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FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS

  • Chon, Inheung
    • Korean Journal of Mathematics
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    • 제21권2호
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    • pp.171-180
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    • 2013

  • We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

  • https://doi.org/10.11568/kjm.2013.21.2.171 인용 PDF KSCI

GENERALIZED WEYL'S THEOREM FOR ALGEBRAICALLY $k$-QUASI-PARANORMAL OPERATORS

  • Senthilkumar, D.;Naik, P. Maheswari;Sivakumar, N.
    • 충청수학회지
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    • 제25권4호
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    • pp.655-668
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    • 2012

  • An operator $T\;{\varepsilon}\;B(\mathcal{H})$ is said to be $k$-quasi-paranormal operator if $||T^{k+1}x||^2\;{\leq}\;||T^{k+2}x||\;||T^kx||$ for every $x\;{\epsilon}\;\mathcal{H}$, $k$ is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. In this paper, using the operator matrix representation of $k$-quasi-paranormal operators which is related to the paranormal operators, we show that every algebraically $k$-quasi-paranormal operator has Bishop's property ($\beta$), which is an extension of the result proved for paranormal operators in [32]. Also we prove that (i) generalized Weyl's theorem holds for $f(T)$ for every $f\;{\epsilon}\;H({\sigma}(T))$; (ii) generalized a - Browder's theorem holds for $f(S)$ for every $S\;{\prec}\;T$ and $f\;{\epsilon}\;H({\sigma}(S))$; (iii) the spectral mapping theorem holds for the B - Weyl spectrum of T.

  • https://doi.org/10.14403/jcms.2012.25.4.655 인용 KSCI

A Pediatric Case of Inflammatory Bowel Disease with Renal Amyloidosis

  • Hyun, Hyesun;Park, Eujin;Kim, Ji Hyun;Cho, Myung Hyun;Kang, Hee Gyung;Moon, Jin Soo;Moon, Kyung Chul;Ha, Il-Soo;Cheong, Hae Il
    • Childhood Kidney Diseases
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    • 제22권2호
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    • pp.81-85
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    • 2018

  • Amyloidosis is a rare disease that results from the deposition of extracellular protein in various body tissues, causing progressive organ dysfunction. Secondary renal amyloidosis is a rare but serious complication of chronic inflammatory bowel disease, particularly in patients with Crohn's disease or ulcerative colitis. We report a case of secondary renal amyloidosis in a pediatric patient who reported a 16-year history of "very early onset inflammatory bowel disease". Intensive treatment including repeated infliximab infusions improved clinical parameters of inflammatory bowel disease, although renal dysfunction showed progression. Amyloidosis should be considered in patients with IBD, particularly if they suffered disease progression.

  • https://doi.org/10.3339/jkspn.2018.22.2.81 인용 PDF KSCI