• 대한수학회보
• /
• 제52권4호
• /
• pp.1107-1112
• /
• 2015

A recursive family $\{F_n\}$ of holomorphic functions on the Riemann sphere is defined and some elementary properties of this family is described. Then the Julia set of $F_n$ is computed. Finally this family as a real recursive family is studied and it is shown that $F_n$ is chaotic on a specific subset of $\mathbb{R}$.

• 대한기계학회논문집
• /
• 제7권4호
• /
• pp.386-391
• /
• 1983

Two-dimensional slow viscous flow due to a stokeslet near a slit is investigated on the basis of Stokes approximation. Velocity fields and stream function are obtained in closed forms by finding two sectionally holomorphic functions which are determined by reducing the problem to Riemann-Hilbert problems. The force exerted on a small cylinder is calculated for the arbitrary position of the cylinder translating in an arbitrary direction. The features of fluid flow are also investigated.

• 대한수학회보
• /
• 제45권2호
• /
• pp.277-283
• /
• 2008

The paper deals with the values at the negative integers of a certain Dirichlet series related to the Riemann zeta function and with the expression of these values in terms of Bernoulli numbers.

• 충청수학회지
• /
• 제21권1호
• /
• pp.21-28
• /
• 2008

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

• 호남수학학술지
• /
• 제36권2호
• /
• pp.263-273
• /
• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• 호남수학학술지
• /
• 제36권4호
• /
• pp.777-786
• /
• 2014

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

• 대한수학회논문집
• /
• 제22권4호
• /
• pp.553-564
• /
• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.183-198
• /
• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• East Asian mathematical journal
• /
• 제31권1호
• /
• pp.119-126
• /
• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.

• 대한수학회논문집
• /
• 제18권4호
• /
• pp.781-789
• /
• 2003

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.