• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.115-121
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• 1996

Let $\{X(t);\;t{\in}R^n\}$ be a measurable, separable and H-sssis random fields. Here, we suppose that the increments are invariant under all Euclidean rigid body motions. We investigate some properties of H-sssis random fields and monotonicity of projection process $\{X_e(t);\;t{\in}R^1\}$ in any direction $e{\in}R^n$.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.460-465
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• 2004

In this paper, we present some properties on receding horizon $H_{\infty}$ control for nonlinear discrete-time systems. First, we propose the nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures the closed-loop internal stability. The proposed receding horizon $H_{\infty}$ control guarantees the infinite horizon $H_{\infty}$ norm bound of the closed-loop systems. Also, using this cost monotonicity condition, we can guarantee the asymptotic infinite horizon optimality of the receding horizon value function. With the additional condition, the global result and the input-to-state stable property of the receding horizon value function are also given. Finally, we derive the stability margin for the saddle point value based receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.479-495
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• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.749-754
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• 1999

The cost is known to be proportional to the size of sample. We consider a cost function of the form Cost=c1np+c2npmq where c1, c2 p, and q are all positive constants. This cost function is to be used in finding an optimal allocation in two-stage cluster sampling. The optimal allocations of n and m gives the properties of uniqueness under some conditions and of monotonicity with p>0 when q=1.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.769-778
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• 1997

Assembly/Disassembly Queueing Networks (ADQNs) with finite buffers have been used as a major tool for evaluating the performances of manufacturing and parallel processing systems. In this study, we present simple but effective methods which yield throughput upper and lower bounds for ADQNs with exponential service times and finite buffers. These methods are based on the monotonicity properties of throughputs with respect to service times and buffer capacities. The throughput-upper bounding method is elaborated on with general network configuration (specifically acyclic configuration). But our lower bounding method is restricted to the ADQNs with more specialized configuration. Computational experiments will be performed to confirm the effectiveness of our throughput-bounding methods.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.209-212
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}_1,\;{\mu}_2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.7-7
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• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.111-125
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• 1992

Since Zadeh's definition for probability of fuzzy event is presented, alternative definitions for probability of fuzzy event is suggested. Also various properties of these new definitions have been presented. In this paper it is our purpose to show the works continued by finding a natural definition of a fuzzy probability measure on an arbitrary fuzzy measurable space. Thus, the main process is to observe fuzzy probability measure to be qualified by weak axioms of boundary condition, monotonicity and continuity suggested by Klir (1988). Especially, we will show that these axioms are satisfied through in succession of modifications from the Yager's method.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1283-1297
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• 2010

In this article, the logarithmically complete monotonicity of some functions such as $\frac{1}{[\Gamma(x+1)]^{1/x}$, $\frac{[\Gamma(x+1)]^{1/x}}{x^\alpha}$, $\frac{[\Gamma(x+1)]^{1/x}}{(x+1)^\alpha}$ and $\frac{[\Gamma(x+\alpha+1)]^{1/(x+\alpha})}{[\Gamma(x+1)^{1/x}}$ for $\alpha{\in}\mathbb{R}$ on ($-1,\infty$) or ($0,\infty$) are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.433-448
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• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.