• Title/Summary/Keyword: monotonicity

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Zigzag Gait Planning of n Quadruped Walking Robot Using Geometric Search Method (기하학적 탐색을 이용한 4각 보행로봇의 지그재그 걸음새 계획)

  • Park, Se-Hoon;Lee, Seung-Ha;Lee, Yun-Jung
    • 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.

A NEW PREDICTOR-CORRECTOR METHOD FOR NONCOERCIVE MIXED VARIATIONAL INEQUALITIES

  • Noor, Muhammad Aslam
    • 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.

ON CHOQUET INTEGRALS OF MEASURABLE FUZZY NUMBER-VALUED FUNCTIONS

  • Jung, Lee-Chae;Kim, Tae-Kyun;Jeon, Jong-Duek;Kim, Won-Ju
    • 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.

A Note on Statistically Monotonic and Bounded Sequences of Fuzzy Numbers

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • 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.

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Bounding Methods for Markov Processes Based on Stochastic Monotonicity and Convexity (확률적 단조성과 콘벡스성을 이용한 마코프 프로세스에서의 범위한정 기법)

  • Yoon, Bok-Sik
    • 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.

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A note on mean value property and monotonicity

  • Lahiri, Indrajit
    • 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.

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NEW CONDITIONS ON EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Zhengqiu;Zhou, Zheng
    • 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.

CONNECTEDNESS AND COMPACTNESS OF WEAK EFFICIENT SOLUTIONS FOR VECTOR EQUILIBRIUM PROBLEMS

  • Long, Xian Jun;Peng, Jian Wen
    • 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].

POSITIVE SOLUTIONS OF SUPERLINEAR AND SUBLINEAR BOUNDARY VALUE PROBLEMS

  • Gatica, Juan A.;Kim, Yun-Ho
    • 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.

MIXED VECTOR FQ-IMPLICIT VARIATIONAL INEQUALITIES WITH FQ-COMPLEMENTARITY PROBLEMS

  • Lee, Byung-Soo
    • Honam Mathematical Journal
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    • v.31 no.2
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    • pp.247-258
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    • 2009
  • This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].