• 대한수학회논문집
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• 제36권1호
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• pp.19-26
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• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

• 대한수학회보
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• 제33권1호
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Advances in nano research
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• 제9권2호
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• pp.91-104
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• 2020

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e₀a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

• Journal of the Korean Data and Information Science Society
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• 제28권4호
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• pp.783-796
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• 2017

Bernoulli 시행은 시행 결과가 성공 (success) 혹은 실패 (failure)처럼 매 번의 시행에서 두 가지만 나오는 독립시행을 말한다. 가위바위보 게임과 같이 두 사람이 벌이는 연속적인 경기 인 경우 매번의 시합에서 둘 중 하나가 반드시 이기는 경우인 Bernoulli 시행이 아닌 게임도 존재한다. 각 종 게임의 경우 우리는 게임이 두 사람 중 한 사람이 게임을 이기고 끝날 때까 지의 게임의 지속시간과 두 사람 중 특정한 사람이 최종 승리할 확률에 관심을 갖는다. 본 연구에서는 두 사람이 벌이는 연속적인 게임에서 k번을 먼저 이기면 최종 승리하는 시합인 경우 매 시합에서 비기는 경우가 있는 시합과 비김이 없는 시합에 대하여 참가한 두 사람의 각 각 최종 승리할 확률과 시합이 끝날 때까지의 기대 게임수를 구하였다. 본 연구 결과를 이용 하면 비김이 있거나 없는 연속적인 게임의 경우 각 사람이 최종 승리할 확률 및 시합이 끝날 때까지의 기대 게임수를 구할 수 있다.

• 호남수학학술지
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• 제36권3호
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• pp.647-657
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• 2014

In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when $n=2^mp$. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.

• Journal of the Korean Statistical Society
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• 제6권1호
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• pp.3-20
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• 1977

In many applications one is concerned with repeated Bernoulli trials whose parameter (success probability) is usually unknown and has to be estimated from a sample. The probability distribution and statistical inference on the repeated independent Bernoulli trials have been studied extensively for the cases of fixed sample size sampling plan, and inverse binomial sampling plan in which observations are cotinued until a pressigned number of successes are obtained. See, for example, Haldane, Girschick et al., DeGroot and Johnson and Kotz.

• Advances in materials Research
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• 제7권3호
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• pp.163-174
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• 2018

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler-Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

• 대한수학회지
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• 제44권5호
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• 대한산업공학회지
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• 제1권1호
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• pp.99-103
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• 1975

A procedure for the test of independence of the observations and the null distribution are studied for a waiting-time distribution of the number of Bernoulli trials required to obtain a preassigned number of successes under Markov dependence. Selected critical values for the test statistic are tabulated.

• 대한수학회보
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• 제33권1호
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• pp.111-118
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• 1996

Throughout this paper Z and C will respectively denote the ring of rational integers and the complex number field.