• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.65-70
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• 1993

In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

• Journal of the Korean institute of surface engineering
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• v.44 no.5
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• pp.201-206
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• 2011

Fe-2%Mn-0.5%Si alloys were corroded at 600, 700 and $800^{\circ}C$ for up to 70 h in 1 atm of $N_2$ gas, or 1 atm of $N_2/H_2O$-mixed gases, or 1 atm of $N_2/H_2O/H_2S$-mixed gases. Oxidation prevailed in $N_2$ and $N_2/H_2O$ gases, whereas sulfidation dominated in $N_2/H_2O/H_2S$ gases. The oxidation/sulfidation rates increased in the order of $N_2$ gas, $N_2/H_2O$ gases, and, much more seriously, $N_2/H_2O/H_2S$ gases. The base element of Fe oxidized to $Fe_2O_3$ and $Fe_3O_4$ in $N_2$ and $N_2/H_2O$ gases, whereas it sulfidized to FeS in $N_2/H_2O/H_2S$ gases. The oxides or sulfides of Mn or Si were not detected from the XRD analyses, owing to their small amount or dissolution in FeS. Since FeS was present throughout the whole scale, the alloys were nonprotective in $N_2/H_2O/H_2S$ gases.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.601-614
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• 2016

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [12] obtained an explicit finite presentation for the mapping class group $\mathcal{M}(N_{g,s})$ of the surface $N_{g,s}$, where $s{\in}\{0,1\}$ and g + s > 3. Following this work, we obtain a finite presentation for the subgroup $\mathcal{T}(N_{g,s})$ of $\mathcal{M}(N_{g,s})$ generated by Dehn twists.

• Archives of Pharmacal Research
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• v.22 no.5
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• pp.491-495
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• 1999

In order to examine the effects of N-substituted alkyl group on the anticonvulsant activities of N-Cbz-$\alpha$-aminoglutarimides as novel anticonvulsants with broad spectrum, a series of (R) or (S) N-Cbz-$\alpha$-amino-N-alkylglutarimides (1 and 2) were prepared from the corresponding (R) or (S) N-Cbz-glutamic acid and evaluated for the anticonvulsant activities in the maximal electroshock seizure (MES) test and pentylenetetrazol induced seizure(PTZ) test, including the neurotoxicity. The most potent compound in the MES test was (S) N-Cbz-$\alpha$-amino-N-methylglutarimide($ED_{50}$=36.3 mg/kg, PI=1.7). This compound was also most potent in the PTZ test ($ED_{50}$=12.5 mg/kg, PI=5.0). The order of anticonvulsant activities against the MES test as evaluated form $ED_{50}$ values for (R) series was N-methyl > N-H > N-ethyl > N-allyl ; for the (S) series N-methyl > N-H > N-ethyl > N-alkyl > N-isobutyl compound. Against the PTZ tests, the order of anticonvulsant activities showed similar pattern ; for the (R) series, N-methyl > N-H > N-ethyl > N-allyl ; for the (S) series N-methyl > N-H > N-ethyl > N-allyl > N-isobutyl compound. From the above results, N-substituted alkyl groups were though to play an important role for the anticonvulsant activities of N-Cbz-$\alpha$-amino-N-alkylgutarimides.

• Journal of the Korean Chemical Society
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• v.23 no.6
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• pp.368-373
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• 1979

Kinetic studies have been carried out on solvolyses and halide exchanges $(Cl^-,\;Br^-,\;I^-)$ of N,N-dimethyl-, N,N-diethylcarbamoyl chlorides, and solvolyses of N,N-diphenylcarbamoyl chloride. Kinetic results together with simple MO analysis indicated that: (a) N,N-dialkylcarbamoyl chlorides reacted via the $S_N2$ mechanism, while N,N-diphenylcarbamoylchloride reacted via the $S_N1$ mechanism; (b) in chloride exchanges, the bond-breaking appeared to be important, whereas in bromide and iodide exchanges, the bond-formation was shown to be important.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.783-801
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• 2006

Let A be the mod p Steenrod algebra for p an arbitrary odd prime and S the sphere spectrum localized at p. In this paper, some useful propositions about the May spectral sequence are first given, and then, two new nontrivial homotopy elements ${\alpha}_1{\jmath}{\xi}_n\;(p{\geq}5,n\;{\geq}\;3)\;and\;{\gamma}_s{\alpha}_1{\jmath}{\xi}_n\;(p\;{\geq}\;7,\;n\;{\geq}\;4)$ are detected in the stable homotopy groups of spheres, where ${\xi}_n\;{\in}\;{\pi}_{p^nq+pq-2}M$ is obtained in [2]. The new ones are of degree 2(p - 1)($p^n+p+1$) - 4 and 2(p - 1)($p^n+sp^2$ + sp + (s - 1)) - 7 and are represented up to nonzero scalar by $b_0h_0h_n,\;b_0h_0h_n\tilde{\gamma}_s\;{\neq}\;0\;{\in}\;Ext^{*,*}_A^(Z_p,\;Z_p)$ in the Adams spectral sequence respectively, where $3\;{\leq}\;s\;<\;p-2$.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.591-600
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• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1425-1432
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• 2014

The Euler zeta function is defined by ${\zeta}_E(s)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n^8}$. The purpose of this paper is to find formulas of the Euler zeta function's values. In this paper, for $s{\in}\mathbb{N}$ we find the recurrence formula of ${\zeta}_E(2s)$ using the Fourier series. Also we find the recurrence formula of $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{(2_{n-1})^{2s-1}}$, where $s{\geq}2({\in}\mathbb{N})$.

• East Asian mathematical journal
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• v.28 no.2
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• pp.159-172
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• 2012

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.