine [5] proved that Rolle's theorem holds for approximate derivatives and Tolstoff [8] proved that every approximate derivative is of Baire class 1 and has Darboux property. Goffman and Neugebauer [4] proved the above results of Tolstoff [8] in a different and simplified method. Also they [4] proved indirectly (via Darboux property) that approximate derivatives possess mean value property.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.37-43
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• 2017

We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.