• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.591-600
• /
• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.67-75
• /
• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.565-583
• /
• 2007

We offer a refinement of the classical Clifford inequality about special linear series on smooth irreducible complex curves. Namely, we prove about curves of genus g and odd gonality at least 5 that for any linear series $g^r_d$ with $d{\leq}g+1$, the inequality $3r{\leq}d$ holds, except in a few sporadic cases. Further, we show that the dimension of the set of curves in the moduli space for which there exists a linear series $g^r_d$ with d<3r for $d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3$, is bounded by $2g-1+\frac{1}{3}(g+2l+1)$.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1999.05a
• /
• pp.155-155
• /
• 1999

Pool boiling critical heat flux (CHF) have been investigated using plate type test sections with different widths (3 cm & 4 cm) and lengths (10 cm, IS cm & 20 cm) under various incli- nation angles. As the inclination angle increases from $0^{\circ}$ (horizontally facing downward plate) to $30^{\circ}$, CHF sharply increases. After that angle, CHF gradually increases with the increase of the inclination angle. There must be a transition angle between $0^{\circ}$ and $30^{\circ}$, at which the CHF increase rate remarkably changes. According to the comparison of present and previous ex- periments, the transition angle may be affected by heater size and increase with the increase of heater size. The size effect of heated surface on CHF is noticeable in the L15 & L20 series and W4 series; however, it seems to be difficult to find the size effect in L10 series and W3 series.

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.383-395
• /
• 2012

In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

• Journal of Integrative Natural Science
• /
• v.1 no.3
• /
• pp.216-220
• /
• 2008

In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.280-280
• /
• 2000

In this paper, we propose a method of constructing equation using bio-inspired emergent and evolutionary concepts. This method is algorithm that is based on the characteristics of the biological DNA and growth of plants. Here is. we propose a constructing method to make a DNA coding method for production rule of L-system. L-system is based on so-called the parallel rewriting mechanism. The DNA coding method has no limitation in expressing the production rule of L-system. Evolutionary algorithms motivated by Darwinian natural selection are population based searching methods and the high performance of which is highly dependent on the representation of solution space. In order to verify the effectiveness of our scheme, we apply it to one step ahead prediction of Mackey-Glass time series.

• Proceedings of the KIEE Conference
• /
• 1994.11a
• /
• pp.9-11
• /
• 1994

FACTS concept is the control of power flow and increase of the loading on existing lines to the thermal limuts. This paper focuses on the ability of the thyristor controlled series compensator (TCSC) to stabilize the disturbed power systems. The result shows the potential benefit of the TCSC in addition to the role of controlling the steady state power flow. In order to show the effectiveness of controlled series capacitor, power system dynamic model is augmented and the effect of the SC into the power system dynamics is included. As a control algorithm, Linear Optimal Control theory is applied.

• Journal for History of Mathematics
• /
• v.22 no.1
• /
• pp.25-40
• /
• 2009

This study concerns with John B. Fourier' s life, his teachers, his younger scholars and the $L^1$-convergence of Fourier series. First, we introduce the correlation between the French Revolution and Fourier who is significant in the history of mathematics. Second, we investigate Fourier' s teachers, students and a minor lineage of his younger scholars from 19th century to 20th century. Finally, we compare the theorem of Telyakovskii with the theorem of kolmogorov on $L^1$-convergence of Fourier series.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.699-716
• /
• 2009

We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.