• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.571-579
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• 2014

In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.109-132
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• 2024

The Clifford algebra of a direct sum of real quadratic spaces appears as the superalgebra tensor product of the Clifford algebras of the summands. The purpose of the current paper is to present a purely settheoretical version of the superalgebra tensor product which will be applicable equally to groups or to their non-associative analogues - quasigroups and loops. Our work is part of a project to make supersymmetry an effective tool for the study of combinatorial structures. Starting from group and quasigroup structures on four-element supersets, our superproduct unifies the construction of the eight-element quaternion and dihedral groups, further leading to a loop structure which hybridizes the two groups. All three of these loops share the same character table.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.4
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• pp.605-610
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• 2013

A cryptography for enforcing hierarchic groups in a system where hierarchy is represented by a partially ordered set was introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. To overcome this shortage, in 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment. In 2005, Kim et al. proposed the key management systems for using one-way hash function, RSA algorithm, poset dimension and Clifford semigroup in the context of modern cryptography, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders. We, in this paper, show that Kim et al. cryptosystem is insecure in some reasons and propose a revised cryptosystem.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.177-184
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• 2016

In this paper, we establish some conjugacy criteria of $M\ddot{o}bius$ groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.481-492
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• 2000

As an application of Clifford theory, we are interested in a situation in which every irreducible projective character of a finite group G is an induced character of an irreducible linear character of some subgroup H of G. For this purpose, we study relative projective monomial groups with respect to subgroups.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.1-11
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• 1994

The theory of inverse semigroups has many features in common with the theory of groups. Many different properties of semigroup become the same condition on ring. In this paper, we want to find the properties of semigroups which is preserved by the properties of ring. Also we find that many different properties become the equivalent conditions.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1187-1237
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• 2020

Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

• Journal of Periodontal and Implant Science
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• v.52 no.5
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• pp.352-369
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• 2022

The aim of this systematic review was to evaluate clinical and microbiological outcomes with the use of azithromycin as an adjunct to non-surgical subgingival professional mechanical plaque removal (PMPR) in the treatment of grade C periodontitis. Online database searches using high-level MeSH terms in a PICO structure were conducted along with hand-searching of relevant periodontal journals. Titles and abstracts of identified studies were independently reviewed by both authors and the full texts of studies meeting the inclusion criteria were independently reviewed. In total, 122 studies were identified through searches, of which 6 were included in the qualitative analysis and 4 in the meta-analysis. Three studies included in the meta-analysis were deemed at low risk of bias and 1 at serious risk. There were conflicting results on whether azithromycin reduced the number of subgingival pathogens or detectable subgingival Aggregatibacter actinomycetemcomitans between the included studies. The meta-analysis revealed a statistically significant probing depth reduction difference in favour of azithromycin compared to the control at 3 months (weighted mean difference [WMD]=-0.39 mm; 95% confidence interval [CI], -0.66 to -0.13 mm; I²=0%) and 12 months (WMD=-1.32 mm; 95% CI, -1.71 to -0.93 mm; I²=0%). The clinical attachment level change was also statistically significant in favour of azithromycin compared to the control at 3 months (WMD=-0.61 mm; 95% CI, -1.13 to -0.10 mm; I²=71%) and 12 months (WMD=-0.88 mm; 95% CI, -1.32 to -0.44 mm; I²=0%). Based upon these results, azithromycin offers additional improvements in some clinical parameters when used in conjunction with subgingival PMPR in patients with aggressive periodontitis over control groups. These improvements appear to be maintained for up to 12 months after treatment completion. However, due to a lack of well-designed studies, the conclusions that can be drawn from the available evidence are limited.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.409-419
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• 2015

The concept of Cayley-symmetric semigroups is introduced, and several equivalent conditions of a Cayley-symmetric semigroup are given so that an open problem proposed by Zhu [19] is resolved generally. Furthermore, it is proved that a strong semilattice of self-decomposable semigroups $S_{\alpha}$ is Cayley-symmetric if and only if each $S_{\alpha}$ is Cayley-symmetric. This enables us to present more Cayley-symmetric semi-groups, which would be non-regular. This result extends the main result of Wang [14], which stated that a regular semigroup is Cayley-symmetric if and only if it is a Clifford semigroup. In addition, we discuss Cayley-symmetry of Rees matrix semigroups over a semigroup or over a 0-semigroup.

• Korean Security Journal
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• no.1
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• pp.371-408
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• 1997

This article is the reserch on actual condition of crime of arson which occurs in Korea and its countermeasures. The the presented problem in this article are that (1) we have generally very low rate concern about the crime of arson contrary to realistic problems of rapid increase of crime of arson (2) as such criminal motives became so diverse as to the economic or criminal purpose unlike characteristic and mental deficiency of old days, and to countermeasure these problems effectively it presentation the necessity of systemantic research. Based on analysis of reality of arson, the tendency of this arson in Korea in the ratio of increase is said to be higher than those in violence crime or general fire rate. and further its rate is far more greater than those of the U.S.A. and Japan. Arson is considered to be a method of using fire as crime and in case of presently residence to be the abject, it is a public offense crime which aqccompany fatality in human life. This is the well It now fact to all of us. And further in order to presentation to the crime of arson, strictness of criminal law (criminal law No, 164 and 169, and fire protection law No. 110 and 111) and classification of arsonist as felony are institutionary reinforced to punish with certainty of possibility, Therefore, as tendency of arson has been increased compared to other nations, it is necessary to supplement strategical policy to bring out overall concerns of the seriousness of risk and damage of arson, which have been resulted from the lack of understanding. In characteristics analysis of crime of arson, (1) It is now reveald that, in the past such crime rate appeared far more within the boundary of town or city areas in the past, presently increased rate of arsons in rural areas are far more than in the town or small city areas, thereby showing characteristics of crime of arson extending nation wide. (2) general timetable of arson shows that night more than day time rate, and reveald that is trait behavior in secrecy.(3) arsonists are usually arrested at site or by victim or report of third person(82,9%).Investigation activities or self surrenders rate only 11.2%. The time span of arrest is normally the same day of arson and at times it takes more than one year to arrest. This reveals its necessity to prepare for long period of time for arrest, (4) age rate of arson is in their thirties mostly as compared to homicide, robbery and adultery, and considerable numbers of arsons are in old age of over fifties. It reveals age rate is increased (5) Over half of the arsonists are below the junior high school (6) the rate of convicts by thier records is based on first offenders primarily and secondly more than 4 time convicts. This apparently shows necessity of effective correctional education policy for their social assimilation together with re-investigation of human education at the primary and secondary education system in thier life. The examples of motivation for arosnits, such as personal animosity, fury, monetary swindle, luscious purpose and other aims of destroying of proof, and other social resistance, violence including ways of threatening, beside the motives of individual defects, are diverse and arsonic suicide and specifically suicidal accompany together keenly manifested. When we take this fact with the criminal theory, it really reveals arsons of crime are increasing and its casualities are serious and a point as a way of suicide is the anomie theory of Durkheim and comensurate with the theory of that of Merton, Specifically in the arson of industrial complex, it is revealed that one with revolutionary motive or revolting motive would do the arsonic act. For the policy of prevention of arsons, professional research work in organizational cooperation for preventive activities is conducted in municipal or city wise functions in the name of Parson Taskforces and beside a variety of research institutes in federal government have been operating effectively to countermeasure in many fields of research. Franch and Sweden beside the U.S. set up a overall operation of fire prevention research funtions and have obtained very successful result. Japan also put their research likewise for countermeasure. In this research as a way of preventive fire policy, first, it is necessary to accomodate the legal preventitive activities for fire prevention in judicial side and as an administrative side, (1) precise statistic management of crime of arson (2) establishment of professional research functions or a corporate (3) improvement of system for cooperative structural team for investigation of fires and menpower organization of professional members. Secondly, social mentality in individual prospect, recognition of fires by arson and youth education of such effect, educational program for development and practical promotion. Thirdly, in view of environmental side, the ways of actual performance by programming with the establishment of cooperative advancement in local social function elements with administrative office, habitants, school facilities and newspapers measures (2) establishment of personal protection where weak menpowers are displayed in special fire prevention measures. These measures are presented for prevention of crime of arson. The control of crime and prevention shall be prepared as a means of self defence by the principle of self responsibility Specifically arsonists usually aims at the comparatively weak control of fire prevention is prevalent and it is therefore necessary to prepare individual facilities with their spontaneous management of fire prevention instead of public municipal funtures of local geverment. As Clifford L. Karchmer asserted instead of concerns about who would commit arson, what portion of area would be the target of the arson. It is effective to minister spontaveously the fire prevention measure in his facility with the consideration of characteristics of arson. On the other hand, it is necessary for the concerned personnel of local goverment and groups to distribute to the local society in timely manner for new information about the fire prevention, thus contribute to effective result of fire prevention result. In consideration of these factors, it is inevitable to never let coincide with the phemonemon of arsons in similar or mimic features as recognized that these could prevail just an epedemic as a strong imitational attitude. In processing of policy to encounter these problems, it is necessary to place priority of city policy to enhancement of overall concerns toward the definitive essense of crime of arson.