• Bulletin of the Korean Mathematical Society
• /
• v.60 no.5
• /
• pp.1375-1390
• /
• 2023

In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.3
• /
• pp.831-850
• /
• 2023

Our long-standing Metatheorem in Ordered Fixed Point Theory is applied to some well-known order theoretic fixed point theorems. In the first half of this article, we introduce extended versions of the Zermelo fixed point theorem, Zorn's lemma, and the Caristi fixed point theorem based on the Brøndsted-Jachymski principle and our 2023 Metatheorem. We show some of their applications to other fixed point theorems or theorems on the existence of maximal elements in partially ordered sets. In the second half, we collect and improve order theoretic fixed point theorems in the collection of Howard-Rubin in 1991 and others. In fact, we improve or extend several ordering principles or fixed point theorems due to Brézis-Browder, Brøndsted, Knaster-Tarski, Tarski-Kantorovitch, Turinici, Granas-Horvath, Jachymski, and others.

• Proceedings of the Korean Institute of Building Construction Conference
• /
• 2022.11a
• /
• pp.23-24
• /
• 2022

There are many demands for vertical extension construction method in domestic large cities. In this paper, we analyzed and presented the results of examining the cases of ground floor extension and basement extension using the jack pile method. Since the Jack Pile method presses in all the piles without excavating the ground, the bearing capacity of the all the piles can be checked. It was investigated as a safe construction method unlike other small-diameter pile construction methods during underground extension.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.365-376
• /
• 2023

The goal of this article is to present the graded J-ideals of G-graded rings which are extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a graded J-ideal if whenever x, y ∈ h(R), if xy ∈ P and x ∉ J(R), then y ∈ P, where h(R) and J(R) denote the set of all homogeneous elements and the Jacobson radical of R, respectively. Several characterizations and properties with supporting examples of the concept of graded J-ideals of graded rings are investigated.

• The Korean Journal of Applied Statistics
• /
• v.3 no.1
• /
• pp.1-9
• /
• 1990

Engineering approach of statistics processing is defined for the statistical expert system. First, the engineering approach requirement are conceptualized by using an artificial intelligence in statistics, with the extensions being additional statistical knowlege engineering such as software engineering, optinal relationships, and the generalization abstraction. The methodology produces statistical expert system designes that are not only accurate representations of reality but also enough to accommodate future processing requirements. It also representions of knowledge that must be constructed, using the extended engineering processing model conceptualization and proposed engineering approach of the problem.

• Annual Conference of KIPS
• /
• 2011.04a
• /
• pp.597-600
• /
• 2011

멀티패스 전송은 단대 노드간 다중 경로를 동시에 사용함으로써 효과적인 대용량 전송을 실현하는 미래 인터넷 설계의 한 부분이다. 이에 따라 draft-‘TCP Extensions for Multipath Operation with Multiple Addresses'에서 MPTCP 가 언급되었으며 기존 TCP 를 활용한 다중 전송에서 발생할 수 있는 다양한 오픈 이슈가 나오게 되었다. 본 논문에서는 위 논의로부터 나온 다양한 오픈 이슈 중 수신측에서 발생 할 수 있는 패킷의 재조합(packet reordering)을 줄이는데 초점을 둔다. 패킷의 재조합은 불필요한 에너지 소비와 빈번한 패킷 재전송(packet retransmission) 문제를 초래하며, 특히 에너지 효율이 중요한 모바일기기에 있어 반드시 해결되어야 문제라 할 수 있다. 이를 해결하기 위해 본 논문에서는 전송 경로들의 RTT 값을 비교하여 패킷의 스케줄링 하는 기법을 제안하였으며 시뮬레이션을 통해 성능을 검증하였다.

• Communications for Statistical Applications and Methods
• /
• v.30 no.2
• /
• pp.135-147
• /
• 2023

Skipped median is more robust than median when outliers are not symmetrically distributed. In this work, we propose a novel algorithm to estimate the skipped median. The idea of skipped median and the new algorithm are extended to regression problem, which is called least clipped absolute deviation (LCAD). Since our proposed algorithm for nonconvex LCAD optimization makes use of convex least absolute deviation (LAD) procedure as a subroutine, regularizations developed for LAD can be directly applied, without modification, to LCAD as well. Numerical studies demonstrate that skipped median and LCAD are useful and outperform their counterparts, median and LAD, when outliers intervene asymmetrically. Some extensions of the idea for skipped median and LCAD are discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.453-468
• /
• 2022

In this article, we define a module M to be G^z-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of G^z-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G^z-extending modules. We obtain that if a ring is right G^z-extending, then so is its essential overring. Also it is shown that the G^z-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G^z-extending ring.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.161-180
• /
• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.985-1001
• /
• 2023

Recently, Alzer and Choi [2] introduced and studied a set of the four linear Euler sums with parameters. These sums are parametric extensions of Flajolet and Salvy's four kinds of linear Euler sums [9]. In this paper, by using the method of residue computations, we will establish two explicit combined formulas involving two parametric linear Euler sums S⁺⁺_p,q (a, b) and S^+-_p,q (a, b) defined by Alzer and Choi, which can be expressed in terms of a linear combinations of products of trigonometric functions, digamma functions and Hurwitz zeta functions.