• 대한수학회지
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• 제58권6호
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• pp.1529-1547
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• 2021

In this series, we investigate the calculation of mean values of derivatives of Dirichlet L-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields. The present paper generalizes the results obtained in the first paper. For µ ≥ 1 an integer, we compute the mean value of the µ-th derivative of quadratic Dirichlet L-functions over the rational function field. We obtain the full polynomial in the asymptotic formulae for these mean values where we can see the arithmetic dependence of the lower order terms that appears in the asymptotic expansion.

• 대한수학회보
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• 제59권2호
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• pp.431-452
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• 2022

For any positive integer 𝜇, we compute the mean value of the 𝜇-th derivative of quadratic Dirichlet L-functions over the rational function field 𝔽_q(t), where q is a power of 2.

• 대한수학회논문집
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• 제37권3호
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• pp.635-648
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• 2022

In this paper, we establish an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_P)$ averaging over ℙ_2g+1 and over ℙ_2g+2 as g → ∞ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_u)$ averaging over 𝓘_g+1 and over 𝓕_g+1 as g → ∞ in even characteristic.

• 대한수학회지
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• 제44권6호
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• pp.1243-1254
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• 2007

In this paper, we study the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals $[1,\;\frac{p}{3}]\;and\;[1,\;\frac{p}{4}]$, and give some asymptotic formulae by using the mean values of the Dirichlet L-functions.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제46권1호
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• pp.36-40
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• 2020

Objectives: The aim of this study was to evaluate pulmonary function in patients with mandibular fractures and to determine the pattern of pulmonary functions in these patients. Materials and Methods: This was a cross-sectional study of pulmonary functions in Nigerian non-smoking patients with isolated mandibular fractures managed at our health institution from December 2015 to June 2017. Forced vital capacity (FVC), forced expiratory volume in one second (FEV₁), peak expiratory flow rate (PEFR), and ratio of FEV₁ to FVC (FEV₁/FVC) were measured for all participants using a portable spirometer just before treatment. The pulmonary indices were compared with the predicted reference values for Nigerians to determine the respiratory pattern. Results: Forty participants consisting of six females (15.0%) and thirty-four males (85.0%) with a female to male ratio of 1:5.7 were included in this study. The mean patient age was 34.5±13.1 years (range, 17-63 years). The mean FVC, FEV₁, FEV₁/FVC, and PEFR were 3.8±1.2 L, 3.0±1.0 L, 74.3%±13.8%, and 5.2±2.2 L/s, respectively. Comparison of data with predicted values revealed that 17 subjects (42.5%) had normal pulmonary function pattern while 23 subjects (57.5%) had features suggestive of obstructive and restrictive pulmonary function patterns. Conclusion: Isolated mandibular fractures presented with abnormal pulmonary function pattern.

• Communications for Statistical Applications and Methods
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• 제31권5호
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• pp.497-519
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• 2024

In reliability analysis, the probability P(Y < X) is significant because it denotes availability and dependability in a stress-strength model where Y and X are the stress and strength variables, respectively. In reliability theory, the inverse Lomax distribution is a well-established lifetime model, and the literature is developing inference techniques for its reliability attributes. In this article, we are interested in estimating the stress-strength reliability R = P(Y < X), where X and Y have an unknown common scale parameter and follow the inverse Lomax distribution. Using Bayesian and non-Bayesian approaches, we discuss this issue when both stress and strength are expressed in terms of lower record values. The parametric bootstrapping techniques of R are taken into consideration. The stress-strength reliability estimator is investigated using uniform and gamma priors with several loss functions. Based on the proposed loss functions, the reliability R is estimated using Bayesian analyses with Gibbs and Metropolis-Hasting samplers. Monte Carlo simulation studies and real-data-based examples are also performed to analyze the behavior of the proposed estimators. We analyze electrical insulating fluids, particularly those used in transformers, for data sets using the stress-strength model. In conclusion, as expected, the study's results showed that the mean squared error values decreased as the record number increased. In most cases, Bayesian estimates under the precautionary loss function are more suitable in terms of simulation conclusions than other specified loss functions.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• 대한수학회보
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• 제52권6호
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• pp.2095-2105
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• 2015

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

• 대한기계학회논문집A
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• 제36권2호
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• pp.157-164
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• 2012

많은 기능 또는 임무를 수행하는 다수의 부품들로 구성되어 있는 다기능 시스템 개발에 있어 시스템과 부품의 신뢰도(reliability), 가용도(availability) 그리고 정비도(maintainability)를 결정하는 것은 설계 단계에서의 중요한 일이다. 본 논문에서는 시스템을 구성하고 있는 최하위 부품을 대상으로 개발기준의 시스템 목표가용도(target availability)를 만족하는 각 구성품의 MTBF 와 MTTR 을 결정하고자 한다. 대안 생성을 위해 휴리스틱 기법(heuristic method)을 개발하였으며, 각 대안의 시스템 가용도와 수명주기비용을 계산하기 위해 시뮬레이션을 이용한다. 그리고 수치예제를 통해 모형매개변수의 영향을 알아 본다.