• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.451-458
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• 2013

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind mean value of the generalized Kloosterman sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.169-178
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• 2011

In this paper, we find character analogues of infinite series identities which come from a certain modular transformation formula given by B. C. Berndt.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• East Asian mathematical journal
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• v.32 no.5
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• pp.609-619
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• 2016

Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.947-965
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• 2010

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.245-261
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• 2015

The notion of a parabolically semistandard tableau is a generalisation of Young tableau, which explains combinatorial aspect of various Howe dualities of type A. We prove a Jacobi-Trudi type formula for the character of parabolically semistandard tableaux of a given generalised partition shape by using non-intersecting lattice paths.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.809-818
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• 2016

Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.

• Korean Journal of Childcare and Education
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• v.12 no.5
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• pp.47-69
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• 2016

The purpose of this study was to examine teaching competency for character education of early childhood teachers and their demands to improve their capacities. 152 kindergarten and child care teachers responded to 30 survey questionnaires, which included 3 sub-factors(commutative, practical, instrumental) of teaching competency for character education of the teachers, as well as 16 detailed components, designed to check their current competency for character education and to investigate the priority elements that they desired to improve. The data were analyzed based on the Borich request formula, the locus for focus model, and the independent sample t-test across the teacher groups. The results were as follows: Firstly, the most highly demanded teaching competency by the teachers was using tools interactively for character education. And the teachers, among the sub-elements, requested (a) recording and evaluating character education systematically, (b) using local or national resources, (c) planning member's participation, and (d) performing character education related activities systematically. Secondly, more new teachers demanded instrumental competency and answered the need of parents' participation among the sub-elements, more than the more experienced teachers, respectively. The study discussed the implications of promoting early childhood teachers' teaching competency for character education.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.4
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• pp.29-35
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• 2014

The formula contains up between the text and the structural information, as well as their mathematical symbols. Research on-line or off-line recognition formula is underway actively used in various fields, and various forms of the equation are implemented recognition system. Although many documents are included in the various formulas, it is not easy to enter a formula into the computer. Recognition of the expression is divided into two processes of symbol recognition and structural analysis. After analyzing the location information of each character is specified to recognize the effective area after each symbol, and to the structure analysis based on the proximity between the characters is recognized as an independent single formula. Furthermore, analyzing the relationship between the front and back each time a combination of the position relationship between each symbol, and then to add the symbol which was able to easily update the structure of the entire formula. In this paper, by using a scanner to scan the book formula was used to interpret the meaning of the recognized symbol has a relative size and location information of the expression symbol. An algorithm to remove the formulas for calculation of the number of formula is present at the same time is proposed. Using the proposed algorithms to scan the books in the formula in order to evaluate the performance verification as 100% separation and showed the recognition rate equation.

• Journal of environmental and Sanitary engineering
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• v.10 no.1
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• pp.12-24
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• 1995

I tried to evaluate the reason of the monthly variation of water quality according to the hydrologic character of Pal- dang reservoir inflow variation. The result of this study is as below; 1 ) COD, BOD, Total- nitrogen and Total- phosphate concentration increase generally according to the flux and Total- phosphate concentration is the most affected item by flux. 2) COD, BOD, Total- nitrogen and Total- phosphate concentration increase according the flux, but they begin to decrease at the below point ; COD · 1,154 CMS, BOD : 1,007 (CMS cubicmeter per second ) and Inflow- Concentration interrelation formula is as below; table omitted.