• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-667
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• 2011

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• The Mathematical Education
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• v.49 no.2
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• pp.247-257
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• 2010

In this article an explanation of monotonicity of functions and the definition of local extrema in Korean highschool textbooks based on national curriculum(revised in 2007) are analyzed critically. On the basis of this analysis, we indicate some problems and propose its improvements.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1441-1461
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• 2019

In this paper we consider the monotonicity of the lowest constant ${\lambda}_a^b(g)$ under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow such that the equation $$-{\Delta}u+au\;{\log}\;u+bRu={\lambda}_a^b(g)u$$ with ${\int}_{M}u^2dV=1$, has positive solutions, where a and b are two real constants. We also construct various monotonic quantities under the Ricci-Bourguignon flow and the normalized Ricci-Bourguignon flow. Moreover, we prove that a compact steady breather which evolves under the Ricci-Bourguignon flow should be Ricci-flat.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• Journal of English Language & Literature
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• v.57 no.3
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• pp.429-455
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• 2011

Numbers have been regarded as one-sided, and their exactly readings have been understood as the results of scalar implicature. This Neo-Gricean view on numbers becomes less persuasive due to theoretical and experimental counterarguments. In spite of growing evidence for theirtwo-sided readings, numbers are still one-sided in modal sentences. Moreover, the occurrence of a negative operator may worsen the acceptability of modal sentences with numbers. In the framework of Vector Space Semantics, I have derived two-sided readings of numbers with the simple notions of monotonicity of modals and scopal relations between modals and numbers. I have also argued that the awkwardness incurred by negation is the result of a split set of vectors for a number. The incoherent set of vectors is understood as the lack of an ideal behavior, which is against the deontic modality of the sentence.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.701-708
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• 2001

In this article, using the properties of power mean, some new generalizations of the strengthened Hardy's inequalities are given.

• 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.

• 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.