• East Asian mathematical journal
• /
• 제18권2호
• /
• pp.219-224
• /
• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• Kyungpook Mathematical Journal
• /
• 제55권4호
• /
• pp.983-996
• /
• 2015

In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).

• 충청수학회지
• /
• 제29권4호
• /
• pp.599-611
• /
• 2016

Let $k={\mathbb{F}}_q(t)$ be a rational function field over the finite field ${\mathbb{F}}_q$. In this paper we obtain formulas of average values of L-functions of some family of Artin-Schreier extensions over k.

• Journal of Power Electronics
• /
• 제10권2호
• /
• pp.138-145
• /
• 2010

This paper presents a single phase multilevel inverter for using as a voltage harmonic source. First, a single phase multilevel inverter system is presented and the structural parts of the inverter are described. In order to obtain multilevel output voltage waveforms, a switching strategy based on calculating switching angles is explained and an improved formula for determining switching angles is given. Simulation and experimental results of multilevel voltage waveforms are given for 15, 31 and 127 levels. The proposed topology does not only produce output voltages with low THD values. It also produces the required harmonic components on the output voltage. For this purpose, equations for switching angles are constituted and the switching functions are obtained. These angles control the output voltage as well as provide the required specific harmonics. The proposed inverter structure is simulated for various functions with the required harmonic components. The THD values of the output voltage waves are calculated. The simulated functions are also realized by the proposed inverter structure. By using a harmonic analyzer, the harmonic spectrums, which belong to the output voltage forms, are found and the THD values are measured. Simulation and experimental results are given for the specific functions. The proposed topology produces perfectly suitable results for obtaining the specific harmonic components. Therefore, it is possible to use the structure as a voltage harmonic source in various applications.

• 대한수학회지
• /
• 제55권1호
• /
• pp.185-210
• /
• 2018

The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: $${\zeta}_E(s,x)={\sum_{n=0}^{\infty}}{\frac{(-1)^n}{(n+x)^s}}$$. In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ${\zeta}_E(s,x)$. Furthermore, the relations between the values of a class of the Hurwitz-type (or Lerch-type) Euler zeta functions at rational arguments have also been given.

• Wind and Structures
• /
• 제7권6호
• /
• pp.405-420
• /
• 2004

In common approaches, bridge dynamics under wind action is analyzed by modeling the interaction between fluid and structure by means of transient wind loads acting over the structure itself. Amid various possible manners to describe such types of loads, a representation based on families of 'indicial functions' is adopted here. The aim is to investigate its flexibility to capture the main features of wind-bridge interaction. A set of coefficients is involved in indicial functions. The values that one may attribute to them suffer uncertainties coming from experimental errors affecting data. Here, the sensitivity of a 2-DOF schematic model to the variations of these coefficients is investigated at fixed values of dynamic derivatives and for various types of indicial functions. It is shown how parameter variations influence phase portraits.

• 대한수학회보
• /
• 제57권5호
• /
• pp.1083-1094
• /
• 2020

In this paper, we give some uniqueness theorems of nonconstant meromorphic functions of hyper-order less than one sharing partially three or four small periodic functions with their shifts. As an application, some sufficient conditions for periodicity of meromorphic functions are given. Our results improve and extend previous results of W. Lin, X. Lin and A. Wu [11].

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

• 산업경영시스템학회지
• /
• 제36권2호
• /
• pp.8-16
• /
• 2013

In this paper, we proposed a new method for the determination of strategies that are required in a continuous optimization algorithm based on the fictitious play theory. In order to apply the fictitious play theory to continuous optimization problems, it is necessary to express continuous values of a variable in terms of discrete strategies. In this paper, we proposed a method in which all strategies contain an equal number of selected real values that are sorted in their magnitudes. For comparative analysis of the characteristics and performance of the proposed method of representing strategies with respect to the conventional method, we applied the method to the two types of benchmarking functions: separable and inseparable functions. From the experimental results, we can infer that, in the case of the separable functions, the proposed method not only outperforms but is more stable. In the case of inseparable functions, on the contrary, the performance of the optimization depends on the benchmarking functions. In particular, there is a rather strong correlation between the performance and stability regardless of the benchmarking functions.

• Kyungpook Mathematical Journal
• /
• 제47권1호
• /
• pp.57-68
• /
• 2007

In this article, we investigate the problem of uniqueness of meromorphic functions sharing one set and having deficient values, and obtain a result which improves some earlier results.