• 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.

• ALGAE
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• v.22 no.1
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• pp.31-36
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• 2007

The gametophytic filaments of two genetically distinct taxa of Bangia from New Zealand showed unusual rhizoidal development in comparative culture experiments. In the past Bangia has been reported to possess simple, colourless rhizoids that extend from the basal cells of the unbranched filaments, whereas in this study the rhizoids observed became pigmented and multicellular. A reversal of growth direction occurred and filamentous extensions developed from the rhizoids under some culture conditions. These extensions were either prostrate or resembled new gametophytic filaments. This is the first report for filamentous members of the Bangiales of the development of such stolon-like rhizoids, apparently serving as a form of vegetative reproduction.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.313-317
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• 2001

본 논문에서는 전자메일에 보안기능과 공중기능을 함께 부여하는 방법에 대해 기술하고 있다. MIME(Multipurpose Internet Mail Extensions)[8]에 대하여 메시지의 무결성과 전자서명 생성 및 검증, 메시지의 암호화 및 복호화, 부인방지 기능을 지원하기 위해S/MIME(Secure/Multipurpose Internet Mail Extensions)[1][2]을 적용하고 또한 문서에 대한 공증기능을 부여하기 위하여 서명 생성 후 오랜 기간 뒤에도 서명과 서명 생성 시 사용된 인증서의 유효성과 폐지여부를 검증 할 수 있도록 제 3 신뢰기관에 의해 발행된 Timestamp[7]를 적용하였다. 그리고 서명된 메일 형식에 receiptRequest[4] 식별자를 사용하여 수신자의 서명을 포함한 signed receipt[4]를 송신자에게 다시 보내게 하여 메일 수신여부를 검증 할 수 있도록 하였다.

• ALGAE
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• v.21 no.4
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• pp.445-452
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• 2006

The morphometry and distribution of the unarmoured dinoflagellates Brachidinium capitatum F.J.R. Taylor, Asterodinium gracile Sournia, Microceratium orstomii Sournia and the toxic species Karenia papilionacea Haywood et Steidinger have been investigated in open waters of the SE Pacific Ocean. The genus Microceratium Sournia is recorded for the first time since the initial description. These taxa showed a high morphological similarity and they may correspond to life stages of a highly versatile single species that is able to project body extensions. Karenia papilionacea showed the higher abundance in the surface waters of the more productive areas (the Marquesas Archipelago and the Perú-Chile Current). Brachidinium capitatum and K. papilionacea often co-occurred, predominating B. capitatum in offshore surface waters. Asterodinium gracile was recorded at the bottom of the euphotic zone (down to 210 m depth), with a shallower distribution in more productive areas. Intermediate specimens of Asterodinium-Brachidinium-Karenia, with variable disposition and size of the body extensions were illustrated.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.339-348
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• 2011

A ring R is called symmetric, if abc = 0 implies acb = 0 for a, b, c ${\in}$ R. An ideal I of a ring R is called symmetric (resp. radically-symmetric) if R=I (resp. R/$\sqrt{I}$) is a symmetric ring. We first show that symmetric ideals and ideals which have the insertion of factors property are radically-symmetric. We next show that if R is a semicommutative ring, then $T_n$(R) and R[x]=($x^n$) are radically-symmetric, where ($x^n$) is the ideal of R[x] generated by $x^n$. Also we give some examples of radically-symmetric ideals which are not symmetric. Connections between symmetric ideals of R and related ideals of some ring extensions are also shown. In particular we show that if R is a symmetric (or semicommutative) (${\alpha}$, ${\delta}$)-compatible ring, then R[x; ${\alpha}$, ${\delta}$] is a radically-symmetric ring. As a corollary we obtain a generalization of [13].

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.777-788
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• 2007

An endomorphism ${\alpha}$ of a ring R is called right(left) symmetric if whenever abc=0 for a, b, c ${\in}$ R, $ac{\alpha}(b)=0({\alpha}(b)ac=0)$. A ring R is called right(left) ${\alpha}-symmetric$ if there exists a right(left) symmetric endomorphism ${\alpha}$ of R. The notion of an ${\alpha}-symmetric$ ring is a generalization of ${\alpha}-rigid$ rings as well as an extension of symmetric rings. We study characterizations of ${\alpha}-symmetric$ rings and their related properties including extensions. The relationship between ${\alpha}-symmetric$ rings and(extended) Armendariz rings is also investigated, consequently several known results relating to ${\alpha}-rigid$ and symmetric rings can be obtained as corollaries of our results.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1251-1267
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• 2014

The semicommutative property of rings was introduced initially by Bell, and has done important roles in noncommutative ring theory. This concept was generalized to one of nil-semicommutative by Chen. We first study some basic properties of nil-semicommutative rings. We next investigate the structure of Ore extensions when upper nilradicals are ${\sigma}$-rigid ${\delta}$-ideals, examining the nil-semicommutative ring property of Ore extensions and skew power series rings, where ${\sigma}$ is a ring endomorphism and ${\delta}$ is a ${\sigma}$-derivation.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.151-156
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• 2011

In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch$\ddot{u}$tz's summation theorem for the series $_3F_2$ has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch$\ddot{u}$tz's summation theorem are given.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.81-93
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• 2020

Let m ∈ ℕ₀, p > 1 and $${\alpha}^{[m,p]}(x)\;:\;{\sqrt{x}},\;\{{\sqrt{\frac{(m+n-1)p-(m+n-2)}{(m+n)p-(m+n-1)}}}\}^{\infty}_{n=1}$$. In this paper, we consider the backward extensions of Bergman-type weighted shift W_α^[m,p](x). We consider its subnormality, k-hyponormality and positive quadratic hyponormality. Our results include all the results on Bergman weighted shift W_α(x) with m ∈ ℕ and $${\alpha}(x)\;:\;{\sqrt{x}},\;{\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m}{m+2}},\;{\sqrt{\frac{m+2}{m+3}},{\cdots}$$.

• Korean Journal of Logic
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• v.17 no.1
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• pp.181-196
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• 2014

This paper deals with Kripke-style semantics for fuzzy logics. More exactly, I introduce algebraic Kripke-style semantics for some weakening-free extensions of the uninorm based fuzzy logic UL. For this, first, I introduce several weakening-free extensions of UL, define their corresponding algebraic structures, and give algebraic completeness. Next, I introduce several algebraic Kripke-style semantics for those systems, and connect these semantics with algebraic semantics.