• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.1
• /
• pp.83-88
• /
• 2015

In this paper we give a determinant formula for the relative congruent zeta function in cyclotomic function fields.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.455-464
• /
• 2012

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.307-315
• /
• 2019

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.

• Honam Mathematical Journal
• /
• v.32 no.3
• /
• pp.389-397
• /
• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.293-303
• /
• 1997

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.3C
• /
• pp.368-373
• /
• 2004

Extremely fine tine resolution of ultra-wideband (UWB) signal poses a new problems to the system designer. A reasonable accuracy of the system clock is necessary to process signals with such a high space resolution. A useful way of illustrating the time resolution of a signal is to evaluate the ambiguity function. The ambiguity function for carrierless UWB defined using the time mismatch and time scaling factor as its two parameters. The UWB ambiguity function is evaluated for various signaling schemes of impulse radio.

• Journal of Magnetics
• /
• v.2 no.3
• /
• pp.105-109
• /
• 1997

The Preisach model neds a density function or Everett function for the hysterisis operator to simulate the hysteresis phenomena. To obtain the function, many experimental data for the first order transition curves are required. However, it needs so much efforts to measure the curves, especially for the hard magnetic materials. By the way, it is well known that the density function has the Gaussian distribution for the interaction axis on the Preisach plane. In this paper, we propose a simple technique to determine the distribution function or Everett function analytically. The initial magnetization curve is used for the distribution of the Everett function for the coercivity axis. A major, minor loop and the initial curve are used to get the Everett function for the interaction axis using the Gaussian distribution function and acceptable results were obtained.

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.347-354
• /
• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.143-155
• /
• 2018

In this present paper, our aim is to introduce an extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ which is established with the help of the extended beta function. Also, we investigate certain integral transforms and generalized integration formulas for the newly defined extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ and the obtained results are expressed in terms of Fox-Wright function. Some interesting special cases involving an extended Mittag-Leffler functions are deduced.

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.23-30
• /
• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.