• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.603-617
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• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.133-138
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• 2020

It is shown that each sequence lying sufficiently close in the hyperbolic sense to a Q^#_p-sequence for a meromorphic function f in the unit disc is also a Q^#_p-sequence for f.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.35-41
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• 1995

We consider the linear differential equations y〃'＋ P($\chi$)y'＋Q($\chi$)y=0 (1)(y"＋P($\chi$)y)'-Q($\chi$)y =0 (2) Where (2) in the adjoint of (1) and P($\chi$), Q($\chi$) are continuous functions satisfying P($\chi$)$\geq$0, Q($\chi$)$\leq$0, P($\chi$)-Q($\chi$)$\geq$0 on [a, ${\alpha}$). (3) In this, we show that a condition a oscillatory of(1).(omitted)

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.873-882
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• 2022

In this paper, we construct the multiple (h, p, q)-Hurwitz-Euler eta function by generalizing the multiple Hurwitz-Euler eta function. We get some explicit formulas and properties of the higher-order (h, p, q)-Euler numbers and polynomials.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.21-30
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• 2000

We give a proof of the distribution relation for q-Bernoulli polynomials $B_{k}$(x : q) by using q-integral and evaluate the values of p-adic q-L-function.n.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.243-254
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• 1997

특정분포에 대한 P-P plot과 Q-Q plot의 특징을 분석하고 두 가지 그래프 사이의 관계를 비교해 보았다. NTV의 본질적인 특징을 알아보고 각 특정분포에 대한 NTV plot의 특징을 분석했다. 전형적인 bimodal 분포가 나타날 때 P-P 혹은 Q-Q plot은 뚜렷한 break-point를 갖는다는 것을 알아보고, 단지 skewed된 분포나 skewed된 것처럼 보이는 bimodal 분포 사이에서 발생하는 판단의 어려움에 대하여 여러 plot고찰해 보았다.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.205-215
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• 1998

정규분포에 관한 검정에 있어서 P-P 플롯과 Q-Q 플롯의 가시적인 변동을 이용한 통계량을 제시하고 이 통계량들과 Shapiro-Wilk의 W 통계량과의 비교를 정확도(accuracy)의 측면을 고려하여 실시하였다. 또한, 의학이나 임상에서 척도의 우수성을 검정하기 위해 많이 사용하는 Receiver Operating Characteristic (ROC) 분석 기법을 이용하여 제시된 통계량들에 관한 Power와 Accuracy는 물론 Best Cut-Off 측면에서의 효율성을 검정하였다.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.367-370
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• 2016

In this paper, we consider the generalized Lucas sequence which is the (p, q) - Lucas sequence. Then we used the Binet's formula to show some properties of the (p, q) - Lucas number. We get some generalized identities of the (p, q) - Lucas number.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).