• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.881-887
• /
• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• Communications of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.329-342
• /
• 2016

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

• East Asian mathematical journal
• /
• v.29 no.5
• /
• pp.545-550
• /
• 2013

A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1255-1280
• /
• 2017

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. [2]. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.165-174
• /
• 2012

In this paper, we construct a p-adic analogue of multiple Riemann zeta values and express their values at non-positive integers. In particular, we obtain a new congruence of the higher order Frobenius-Euler numbers and the Kummer congruences for the Bernoulli numbers as a corollary.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.545-555
• /
• 2004

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.137-146
• /
• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• Bulletin of the Korean Chemical Society
• /
• v.26 no.7
• /
• pp.1083-1089
• /
• 2005

Most experimental studies available in the literature on filtration are based on observed average zeta potential of particles (usually 10 measurements). However, analyses of data using the average zeta potential alone can lead to misleading and erroneous conclusions about the attachment behavior because of the variation of particle zeta potentials and the heterogeneous distribution of the collector surface charge. To study characteristics of zeta potential, zeta potential distributions (ZPDs) of silica particles under 9 different chemical conditions were investigated. Contrary to many researchers’ assumptions, most of the ZPDs of silica particles were broad. The solids concentration removal was better near the isoelectric point (IEP) as many researchers have noticed, thus proper destabilization of particles is very important to achieve better particle removal in particle separation processes. While, the mean zeta potential of silica particles at a given coagulant dose was a function of particle concentration; the amount of needed coagulant for particle destabilization was proportional to the total surface charge area of particles in the suspension.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1671-1683
• /
• 2016

Abstract. In this paper, for $a{\in}C$, we investigate functions $g_a$ and ${\psi}_a$ associated with three term relations. $g_a$ is defined by means of function ${\psi}_a$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_a$.

• Honam Mathematical Journal
• /
• v.36 no.2
• /
• pp.467-472
• /
• 2014

With the properties of Riemann zeta function, we find an asymptotic formula of the sum for the absolute value of M$\ddot{o}$bius function, $\sum_{n{\leq}x}{\mid}{\mu}(n){\mid}$, using Dirichlet inversion formula.