• Journal of the Korean Chemical Society
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• v.26 no.5
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• pp.310-319
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• 1982

Cobalt(III) complexes with sexidentate ligands, N,N,N',N'-tetrakis(2-amino-ethyl)-1,2-ethanediamine (ten), -1,3-propanediamine (ttn), -1,4-butanediamine (ttmd), -(R,R)-and -(R,S)-2,4-pentanediamine (tptn) were prepared, and the characterization of d-d absorption band on the variation of chelate ring size and conformation of these complexes were studied by means of electronic spectra. The first d-d absorption bands of $[Co(L)]^{3+}$ complexes are shifted to smaller wave numbers in the order. ttn > (R,R)-tptn > ten > ttmd${\simeq}$(R,S)-tptn for (L). The UV, $^{13}C$ NMR, and Circular Dichroism studies indicate that the R,S-tptn ligand of $[Co(R,S-tptn)]^{3+}$ complex coodinates to cobalt(Ⅲ) ion as a sexidentate with one methyl group in axial position.

• Journal of Life Science
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• v.14 no.1
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• pp.91-97
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• 2004

As a part of our study on the improvement of anticonvulsant, here we report the synthesis of N-acyl-$\alpha$-aminosuc-cinimides 1 and N-acyl-$\alpha$-aminoglutarimides 2. (R)-Benzoic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-ylester 6a, (R)-4-nifro-benzoic acid 4-benzyloxycarbonylamino-2- oxo-pyrrolidin-1-yl ester 6b, (R) -4-nitro-benzoic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-yl ester 6c, and (R)-propionic acid 4-benzyloxycarbonylamino-2-oxo-pyrrolidin-1-yl ester 6d were synthesized from (R)-2-benzyloxy carbonylamino-succinic acid 3 as a starting meterial. (R)-(3- Benzyloxycarbonylamino-2,6-dioxo-piperidin-1-yloxy)-acetic acid methyl ester 10a, (R)-(3-benzyloxycarbonylamino-2,6-dioxo-piperidin-1-yloxy)-acetic acid ethy1 ester 10b, an d (R)-2-(3-benzyloxycarbonylamino-2,6- diox o-piperidin-1-yl oxy)-propionic acid methyl ester l0c were synthesized from (R)- 3-carbobenzyloxy-amino-glutarmic acid 7 as a starting meterial. The yield, mp, IR, $^1H-NMR,\; and^{13}C$- NMR spectra of the products 6a, 6b, 6c, 6d, 10a, l0b, l0c are summarized in footnote. The biological studies of these compounds are in progress and will be reported in future.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.143-153
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• 2018

In this paper, we define 0-minimal (m, n)-ideals in an LA-semigroup ${\mathcal{S}}$ and prove that if R(L) is a 0-minimal right (left) ideal of S, then either $R^mL^n=\{0\}$ or $R^mL^n$ is a 0-minimal (m, n)-ideal of S for $m,n{\geq}3$.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.4
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• pp.543-549
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• 1997

The problems in the existing modeling rules for fishing nets, especially in the Tauti's rule which had been used most commonly, were investigated and it was found that the rules could not give a good similarity between the prototype and model nets because they din neither analyze the flow resistance of nets accurately nor decide the ratio of flow velocity between the two nets properly. Thus, the modeling rule was newly derived by regarding the nets as holey structures sucking water into their mouth and then filtering water through their meshes as in the previous paper. The similarity conditions obtained, between the two nets distinguished by subscript 1 and 2, are as follows; $$\frac{d_2}{d_1}=\sqrt{\frac{l_2}{l_1}},\;\frac{N_2}{N_1}=(\frac{d_1}{d_2})^{1.5}\frac{L_2}{L_1},\;\varphi_1=\varphi_2,\;\frac{d_{r2}}{d_{r1}}=\sqrt{\frac{L_2{(\rho_{r1}-\rho_{w1})}}{{L_1{(\rho_{r2}-\rho_{w2})}}$$ $$\frac{N_{a2}}{N_{a1}}=\frac{W_{a1}}{W_{a2}}(\frac{L_2}{L_1})^2,\;\nu_1=\nu_2\;and\;\frac{R_2}{R_1}=(\frac{L_2}{L_1})^2$$, where L is the length of nettings, d the diameter of netting twines, 2l the mesh size, $2\varphi$ the angle between two adjacent bars, N the number of meshes at the sides of nettings, $d_r$, the diameter of ropes, $\rho_r$, the specific gravity of ropes, $W_a$ the weight in water of one piece of float or sinker, $N_a$ the number of floats or sinkers, $\nu$ the flow velocity, and R the flow resistance of net. In the case where the model experiments aim at investigating the influence of weight in water of nettings on their shapes in nets subjected to the water flow of very low velocity, however, the following condition is added; $$\frac{\rho_2-\rho_{w2}}{\rho_1-\rho_{w1}}=\frac{d_1}{d_2}$$ where $\rho$ is the specific gravity of netting twines.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.451-460
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• 2024

If a₀ + Σⁿ_ν=μ a_νz^ν, 1 ≤ µ ≤ n, is a polynomial of degree n having no zeroin |z| < k, k ≥ 1 and p'(z) its derivative, then Qazi [19] proved $$\max_{{\left|z\right|=1}}\left|p\prime(z)\right|\leq{n}\frac{1+\frac{{\mu}}{n}\left|\frac{a_{\mu}}{a_0} \right|k^{{\mu}+1}}{1+k^{{\mu}+1}+\frac{{\mu}}{n}\left|\frac{a_{\mu}}{a_0} \right|(k^{{\mu}+1}+k^{2{\mu}})}\max_{{\left|z\right|=1}}\left|p(z)\right|$$ In this paper, we not only obtain the L^r version of the polar derivative of the above inequality for r > 0, but also obtain an improved L^r extension in polar derivative.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.319-328
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• 2011

Let $\mathbf{c}=\{c_n\}_{n{\in}\mathbb{Z}}\in{\ell}^1(\mathbb{Z})$ and $\{f_n\}_{n{\in}\mathbb{Z}}$ be a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$. We obtain necessary and sufficient conditions of $\mathbf{c}$ under which $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$, where ${\lambda}$ > 0 and $(\mathbf{c}{\ast}_{\lambda}f)(t)\;:=\;{\sum}_{n{\in}\mathbb{Z}}c_nf(t-n{\lambda})$. When $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame of $L^2(\mathbb{R})$, we present its frame operator and the canonical dual frame in a simple form. Some interesting examples are included.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1433-1439
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• 2013

A ring R is called left morphic if $$R/Ra{\simeq_-}l(a)$$ for every $a{\in}R$. Equivalently, for every $a{\in}R$ there exists $b{\in}R$ such that $Ra=l(b)$ and $l(a)=Rb$. A ring R is called left quasi-morphic if there exist $b$ and $c$ in R such that $Ra=l(b)$ and $l(a)=Rc$ for every $a{\in}R$. A result of T.-K. Lee and Y. Zhou says that R is unit regular if and only if $$R[x]/(x^2){\simeq_-}R{\propto}R$$ is morphic. Motivated by this result, we investigate the morphic property of the ring $$S_n=^{def}R[x_1,x_2,{\cdots},x_n]/(\{x_ix_j\})$$, where $i,j{\in}\{1,2,{\cdots},n\}$. The morphic elements of $S_n$ are completely determined when R is strongly regular.

• Journal of Plant Biology
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• v.29 no.1
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• pp.53-65
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• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.