• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.105-113
• /
• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.197-206
• /
• 2010

We study the restriction estimate of Fourier transform to arbitrary convex curves in $R^2$ with no regularity assumption. Assuming that the convex curve has the lower bound of curvatures, we extend the restriction results from smooth convex curves to arbitrary convex curves. Our work has been motivated by the lecture notes of Terence Tao. The bilinear approach and geometric observations play an important role.

• Journal for History of Mathematics
• /
• v.17 no.3
• /
• pp.109-120
• /
• 2004

This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.575-584
• /
• 2011

In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {$x_n$} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.165-173
• /
• 2002

We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.441-448
• /
• 2012

Let R be a prime ring with center Z and characteristic different from two, U a nonzero Lie ideal of R such that $u^2{\in}U$ for all $u{\in}U$ and $d$ be a nonzero (${\sigma}$, ${\tau}$)-derivation of R. We prove the following results: (i) If $[d(u),u]_{{\sigma},{\tau}}$ = 0 or $[d(u),u]_{{\sigma},{\tau}}{\in}C_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$. (ii) If $a{\in}R$ and $[d(u),a]_{{\sigma},{\tau}}$ = 0 for all $u{\in}U$, then $U{\subseteq}Z$ or $a{\in}Z$. (iii) If $d([u,v])={\pm}[u,v]_{{\sigma},{\tau}}$ for all $u{\in}U$, then $U{\subseteq}Z$.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1113-1121
• /
• 2018

Let R be a prime ring (or semiprime ring) with center Z(R), I a nonzero ideal of R, T an automorphism of $R,S:R^n{\rightarrow}R$ be a symmetric skew n-derivation associated with the automorphism T and ${\Delta}$ is the trace of S. In this paper, we shall prove that S($x_1,{\ldots},x_n$) = 0 for all $x_1,{\ldots},x_n{\in}R$ if any one of the following holds: i) ${\Delta}(x)=0$, ii) [${\Delta}(x),T(x)]=0$ for all $x{\in}I$. Moreover, we prove that if $[{\Delta}(x),T(x)]{\in}Z(R)$ for all $x{\in}I$, then R is a commutative ring.

• Communications of Mathematical Education
• /
• v.26 no.4
• /
• pp.339-349
• /
• 2012

Integer ratios 1:2:3:4 are very important in making eastern and western musical scales. Suggest an educational program of Mathematics in middle school which shows how to make an musical instrument and musical scales by Euclidean constructions. It explains for Mathematics how to make musical notes.

• Honam Mathematical Journal
• /
• v.42 no.3
• /
• pp.461-476
• /
• 2020

The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.