• 대한수학회논문집
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• 제23권3호
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• pp.349-356
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• 2008

In this paper, we generalize the Catalan number to the (n, k)-th Catalan numbers and find a combinatorial description that the (n, k)-th Catalan numbers is equal to the number of partitions of n(k-1)+2 polygon by (k+1)-gon where all vertices of all (k+1)-gons lie on the vertices of n(k-1)+2 polygon.

• 대한수학회논문집
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• 제29권1호
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• pp.187-193
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• 2014

In this paper, we want to represent a method for ranking of two exponential trapezoidal fuzzy numbers. In this study a new Cardinality between exponential trapezoidal fuzzy numbers is proposed. Cardinality in this method is relatively simple and easier in computation and ranks various types of exponential fuzzy numbers. For the validation the results of the proposed approach are compared with different existing approaches.

• 대한수학회보
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• 제33권2호
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• pp.205-211
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• 1996

Throughout this paper, we will work in the category of compact connected manifolds and continuous maps. If $X_1, X_2$ are manifolds, $f, g: X_1 \to X_2$ are maps, then a point $x \in X_1$ is a coincidence of f and g iff f(x) = g(x) ; the set of all such points is denoted by Coin(f,g).

• 대한수학회논문집
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• 제21권1호
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• pp.193-209
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• 2006

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

• 대한수학회지
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• 제37권3호
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• 대한수학회보
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• 제56권3호
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• pp.649-658
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• 2019

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo $p^2$, one of which is $$\sum\limits_{k=1}^{p-1}k^2B_{p,k}B_{p,k-d}{\equiv}4(-1)^d\{{\frac{1}{3}}d(2d^2+1)(4pH_d-1)-p\({\frac{26}{9}}d^3+{\frac{4}{3}}d^2+{\frac{7}{9}}d+{\frac{1}{2}}\)\}\;(mod\;p^2)$$, where a prime number p > 3 and $1{\leq}d{\leq}p$.

• 한국정보과학회논문지:소프트웨어및응용
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• 제28권12호
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• pp.930-937
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• 2001

퍼지숫자의 정렬은 퍼지숫자를 크기 순서로 나열을 하는 것이다. 일반적으로 퍼지숫자의 정렬을 위해서는 퍼지숫자 사이의 비교가 필요한데. 피지숫자가 명확하지 않은 값을 표현하기 때문에. 그 비교 결과 역시 명확하지 않을 수 있다 따라서 그 비교결과를 이용한 정렬결과 역시 명확하지 않을 수 있다 그러나 지금가지 대부분의 연구는 퍼지숫자의 정렬 결과를 하나의 배역로만 명확하게 표현하였다. 본 논문 에서는 이러한 점을 고려하여 퍼지만족함수를 이용한 퍼지숫자 정렬방법을 제안한다. 퍼지만족함수는 두 퍼지숫자를 비교하여 그 대소를 0과 1사이의 퍼지집합으로 표현하는 퍼지비교방법이다. 제안하는 방법은 정렬결과로 단순히 하나의 배열만을 생성하지 않고, 퍼지숫자가 겹쳐서 생길 수 있는, 다른 가능한 정렬결 과들을 생성한다.

• 대한수학회보
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• 제52권3호
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• pp.741-749
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• 2015

The Changhee polynomials and numbers are introduced in [6]. Some interesting identities and properties of those polynomials are derived from umbral calculus (see [6]). In this paper, we consider Witt-type formula for the n-th twisted Changhee numbers and polynomials and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials.

• 대한수학회보
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• 제57권3호
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• pp.623-647
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• 2020

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base b, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base b and omit the proofs for the Thabit numbers of the first kind base b and Cunningham numbers.

• 오토저널
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• 제10권1호
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• pp.26-32
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• 1988

A study has been conducted experimentally on the natural convection heat transfer characteristics of fin arrays on a horizontal flat plate in air. The effects of fin heights and Rayleigh numbers are mainly investigated. The experimental results are as follows; 1. The mean fin and mean total Nusselt numbers increase as dimensionless fin heights increase at 0.67.leg.H/s.leg.1.67. The mean plate Nusselt numbers increase in case of upward facing fins, but they decrease in case of downward facing fins. 2. The mean Nusselt numbers increase as Rayleigh numbers increase. 3. The mean fin surface Nusselt numbers has its maximum outside surface (Y$_{1}$) where there is no interference from each other fin. 4. The mean total Nusselt numbers in case of upward facing fins increase by 47% and 26%, respectively at H/S=0.67 and 1.67 than those in case of downward facing fins for Ra$_{s}$=6.50*10$^{3}$.>.