• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.495-504
• /
• 2017

In this paper we construct the Carlitz's type q-tangent numbers $T_{n,q}$ and polynomials $T_{n,q}(x)$. From these numbers and polynomials, we establish some interesting identities and relations.

• The Pure and Applied Mathematics
• /
• v.19 no.2
• /
• pp.87-102
• /
• 2012

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional $[{\Delta}^kF]^{\^}$. We conclude by applying our series expansion to several interesting functionals.

• Journal of applied mathematics & informatics
• /
• v.35 no.1_2
• /
• pp.205-215
• /
• 2017

In this paper, we consider a modified Euler polynomials ${\tilde{E}}_{n,q}(x)$ with variable $[x]_q$ and investigate some interesting properties of the Euler polynomials. We also give some relationships between the modified Euler polynomials and their Hurwitz zeta function. Finally, we derive some identities associated with Bernstein polynomials.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.585-593
• /
• 2004

In this paper we shall discuss the minimal, maximal and primary subautomata. Also the concepts of the totally reachable state and source will be introduced. It is an interesting part that mX＊ is minimal iff the source S(m) is maximal. We shall point out that the characterization of primary subautomaton comes from the properties associated with the sources S(m)'s.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.595-604
• /
• 2004

In this paper We shall give some characterizations for mX＊ derived from the relationships between S(m) and C(m). Also we shall discuss the minimal, maximal, strongly cyclic and minmaxCR-automata. There is an interesting part for the relationship between mX＊ and S(m). That is to say, that mX＊ is minimal has the same meaning as S(m) is strongly cyclic. We shall note that the minimality implies ‘ strongly cyclic’ and ‘strongly cyclic’ implies ‘cyclic’ and ‘cyclic’ implies ‘a MaxCR-automaton’.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.107-119
• /
• 2009

In this paper we define a Banach algebra on very general function space induced by a generalized Brownian motion process rather than on Wiener space, but the Banach algebra can be considered as a generalization of Fresnel class defined on Wiener space. We then show that several interesting functions in quantum mechanic are elements of the class.

• Communications for Statistical Applications and Methods
• /
• v.2 no.1
• /
• pp.89-98
• /
• 1995

This paper presents the interesting properties of a certain patterned matrix that plays an significant role in the multi-way balanced designs. The necessary and sufficient condition on the existence of the inverse of the patterned matrix and its determinant are described. In special cases of the pattermed matrix, explicit formulas for its inverse, determinant and the characteristic equation are obtained.

• Kyungpook Mathematical Journal
• /
• v.53 no.4
• /
• pp.553-563
• /
• 2013

We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.201-210
• /
• 1999

Morley provided an interesting identity about 20 years earlier before its more generalized form was given by Dixon. In this note some of its generalized forms and an application of Morley's formula are considered.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.449-461
• /
• 2019

The aim of this paper is to extend the concept of quasi and bi-ideals from left almost semigroups to left almost rings which are the generalization of one sided ideals. Further, we discuss quasi and bi-ideals in regular left almost rings and intra regular left almost rings. We then explore many interesting and elegant properties of quasi and bi-ideals.