• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.1-4
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• 2003

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX= Y. An interpolating operator for n-operators satisfies the equation AXi= Yi, for i = 1,2,...,n, In this article, we showed the following : Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that rangeX is dense in H. Then the following statements are equivalent : (1) There exists an operator A in AlgL such that AX = Y, A$\^$*/=A and every E in L reduces A. (2) sup｛(equation omitted) : n $\in$ N f$\sub$I/ $\in$ H and E$\sub$I/ $\in$ L｝<$\infty$ and = for all E in L and all f, g in H.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.485-490
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i=y_i$ , for i, = 1,2,…,n. In this article, we investigate compact interpolation problems in tridiagonal algebra : Given vectors x and y in a Hilbert space, when is there a compact operator A in a tridiagonal algebra such that Ax = y?

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.845-850
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• 2002

Given vectors x and y in a filbert space H, an interpolating operator for vectors is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i=y_i$, for i = 1, 2 …, n. In this article, we investigate self-adjoint interpolation problems for vectors in tridiagonal algebra.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.441-446
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• 2014

In this paper the following is proved: Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$ and X and Y be operators acting on $\mathcal{H}$. Then there exists a compact operator A in $Alg\mathcal{L}$ such that AX = Y if and only if ${\sup}\{\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}\;:\;f{\in}\mathcal{H},\;E{\in}\mathcal{L}\}$ = K < ${\infty}$ and Y is compact. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel}=K$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.18 no.2
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• pp.124-130
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• 1985

In the previous papers (Kim and Park, 1984 a, b; 1985 a), we have reported on alginic acid from Ecklonia cava and Sargassum ringgoldianum. The seasonal variation in the composition of uronic acids and their block structures of alginic acid from Myagropsis myagroides Fensholt and Sargassum horneri C. Agardh (collected from Iee Chun village on the coast of Ilgwang-myon, Yansan-gun, Kyungnam, Korea, in the period of January to December in 1982) are investigated, and their relationship between the chemical composition and some related properties are discussed in this study. One year average contents of alginic acid were $25.2\%$ in the M. myagroides and $26.5\%$ in the S. horneri, and one year average values of M/G ratios were 1.97 in the M. myagroides and 1.38 in the S. horneri. The value of M. myagroides was largest in the period of December to April, and smallest in May to June and October to November. The value of S. horneri was largest in January and smallest in March to April. The proportion of alternating, M and G block in M. myagroides were $18.4\%,\;40.4\%$, and $41.2\%$, and those in S. horneri $9.8\%,\;33.3\%$ and $56.9\%$, respectively. The higher viscosity showed the value of 45.3 cP in M. myagroides (in November), and 26.0 cP in S. horneri(in January), respectively. Furthermore, the dependence on temperature of M. myagroides alginic acid was also larger in November, that of S. horneri alginic acid in June. Ion exchange ability of M. myagroides alginic acid was highest in November and the exchange amounts were $Pb^{2+}\;4.4,\;Cu^{2+}\;1.8,\;Zn^{2+}\;2.5$ and $Co^{2+}\;2.0\;meq/g$. Na-Alg., and the ability of S. horneri alginic acid was highest in June and the amounts were $Pb^{2+}\;4.5,\;Cu^{2+}\;2.2,\;Zn^{2+}\;2.4$ and $Co^{2+}\;2.1\;meq/g.$ Na-Alg. The affinity with metallic ions appeared higher in order of $Pb^{2+}>Cu^{2+}>Zn^{2+}>Co^{2+}$, and the exchange ability assumed to relate with the block ratio of uronic acid.

• Journal of Life Science
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• v.25 no.2
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• pp.121-129
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• 2015

Alginates are found in marine brown seaweeds and in extracellular biofilms secreted by some bacteria. Previously, we reported an oligoalginate lyase from Sphingomonas sp. MJ-3 (MJ3-Oal) that had an exolytic activity and protein sequence homology with endolytic polymannuronate (polyM) lyase in the N-terminal region. In this study, the MJ3-Oal was tested for both exolytic and endolytic activity by homology modeling using the crystal structure of Alg17c from Saccharophagus degradans 2-40T. The tyrosine residue at the $426^{th}$ position, which possibly formed a hydrogen bond with the substrate, was mutated to phenylalanine. The FPLC profiles showed that MJ3-Oal degraded alginate quickly to monomers as a final product through the oligmers, whereas the Tyr426Phe mutant showed only exolytic alginate lyase activity. $^1H$-NMR spectra also showed that MJ3-Oal degraded the endoglycosidic bond of polyM and polyMG (polymannuronate-guluronate) blocks. These results indicate that oligoalginate lyase from Sphingomonas sp. MJ-3 probably catalyzes the degradation of both exo- and endo-glycosidic bonds of alginate.