• Title, Summary, Keyword: gamma

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THE QUARTIC MOMENT PROBLEM

  • Li, Chun-Ji;Lee, Sang-Hoon
    • Journal of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.723-747
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    • 2005
  • In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure ${\mu}$, supported in the complex plane C such that ${\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)$. We obtain sufficient conditions for flat extension of the quartic moment matrix M(2). Moreover, we examine the existence of flat extensions for nonsingular positive quartic moment matrices M(2).

REGULARITY OF THE GENERALIZED CENTROID OF SEMI-PRIME GAMMA RINGS

  • Ali Ozturk, Mehmet ;Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.19 no.2
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    • pp.233-242
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    • 2004
  • The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.

On a Class of γ*-pre-open Sets in Topological Spaces

  • Krishnan, G. Sai Sundara;Saravanakumar, D.;Ganster, M.;Ganster, M.
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.173-188
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    • 2014
  • In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

ON CLOSURE GAMMA-SEMIGROUPS

  • Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.639-641
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    • 2004
  • We introduce the notion of closure $\Gamma$-semigroups. We give a condition for a closure $\Gamma$-semigroup to be $\Gamma$-central, and we show that the $\Gamma$-centralizer of a closure $\Gamma$-semigroup is a $\Gamma$-subsemigroup.

REMARKS ON γ-OPERATIONS INDUCED BY A TOPOLOGY

  • Min, Won-Keun
    • Communications of the Korean Mathematical Society
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    • v.26 no.2
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    • pp.291-296
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    • 2011
  • Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

ON A CLASS OF $\gamma$-PREOPEN SETS IN A TOPOLOGICAL SPACE

  • Krishnan, G. Sal Sundara;Balachandran, K.
    • East Asian mathematical journal
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    • v.22 no.2
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    • pp.131-149
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    • 2006
  • In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

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FUZZY INTERIOR $\Gamma$-IDEALS IN ORDERED $\Gamma$-SEMIGROUPS

  • Khan, Asghar;Mahmood, Tariq;Ali, M. Irfan
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1217-1225
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    • 2010
  • In this paper we define fuzzy interior $\Gamma$-ideals in ordered $\Gamma$-semigroups. We prove that in regular(resp. intra-regular) ordered $\Gamma$-semigroups the concepts of fuzzy interior $\Gamma$-ideals and fuzzy $\Gamma$-ideals coincide. We prove that an ordered $\Gamma$-semigroup is fuzzy simple if and only if every fuzzy interior $\Gamma$-ideal is a constant function. We characterize intra-regular ordered $\Gamma$-semigroups in terms of interior (resp. fuzzy interior) $\Gamma$-ideals.

FUZZY ${\gamma}$-PREOPEN SETS AND FUZZY ${\gamma}$-PRECONTINUOUS MAPS

  • Lee, Seok-Jong;Lee, Eun-Pyo
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.91-108
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    • 1999
  • In this paper, we introduce the notions of fuzzy ${\gamma}$-peropen (${\gamma}$-perclosed) sets and fuzzy ${\gamma}$-percontinuous (${\gamma}$-peropen, ${\gamma}$-perclosed) maps, and investigate some of their properties.

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Reactions of $\gamma$,$\gamma$,$\gamma$-Trichloroethylidene-m-Nitroacetophenone with Hydrazines ($\gamma$,$\gamma$,$\gamma$-Trichloroethylidene-m-Nitroacetophenone과 Hydrazine 들의 반응)

  • Youn Young Lee;Suk Zu Song
    • Journal of the Korean Chemical Society
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    • v.17 no.1
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    • pp.25-30
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    • 1973
  • 2,6-Disubstituted-3-pyridazinones were synthesized by the reactions of $\gamma$,$\gamma$,$\gamma$-trichloroethylidene-m-nitroacetophenone with phenylhydrazine and substituted phenylhydrazines, and hydrazone was isolated as an intermediate from the reaction with 2, 4-dinitrophenylhydrazine. From the reaction with hydrazine hydrate 3-(m-nitrophenyl)-5-trichloromethyl-2-pyrazoline was obtained in good yield. The effect of substituents on phenyl group in the reaction of $\gamma$,$\gamma$,$\gamma$-trichloroethylidene-m-nitroacetophenone with substituted phenylhydrazines was also discussed.

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