• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.555-561
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• 2005

In this note we give characterizations for certain HNN extensions with central associated subgroups to be residually finite. We then apply our results to HNN extensions of polycyclic-by-finite groups.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.23-26
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• 2014

Let E be a graded central division algebra (GCDA) over a grade field R. Let S be an unramified graded field extension of R. We describe the grading on the underlying GCDA E' of $E{\otimes}_RS$ which is analogous to the valuation on a tame division algebra over Henselian valued field.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1199-1211
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• 2012

In this paper we give an introduction to the theory of universal central extensions of perfect Lie algebras. In particular, we will provide a model for the universal coverings of Lie tori and we show that automorphisms and derivations lift to the universal coverings. We also prove that the universal covering of a Lie ${\Lambda}$-torus of type ${\Delta}$ is again a Lie ${\Lambda}$-torus of type ${\Delta}$.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.201-221
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• 2012

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.353-364
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• 2008

The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.791-809
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• 2016

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.475-488
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• 2016

We study the structure of central elements in relation with polynomial rings and introduce quasi-commutative as a generalization of commutative rings. The Jacobson radical of the polynomial ring over a quasi-commutative ring is shown to coincide with the set of all nilpotent polynomials; and locally finite quasi-commutative rings are shown to be commutative. We also provide several sorts of examples by showing the relations between quasi-commutative rings and other ring properties which have roles in ring theory. We examine next various sorts of ring extensions of quasi-commutative rings.

• ALGAE
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• v.22 no.4
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• pp.273-286
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• 2007

Records of selected gymnodinioid dinoflagellates from the open waters in the vicinity of the Kuroshio and Oyashio Currents, the Philippine, Celebes, Sulu and South China Seas, western and central equatorial and southeast Pacific Ocean are described and illustrated. The species Gymnodinium fusus Schütt, Gyrodinium falcatum Kofoid et Swezy, G. caudatum Kofoid et Swezy, G. sugashimanii J. Cachon et al. and Pseliodinium vaubanii Sournia are considered to be morphotypes of a single species, that until further studies can establish the correct genus, are named G. falcatum. This study is the first to record individuals of G. falcatum with very long curly extensions. Other gymnodinioid dinoflagellates that showed bifurcated hyposomes may be related to Gyrodinium bifurcatum Kofoid et Swezy or cells of thecate dinoflagellates exuviated from their thecae. Some specimens showed a rigid cover, although no discernible thecal plates. In this group, the most common species was Ptychodiscus noctiluca Stein and, for the first time, a micrograph of a tentative specimen of the genus Berghiella Kofoid et Michener is reported. The validity of the genera Berghiella and Balechina Loeblich Jr. et Loeblich III with thick cell covers is discussed. Several species with apical extensions, other unknown taxa with distinctive shapes, and colonial forms are illustrated. The diversity of gymnodinioid dinoflagellates is underinvestigated in the open ocean.

• Journal of Arbitration Studies
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• v.30 no.1
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• pp.139-160
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• 2020

Shalish is a key ingredient of the dispute resolution culture in Bangladesh since a formal court system has been known to show inefficiencies, such as overburdened cases and litigation process delays. This paper investigates the main function of Shalish and examines the evolution of Shalish in the perspectives of its three variants: a community-based Shalish, a village court, and an NGO variant of Shalish in modern extensions. It was found that traditional Shalish may play a role in the dispute resolution system in modern villages. A village court is a kind of hybrid dispute resolution system combining an informal dispute resolution with a formal court system. A village court is administered by the Union Parishad without intervention from the central government. Both the Shalish and village court have the weakness of unfair verdict exercised by local elders within a community. For this reason, an NGO variant Shalish is to reflect voices of women and other lower people in the community. To this study's interpretation, a village court is a new kind of Shalish combined with a formal court system while an NGO variant Shalish is also a "new" Shalish combined with a mediation system. In this respect, core elements of Shalish tradition have not been changed although various forms of new dispute resolution systems have emerged in the modern world.