• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.1155-1156
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• 2012

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.371-384
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• 2005

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.33-44
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• 2017

We review weighted power means of positive real numbers and see their properties including the convexity and concavity for weights. We study the mixed power means of positive real numbers related to majorization of weights, which gives us an extension of Muirhead's inequality. Furthermore, we generalize Holland's conjecture to the power means.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.1
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• pp.96-104
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• 1990

In this paper, a novel method of jig-saw puzzle matching is proposed using a modifided boundary matching algorithm without a priori knowledge for the matched puzzle. Specifically, a boundary tracking algorithm is utilised to segment each puzzle from low-resolution image data. Segmented puzzle is described via corner point, angle and distance between two adjacent coner point, and convexity and/or concavity of corner point. Proposed algorithm is implemented and tested in IBM PC and PC version vision system, and applied successfully to real jig-saw puzzles.

• 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.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.229-235
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• 2005

The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class $C^2$. Moreover, we find more characterizations for spherically concave functions.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1495-1510
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• 2022

This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

• Restorative Dentistry and Endodontics
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• v.16 no.2
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• pp.174-181
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• 1991

A model system was used which enabled the same root canal system to be measured before and after coronal flaring of 51 extracted mandibular molars. The concavity of the distal surface of the mesial root was measured and the amount of reduction was compared after coronal flaring using step-back flared preparation, Gates-Glidden dirll or ultrasonic system(Quick-$\varepsilon$) at the furcation and apical 3mm from the furcation. The results were as follows: 1. The mean concavity of mesial root of manchbular molar was $0.73{\pm}0.27mm$ at the bifurcation and $0.65{\pm}0.23mm$ at the 3.0mm apical from the bifurcation. 2. The thickness of the root canal wall of the mesiobuccal canal was $1.08{\pm}0.26mm$ at the bifurcation and $1.00{\pm}0.23mm$ at the 3.0mm apical from the bifurcation. 3. The thickness of the root canal wall of the mesiolingual was $1.09{\pm}0.21mm$ at the bifurcation and $0.98{\pm}0.29mm$ at the 3.0mm apical from the bifurcation. 4. In the amount of reduction at the furcation and at the 3.0mm apical from the furcation there was no statistically significant difference between the step-back preparation and Gates-Glidden drill preparation, and ultrasonic preparation(P>0.05).