• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.275-283
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• 2015

Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^∗k(T^∗2T² − 2T^∗T + I)T^k = 0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl’s theorem holds for polynomially k-quasi-2-isometric operators.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1708-1711
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• 2006

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.59-68
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• 2011

In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$\"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n \atop l})^{3/2}n^{l/2}\;{\times}\;2^{n+1}l\;{\times}\;100^{n^2}\;\[2^l(2^{n+3l}+1)\]\;(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${\in}$ $W_{loc}^{1,q_1}$ (${\Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${\Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.981-997
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• 1998

We shall show first general Metivier operators ${D_y}^2+(x^{2l}+y^{2k}){D_x}^2,l,k=1,2,....,have {G_{x,y}}^{{\theta,d}}$-hypoellipticity in the vicinity of the origin (0,0), where $\theta=\frac{l(1+k)}{l(1+k)-k},\;d=\frac{\theta+k}{1+k}$ (＞1), and finally the optimality of these exponents {$\theta$, d} will be shown.

• Journal of the Korean Chemical Society
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• v.34 no.4
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• pp.319-324
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• 1990

Kinetic of substitution of dibenzoylmethanate (dbm) for one acetylacetonate (acac) in VO (acac)$_2$ have been studied in various solvents by spectrophotometry. Under the condition [VO (acac)$_2$] 》[Hdbm], the rate law for the substitution reaction is expressed as, rate = k$_2$K[VO(acac)$_2$] [Hdbm] / (1 ＋ K[VO(acac)$_2$]) where K = [VO (acac)$_2$dbmH] / [VO(acac)$_2$][Hdbm] and the rate constant k$_2$ corresponds to that of proton transfer from coordinated Hdbm to leaving acac- in VO(acac)$_2$dbmH.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Applied Chemistry for Engineering
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• v.7 no.3
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• pp.580-587
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• 1996

Synthesis of long fibrous $K_2Ti_4O_9$ was attempted to find a method to produce long fibrous $K_2Ti_6O_{13}$ and other derivatives and also phase transformation of $K_2Ti_4O_9$ synthesized was investigated. Long fibrous $K_2Ti_4O_9$ was succesively synthesized by the calcination reaction under the following reaction conditions ; reaction temperature of $1050^{\circ}C$, $TiO_2$ mole ratio to $K_2CO_3$ of 2.8 and reaction time of 3hrs, and scattering of calcined products for 10hrs with hot boiling water. $K_2Ti_4O_9$ showed lower structural stability under heat treatment and the structure of $K_2Ti_4O_9$ was converted to $K_2Ti_6O_{13}$ under heating temperature of over $250^{\circ}C$.

• Biomolecules & Therapeutics
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• v.14 no.4
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• pp.246-252
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• 2006

1,2-Dibromoethane(DBE) has been widely used as a soil fumigant, an additive to leaded gasoline and an industrial solvent. In this study, we have carried out in vitro genetic toxicity test of 1,2-dibromoethane and microarray analysis of differentially expressed genes in response to 1,2-dibromoethane. 1,2-Dibromoethane showed mutations in base substitution strain TA1535 both with and without exogenous metabolic activation. 1,2-Dibromoethane showed mutations in frame shift TA98 both with and without exogenous metabolic activation. 1,2-Dibromoethane showed DNA damage based on single cell gel/comet assay in L5178Y cells both with and without exogenous metabolic activation. 1,2-Dibromoethane increased micronuclei in CRO cells both with and without exogenous metabolic activation. Microarray analysis of gene expression profiles in L5178Y cells in response to 1,2-dibromoethane selected differentially expressed 241 genes that would be candidate biomarkers of genetic toxic action of 1,2-dibromoethane.

• Korean Journal of Microbiology
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• v.35 no.4
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• pp.270-276
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• 1999

Production of stress shock proteins in Burkholderia cepacia YK-2 in response to the phenoxyherbicide 2,4-dichlorophenoxyacetic acid(2,4-D) as an environmental contaminant was investrigated. The stress schock proteins were synthesized at different 2,4-D concentrations in exponentially growing cultures of B. capacia YK-2. This response involved the production of 43kDa and 41kDa GroEL proteins. The proteins were characterized by SDS-PAGE and Western blot using the anti-DnaK nad anti-GroEL monoclonal antibodies. Total stress shock proteins were analyzed by 2-D PAGE. Survival of B. cepacia YK-2 with time in the presence of different concentrations of 2,4-D was monitored, and viable counts paralleled the production of the stress shock proteins in this bacterium.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.187-213
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• 2009

For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,\;k)=\sum\limits_{j=1}^k\(\(\frac{j}{k}\)\)\(\(\frac{hj}{k}\)\),$$ where $$((x))=\{{x-[x]-\frac{1}{2},\;if\;x\;is\;not\;an\;integer; \atop \;0,\;\;\;\;\;\;\;\;\;\;if\;x\;is\;an\;integer.}\$$ J. B. Conrey et al proved that $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^{2m}(h,\;k)=fm(k)\;\(\frac{k}{12}\)^{2m}+O\(\(k^{\frac{9}{5}}+k^{{2m-1}+\frac{1}{m+1}}\)\;\log^3k\).$$ For $m\;{\geq}\;2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^2(h,\;k)=\frac{5}{144}k{\phi}(k)\prod_{p^{\alpha}{\parallel}k}\[\frac{\(1+\frac{1}{p}\)^2-\frac{1}{p^{3\alpha+1}}}{1+\frac{1}{p}+\frac{1}{p^2}}\]\;+\;O\(k\;{\exp}\;\(\frac{4{\log}k}{\log\log{k}}\)\).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.