• 대한수학회보
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• 제54권4호
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• 대한수학회보
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• 제51권4호
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• pp.995-1003
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• 2014

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

• 한국재료학회지
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• 제25권8호
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• pp.365-369
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• 2015

This paper investigates the dependency of the critical content for electrical conductivity of carbon powder-filled polymer matrix composites with different matrixes as a function of the carbon powder content (volume fraction) to find the break point of the relationships between the carbon powder content and the electrical conductivity. The electrical conductivity jumps by as much as ten orders of magnitude at the break point. The critical carbon powder content corresponding to the break point in electrical conductivity varies according to the matrix species and tends to increase with an increase in the surface tension of the matrix. In order to explain the dependency of the critical carbon content on the matrix species, a simple equation (${V_c}^*=[1+ 3({{\gamma}_c}^{1/2}-{{\gamma}_m}^{1/2})^2/({\Delta}q_cR]^{-1}$) was derived under some assumptions, the most important of which was that when the interfacial excess energy introduced by particles of carbon powder into the matrix reaches a universal value (${\Delta}q_c$), the particles of carbon powder begin to coagulate so as to avoid any further increase in the energy and to form networks that facilitate electrical conduction. The equation well explains the dependency through surface tension, surface tensions between the particles of carbon powder.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.439-447
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• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

• 대한수학회논문집
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• 제28권2호
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• pp.297-301
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• 2013

When certain general single or multiple hypergeometric functions were introduced, their reduction formulas have naturally been investigated. Here, in this paper, we aim at presenting a very interesting reduction formula for the Srivastava's triple hypergeometric function $F^{(3)}[x,y,z]$ by applying the so-called Beta integral method to the Henrici's triple product formula for hypergeometric series.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 통신소사이어티 추계학술대회논문집
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• pp.15-19
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• 2003

In this paper, the bit error rate (BER) performance of the fast frequency hopping/M-ary frequency shift keying system using the clipper receiver is analyzed by using the characteristic function (CF) technique in the presence of n=1 band multitone jamming and additive white Gaussian noise environment. The CFs of the clipper receiver outputs are derived as a infinite series representation using Gamma function and Marcum's Q -function. The analytical results are validated with various simulation results. Performance comparisons with linear combining receiver are shown that the BER performance of the clipper receiver is much better than that of the linear combining receiver In addition, as the clipping level approaches to infinity, it is shown that the clipper receiver simply performs a linear combining without clipping and there exists an optimum value of diversity level (the number of hops per symbol) that maximizes the worst case BER performance of the clipper receiver.

• 호남수학학술지
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• 제35권4호
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• pp.701-706
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• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• 대한전자공학회논문지TC
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• 제41권5호
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• pp.69-76
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• 2004

본 논문에서는 낮은 위상잡음을 갖는 X-band용 전압 제어 유전체 공진형 발진기를 설계ㆍ제작하였다. 위상잡음을 개선하기 위하여 저잡음 특성과 프리커 잡음이 낮은 MESFET과 높은 선택도와 Q값이 큰 유전체 공진기를 사용하였다. 또한 바렉터 다이오드는 부하의 영향을 줄이기 위해서 Q-factor가 매우 큰 것을 사용하여야 하며, 전압에 대한 주파수 변동이 선형이 되도록 하기 위해 다이오드의 Gamma가 큰 바렉터 다이오드를 사용하였다. 구현된 회로는 최적의 성능을 갖도록 회로 시뮬레이터인 ABS를 사용하였다. 제작된 전압제어 유전체 공진형 발진기의 특성을 측정한 결과, 중심 주파수 12.05 ㎓에서 5.8㏈m의 출력 파워와 -30 ㏈c의 고조파 억압과 100㎑ offest 주파수에서 -114 ㏈c의 위상잡음 특성을 얻을 수 있었으며, 바렉터 다이오드에 인가되는 전압의 변화에 따른 주파수 동조 범위는 15.2 ㎒를 얻었고 이때의 전력 평탄도는 -0.2㏈ 의 우수한 성능을 얻을 수 있었다. 제작된 발진기는 X-band에서 국부 박진기로 이용될 수 있음을 확인하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• 대한수학회보
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• 제50권5호
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• pp.1673-1681
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• 2013

The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.