• The Mathematical Education
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• v.60 no.3
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• pp.281-295
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• 2021

This study examines the breadth and depth of knowledge of the teacher employment test for secondary mathematics. For the breadth of knowledge, we attempted to figure out the range of knowledge in terms of the content areas using the standards from the Korea Society Educational Studies in Mathematics[KSESM](2008). For the depth of knowledge, we chose Anderson & Krathwohl(2001) framework to analyze levels of each item in the test. The results from the analysis of 180 items in the teacher employment test between 2014 and 2021 show that while items in mathematics education have considerable variation in terms of range and levels of knowledge, those in some subjects of mathematics can be found only certain level of knowledge. i.e., merely certain topics or levels of knowledge have been heavily evaluated. Thus, considering the breadth and depth of knowledge teachers should have, the current exam needs to be improved in terms of teacher knowledge. It does not mean that every topic and every level of knowledge should be evaluated. However, it is a meaningful opportunity to think about what kinds of knowledge teachers should have in relation to K-12 mathematics curriculum and how we can evaluate the knowledge. More collaborative effort is inevitable for the improvement of teacher knowledge and teacher employment test.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1189-1194
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• 2010

Kim and Park investigated the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms, where the absolute value of middle coefficient equals the sum of all other coefficients. In this paper, we extend some of their results to the same kinds of polynomials with arbitrary many nonzero terms.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.411-422
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• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.605-622
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• 2018

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.495-511
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• 2012

In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.213-222
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• 1998

In this paper we propose several estimators of Gini index of the two-parameter exponential distribution and obtain dis-tributions and moments of the proposed estimators. The proposed estimators are shown to cosistency and will be compares in terms of the proposed estimators. The proposed estimators are shown to cosistency and will be compared in terms of the mean squared error (MSE) through Monte Carlo method.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.1009-1020
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• 1999

The minimum permanent and the set of minimizing matrices over the face of the polytope n of all doubly stochastic matrices of order n determined by any staircase matrix was determined in [4] in terms of some parameter called frame. A staircase matrix can be described very simply as a Ferrers matrix by its row sum vector. In this paper, some simple exposition of the permanent minimization problem over the faces determined by Ferrers matrices of the polytope of n are presented in terms of row sum vectors along with simple proofs.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.147-154
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• 2009

Tamanoi proposed higher Schwarzian operators which include the classical Schwarzian derivative as the first nontrivial operator. In view of the relations between the classical Schwarzian derivative and the analogous differential operator defined in terms of Peschl's differential operators, we define the generating function of our generalized higher operators in terms of Peschl's differential operators and obtain recursion formulas for them. Our generalized higher operators include the analogous differential operator to the classical Schwarzian derivative. A special case of our generalized higher Schwarzian operators turns out to be the Tamanoi's operators as expected.