• 대한수학회보
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• 제33권2호
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• pp.289-294
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• 1996

The double Gamma function had been defined and studied by Barnes [4], [5], [6] and others in about 1900, not appearing in the tables of the most well-known special functions, cited in the exercise by Whittaker and Waston [25, pp. 264]. Recently this function has been revived according to the study of determinants of Laplacians [8], [11], [15], [16], [19], [20], [22] and [24]. Shintani [21] also uses this function to prove the classical Kronecker limit formula. Its p-adic analytic extension appeared in a formula of Casson Nogues [7] for the p-adic L-functions at the point 0.

• 대한수학회논문집
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• 제11권1호
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• pp.139-145
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• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• 대한수학회논문집
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• 제13권4호
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• pp.735-741
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• 1998

In this paper we will derive some new properties of q-extensions of p-adic gamma functions and p-adic Euler constants.

• 한국진공학회지
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• 제12권1호
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• pp.16-19
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• 2003

실온에서 p-InP (100) 위에 이온빔 증착법으로 Ni 박막을 성장하였다. Ni 박막의 이차전자방출계수(${\gamma}$)와 일함수를 결정하기 위하여 Ne, Ar, $N_2$, Xe 이온원을 사용하여 가속전압에 따른 $\gamma$를 측정하였다. 여러 가지 기체와 집속이온빔장치의 가속전압에 따른 $\gamma$결과로부터 Ni 박막의 일함 수를 결정하였다. p-InP (100) 위에 성장한 Ni 박막의 일함수는 5.8 eV ~ 5.85 eV 이었다. 실험을 통하여 얻어진 결과들은 실온에서 p-InP (100) 위에 성장한 Ni 박막의 전자적 성질에 관한 중요한 정보를 제공하고 있다.

• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• Journal of Radiation Protection and Research
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• 제35권2호
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• pp.85-90
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• 2010

본 연구에서는, 에너지에 따른 peak의 상대효율을 구하였으며, 검출기의 응답함수를 작성하였다. 이를 위해 고효율, 고분해능을 가진 HPGe 검출기(지름 78.7 mm, 길이 86.5 mm)를 이용하였으며 콤프턴 억제용으로 NaI 검출기를 사용하였다. 감마선 스펙트럼은 $^{23}Na$(p, $\gamma$)$^{24}Mg$ 및 $^{27}Al$(p, $\gamma$)$^{28}Si$ 반응을 이용하여 얻었으며, 이 때 입사 입자의 에너지는 각각 $E_p$ = 1424 keV 및 $E_p$ = 992 keV 이었다. 한편 스펙트럼 측정은 입사 빔 방향에 대해 $55^{\circ}$에서 하였으며, 사용한 가속기는 일본 동경공업대학의 3 MeV Pelletron 가속기를 이용하였다. 검출기의 응답함수는 1.2 MeV에서 9.4 MeV까지 0.75 MeV 간격으로 작성하였다.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.305-310
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• 1998

In this paper, we introduce the conditions that the P-process has the intensity function which it is a standard form of gamma distribution. And we show that the transformed geometric Poisson process which the intensity function is a standard form of gamma distribution is a alternative sign P-process

• 대한수학회논문집
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• 제32권1호
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• 대한수학회지
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• 제54권2호
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• pp.575-598
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• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• 호남수학학술지
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• 제30권3호
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).