• 대한수학회보
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• 제36권2호
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• pp.233-238
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• 1999

Kawamoto generalized the Witt algebra using F[${X_1}^{\pm1},....{X_n}^{\pm1}$] instead of F[x1,…, xn]. We construct the generalized Witt algebra $W_{g,h,n}$ by using additive mappings g, h from a set of integers into a field F of characteristic zero. We show that the Lie algebra $W_{g,h,n}$ is simple if a g and h are injective, and also the Lie algebra $W_{g,h,n}$ has no ad-digonalizable elements.

• 한국결정학회지
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• 제15권2호
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• pp.78-82
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• 2004

벤젠 존재 하에서, DMF와 에탄올의 혼합 용매에서 zinc(II) nitrate $(Zn(NO_3)_2\;{\cdot}\;6H_2O)$와 $ATP(2-aminoterephthalate,\;H_2N-C_6H_3-1,4-(COO)_2)$의 용매열 반응으로 2차원 배위 고분자 [Zn(ATP) (DMF)] (1)이 얻어졌다 X-ray구조 결정 결과, 2개의 아연 금속과 4개의 ATP 리간드가 paddle-wheel유형의 2차 쌓음 단위들을 형성하고, 이것들은 ATP 리간드에 의해서 연결되어 2차원 4각 망을 이룬다는 것이 밝혀졌다. 아연 금속을 기준으로 각 4각형의 크기는 약$11.1\times11.1\;{\AA}$효이다. 고분자 1을 양질의 결정 상태로 얻기 위해서는 벤젠이 요구되었다.

• Clinical and Experimental Pediatrics
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• 제52권8호
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• pp.862-868
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• 2009

Since its identification in April 2009, a swine-origin H1N1 influenza A virus (S-OIV) which is a reassortment of gene segments from both North American triple-reassortant and Eurasian swine influenza has been widely spread among humans in unexpected rapidity. To date, each gene segment of the 2009 influenza A (H1N1) outbreak viruses have shown high (99.9%) neucleotide sequence identity. As of July 6, 94,512 people have been infected in 122 countries, of whom 429 have died with an overall case-fatality rate of <0.5%. Most confirmed cases of S-OIV infection have been characterized by self-limited, uncomplicated febrile respiratory illness and 38% of cases have also included vomiting or diarrhea. Standard plus droplet precautions should be adhered to at all times. Tests on S-OIV have indicated that current new H1N1 viruses are sensitive to neuraminidase inhibitors (oseltamivir). However, current less virulent S-OIV may evolve into a pathogenic strain or acquire antiviral resistance, potentially with more severe clinical consequences. Efforts to control these outbreaks would be based on our understanding of novel S-OIV and previous influenza pandemics.

• 대한수학회지
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• 제38권3호
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 대한수학회보
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• 제59권6호
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• pp.1511-1522
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• 2022

Let H be a subgroup of $\mathbb{Z}^*_n$ (the multiplicative group of integers modulo n) and h₁, h₂, …, h_l distinct representatives of the cosets of H in $\mathbb{Z}^*_n$. We now define a polynomial J_n,H(x) to be $$J_{n,H}(x)=\prod^l_{j=1} \left( x-\sum_{h{\in}H} {\zeta}^{h_jh}_n\right)$$, where ${\zeta}_n=e^{\frac{2{\pi}i}{n}}$ is the nth primitive root of unity. Polynomials of such form generalize the nth cyclotomic polynomial $\Phi_n(x)={\prod}_{k{\in}\mathbb{Z}^*_n}(x-{\zeta}^k_n)$ as J_n,{1}(x) = Φ_n(x). While the nth cyclotomic polynomial Φ_n(x) is irreducible over ℚ, J_n,H(x) is not necessarily irreducible. In this paper, we determine the subgroups H for which J_n,H(x) is irreducible over ℚ.

• 대한수학회보
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• 제38권4호
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• pp.727-733
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• 2001

Let A be a commutative ring with nonzero identity and let M be an A-module. In this note we show that if $x = x_1, ..., x_n\; and\; y = y_1, ..., y_n$ both M-cosequence such that $Hx^T = y^T\; for\; some\; n\times n$ lower triangular matrix H over A, then the map $\beta_H : \;Ann_M(y_1,..., y_n)\;\rightarrow Ann_M(x_1,..., x_n)$ induced by multiplication by ｜H｜ is surjective.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.503-510
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• 2004

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 $Tx_i\;=\;y_i,\;for\;i\;=\;1,\;2,\;\cdots,\;n$. In this paper the following is proved: Let H be a Hilbert space and L be a commutative subspace lattice on H. Let H and y be vectors in H. Let $M_x\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_ix\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;and\;M_y\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_iy\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}. Then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in ${\overline{M_x}}^{\bot}$, AE = EA for all $E\;{\in}\;L\;and\;A^{*}\;=\;A$. (2) $sup\;\{\frac{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;<\;{\infty},\;{\overline{M_u}}\;{\subset}{\overline{M_x}}$ and < Ex, y >=< Ey, x > for all E in L.

• 대한수학회보
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• 제36권4호
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• pp.701-706
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• 1999

A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature $H_1$ does not vanish and the ratio $H_n$/$H_1$ of the Gauss-Kronecker curvature $H_n$ and $H_1$ is constant.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Bulletin of the Korean Chemical Society
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• 제31권7호
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• pp.1869-1874
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• 2010

By reducing PVP with $H_2NOH$.HCl and NaOH 2:2:1 mass ratios in aqueous ethanol, poly-N-vinyl pyrrolidone oxime [PVPO] was prepared with 92% yield. Applying the sol-gel concept, orthosilicic acid [OSA] was made by hydrolyzing TEOS with ethanol in 1:0.5 molar ratios using 1 N KOH aqueous solution as a catalyst. The OSA + PVPO + $_L$-Valine ($\alpha$-amino acid) were mixed with pure ethanolic medium in 1:2:2 mass ratios and refluxed at $78^{\circ}C$ and 6 pH for 6.5 h. A white residue of poly-N-vinyl pyrrolidone oximo-L-valyl-siliconate [POVS] appeared after 5 h. The heating of reaction mixture was stopped and the contents were brought to NTP. The residue formation of POVS was intensified with lowering a temperature and completely solidified within 5 h, was filtered using a vacuum pump with Whatmann filter paper no. 42. The residue of POVS was washed several times with 20% aqueous cold ethanolic solution and dried in vacuum chamber at $25^{\circ}C$ for 24 h. The MP was noted above $350^{\circ}C$. Structural and internal morphology were analyzed with IR and $^1H$-NMR, and SEM respectively. A drug loading and transporting ability of the POVS in water and at pH = 5 and 8 was determined chromatographically.