• Journal of the Korean Mathematical Society
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• v.58 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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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.

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

• Journal of the Korean Mathematical Society
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• v.44 no.6
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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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• v.23 no.4
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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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• v.46 no.1
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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.

• Korean Journal of Mathematics
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• v.21 no.4
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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 $D{\in}\mathcal{H}_{2g+2}$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.157-164
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• 2012

When designing a multifunctional system consisting of many components performing many functions or missions, it is important to determine the reliability, availability, and maintainability (RAM) of the system and components, and we consider system availability to be the optimization criterion. For given intervals of mean time between failure (MTBF) and mean time to repair (MTTR) of the components, we want to determine the values of MTBF and MTTR for all components that satisfy the target availability. A heuristic method is proposed for finding near-optimal solutions through simulation. We also study numerical examples to check effects of model parameters on the optimal solutions.

• Food Engineering Progress
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• v.13 no.2
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• pp.99-104
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• 2009

Tofu has been playing an important role in people's daily diet in most of Asia and recently in North America due to several health-promoting functions, preventing and treating a number of chronic diseases such as cancer, coronary heart disease and osteoporosis. The objective of this study was to investigate the effect of different levels of yakong incorporation (0, 5, 10, and 15%, w/w) in preparation of firm tofu. Quality parameters such as pH, titratable, moisture content, color, and consumer preference were determined, and their correlations were analysed. There were no significant differences in pH, titratable acidity, and moisture content due to different levels of yakong incorporation studied (p>0.05). A significant decrease in L$^{*}$ and b$^{*}$-values whereas significant increase in a$^{*}$-value was observed (p<0.05). Five percent yakong tofu received the most favorable mean scores with respect to color, texture, and overall acceptability. Correlation analysis revealed that yakong incorporation was well correlated with some of physicochemical properties as well as consumer preference.