• Korean Journal of Mathematics
• /
• v.19 no.2
• /
• pp.163-169
• /
• 2011

Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.832-835
• /
• 1997

In this paper, we first analyze the structural limitation of the conventional PID controller in controlling unstable processes through mathematical proof. To overcome this structural limitation, we add an internal feedback loop to the PID controller. Secondly, we obtain conditions when unstable processes can be stabilized by a controller through an analytical analysis. Finally, we propose a simple on-line process identification and autotuning method for unstable processes. Many simulation results show that, in spite of its simplicity, the proposed on-line process identification method provides good accuracy in modeling the unstable process and acceptable robustness to measurement noises and disturbances. Also, the proposed autotuner shows good control performances for both servo and regulatory problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.1
• /
• pp.1-15
• /
• 2016

The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ${\nabla}_h$ with size h > 0, we verify that for an integer $m{\geq}0$ and a strictly decreasing sequence $h_n$ converging to zero, a continuous function f(x) satisfying $${\nabla}_{h_n}^{m+1}f(kh_n)=0,\text{ for every }n{\geq}1\text{ and }k{\in}{\mathbb{Z}}$$, turns to be a polynomial of degree ${\leq}m$. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.

• School Mathematics
• /
• v.6 no.4
• /
• pp.361-372
• /
• 2004

This study is designed to investigate intellectual, emotional, and creative characteristics of mathematically gifted students. In this paper, we analyze their proof examples, responses to questionnaire on mathematical aptitude and social coping, and scores for Torrance creativity test(figure) in comparison with scientific gifted and general students.

• Korean Journal of Mathematics
• /
• v.25 no.4
• /
• pp.555-561
• /
• 2017

We show that a closed curve invariant under inversions with respect to two intersecting circles intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. This generalizes the well known fact that a closed curve symmetric about two lines intersecting at angle of an irrational multiple of $2{\pi}$ is a circle. We use the result to give a different proof of that a compact embedded cmc surface in ${\mathbb{R}}^3$ is a sphere. Finally we show that a closed embedded cmc surface which is invariant under the spherical reflections about two spheres, which intersect at an angle that is an irrational multiple of $2{\pi}$, is a sphere.

• Journal of Computing Science and Engineering
• /
• v.6 no.4
• /
• pp.310-319
• /
• 2012

Next generation wireless receivers demand low computational complexity algorithms with high computing power in order to perform fast signal detections and error estimations. Several signal detection and estimation algorithms have been proposed for next generation wireless receivers which are primarily designed to provide reasonable performance in terms of signal to noise ratio (SNR) and bit error rate (BER). However, none of them have been chosen for direct implementation as they offer high computational complexity with relatively lower computing power. This paper presents a low-complexity power-efficient algorithm that improves the computing power and provides relatively faster signal detection for next generation wireless multiuser receivers. Measurement results of the proposed algorithm are provided and the overall system performance is indicated by BER and the computational complexity. Finally, in order to verify the low-complexity of the proposed algorithm we also present a formal mathematical proof.

• Kyungpook Mathematical Journal
• /
• v.19 no.2
• /
• pp.237-239
• /
• 1979

No matter how one chooses the major arcs in the decomposition of $[x_0,\;x_0+1]$ it is always true with regard to the union, m(n), of the corresponding minor arcs that the integal of $f^2(x,\;n)$ e(-nx) over m(n) is $O(nlog^{-1}n)$. Consequently, to establish a proof of the asymptotic formulation of Goldbach's conjecture one might be tempted to take this fact as a starting point and to then concentrate the attact on trying to obtain the requisite estimate on the integral of $f^2(x,\;n)$ e(-nx) over M(n), the union of a suitably chosen family of major arcs. In this paper I show that this approach is not possible.

• Journal of the Korean Data and Information Science Society
• /
• v.12 no.1
• /
• pp.61-69
• /
• 2001

We present a probabilistic reasoning method for inferring knowledge about mathematical truth before an automated theorem prover completes a proof. We use a Bayesian analysis to update beleif in truth, given theorem-proving progress, and show how decision-theoretic methods can be used to determine the value of continuing to deliberate versus taking immediate action in time-critical situations.

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.403-407
• /
• 2011

In this paper, we study Noetherian Boolean rings. We show that if R is a Noetherian Boolean ring, then R is finite and $R{\simeq}(\mathbb{Z}_2)^n$ for some integer $n{\geq}1$. If R is a Noetherian ring, then R/J is a Noetherian Boolean ring, where J is the intersection of all ideals I of R with |R/I| = 2. Thus R/J is finite, and hence the set of ideals I of R with |R/I| = 2 is finite. We also give a short proof of Hayes's result : For every polynomial $f(x){\in}\mathbb{Z}[x]$ of degree $n{\geq}1$, there are irreducible polynomials $g(x)$ and $h(x)$, each of degree $n$, such that $g(x)+h(x)=f(x)$.

• Kyungpook Mathematical Journal
• /
• v.51 no.2
• /
• pp.205-215
• /
• 2011

Given a knot diagram D, we construct a semi-threading circle of it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles of minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we try to give another proof of the fact that, for every nontrivial knot K, the braid index b(K) of K is not less than the minimum number l(K) of overpasses of diagrams. Also, they are the same for a torus knot.