• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.907-913
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• 2010

Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, $N_*\;=\;\{f\;{\in}\;D[X]|\;(c_D(f))^*\;=\;D\}$ and $R\;=\;D[X]_{N_*}$. Let b be the b-operation on R, and let $*_c$ be the star operation on D defined by $I^{*_c}\;=\;(ID[X]_{N_*})^b\;{\cap}\;K$. Finally, let Kr(R, b) (resp., Kr(D, $*_c$)) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) $\subseteq$ Kr(D, $*_c$) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, $*_c$) if and only if D is a $P{\ast}MD$. As a corollary, we have that if D is not a $P{\ast}MD$, then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.

• Bulletin of the Korean Chemical Society
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• v.8 no.3
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• pp.144-145
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• 1987

The relative stability as function of geometry in the rigid tricyclopropylcarbinyl cations with varied bond angle (${\alpha}$) between the plane of cyclopropane ring and the bond connecting cyclopropane ring to cationic carbon was examined by $^{19}F$ nmr spectroscopy. 7-p-Fluorophenyltricyclo[2.2.2.$0^{2,6}$]octan-7-yl(4) and 8-p-fluorophenyltricyclo[3.2.2.$0^{2,7}$]nonan-8-yl cation (8) were generated from corresponding tertiary alcohols under stable ion conditions, and their $^{19}F$ chemical shifts were compared with those of model compounds such as 7-nortricyclyl cation (3) and tricyclo[3.3.1.$0^{2,7}$]octan-8-yl cation (7). Consequently, it is concluded that the varied orientation of bond angle (${\alpha}$) within in the bisected conformation does not affect degree of the charge delocalization into cyclopropane ring.

• Parasites, Hosts and Diseases
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• v.60 no.6
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• pp.401-407
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• 2022

Antimalarial drugs play an important role in the control and treatment of malaria, a deadly disease caused by the protozoan parasite Plasmodium spp. The development of novel antimalarial agents effective against drug-resistant malarial parasites is urgently needed. The novel derivatives, SKM13-MeO and SKM13-F, were designed based on an SKM13 template by replacing the phenyl group with electron-donating (-OMe) or electron-withdrawing groups (-F), respectively, to reverse the electron density. A colorimetric assay was used to quantify cytotoxicity, and in vitro inhibition assays were performed on 3 different blood stages (ring, trophozoite, and schizonts) of P. falciparum 3D7 and the ring/mixed stage of D6 strain after synchronization. The in vitro cytotoxicity analysis showed that 2 new SKM13 derivatives reduced the cytotoxicity of the SKM13 template. SKM13 maintained the IC₅₀ at the ring and trophozoite stages but not at the schizont stage. The IC₅₀ values for both the trophozoite stage of P. falciparum 3D7 and ring/mixed stages of D6 demonstrated that 2 SKM13 derivatives had decreased antimalarial efficacy, particularly for the SKM13-F derivative. SKM13 may be comparably effective in ring and trophozoite, and electron-donating groups (-OMe) may be better maintain the antimalarial activity than electron-withdrawing groups (-F) in SKM13 modification.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1385-1422
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• 2019

Let p be an odd prime. The algebraic structure of all negacyclic codes of length $8_{p^s}$ over the finite commutative chain ring ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8_{p^s}$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ into 5 cases, i.e., $p^m{\equiv}1$ (mod 16), $p^m{\equiv}3$, 11 (mod 16), $p^m{\equiv}5$, 13 (mod 16), $p^m{\equiv}7$, 15 (mod 16) and $p^m{\equiv}9$ (mod 16). From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.

• Korean Journal of Crystallography
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• v.1 no.1
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• pp.14-18
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• 1990

Econazole nitrate, 1-{2-[(4-chlorophenyl)methoxy]-2-(2,4-dichlorophenyl) ethy1}-1H-imidazole mono-nitrate.C18 H16 CI13 N3 O4 Mw=444.7 Monoclinic P/2₁c,a=17.337(4)A, b=15.191(5), c=7.601(3)A, β=91.72(2)', V=2000.9A3, Z=4, Dc=1.49g/cm3, Dm=1.45g/cm3(mo-ka)= 0.7107A, μ=4.31cm-1, F(000)=912.0, T=298'K, final R=0.061 for 1330 unique observed reflection. Each of the three ring system for the stars with B,A and C ring in order whilst A and C ring of econazole lie close to the same plane which is nearly 60˚with B ring. The hydrogen binding nitrogen of C ring and oxygen of nitrate contributes to stailization of econazole nitrate. Intr and intermolecular distances and angles are within the values recorded for simiar compounds.

• Journal of the Korean Chemical Society
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• v.9 no.3
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• pp.134-141
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• 1965

Crystals of nicotine dihydroiodide, are orthorhombic with space group $p2_12_12_1$.The unit cell of dimensions a=7.61, b=11.01, e=17.27${\AA}$, contains four formula units. The structure has been determined by X-ray diffraction method and has been refined to give the R-index, ${\sum}{\mid}{\mid}F_{\circ}{\mid}-{\mid}F_c{\mid}{\mid}{\div}{\sum}{\mid}F_{\circ}{\mid}$, of 0.16 and 0.14 for $F_{okl}\;and\;F_{hol}$ respectively.The mean lengths of C-C and C-N bonds in pyridine ring are 1.40 and $1.35{\AA}$ and those in pyrolidine ring 1.56 and $1.48{\AA}$ respectively, though accurate measurement of bond length has not been attempted. The six atoms in the pyridine ring are coplanar and on the other hand $C_6,\;C_7,\;C_8$ and $N_2$ atoms in pyrrolidine ring form a plane within accuracy of the analysis, and $C_9$ atom is distant $0.22{\AA}$ out of the plane consist of $C_6,\;C_7,\;C_8$ and $N_2$ aoms. The normals to the two planes form an angle of $94^{\circ}$ with each other. Iodine atom is distant $3.55{\AA}$ from nitrogen atom in pyridine ring and the other iodine atom $3.58{\AA}$ from nitrogen atom in pyrrolidine ring, so that the nitrogen and iodine atoms are firmly linked.It seems that the only forces binding nicotine dihydroiodide molecules together in the crystal are Van der Waals forces.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.867-871
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• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.49-61
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• 2011

Let D be an integral domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D, $N_*$={f $\in$ D[X]|c(f)$^*$= D}, $*_w$ be the star operation on D defined by $I^{*_w}$ = ID[X]${_N}_*$ $\cap$ K, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let $A^g$ (resp., $A^{[*]g}$, $A^{[*]g}$) be the global (resp.,*-global, [*]-global) transform of a ring A. We show that D is a $*_w$-Noetherian domain if and only if D[X] is a [*]-Noetherian domain. We prove that $D^{*g}$[X]${_N}_*$ = (D[X]${_N}_*$)$^g$ = (D[X])$^{[*]g}$; hence if D is a $*_w$-Noetherian domain, then each ring between D[X]${_N}_*$ and $D^{*g}$[X]${_N}_*$ is a Noetherian domain. Let $\tilde{D}$ = $\cap${$D_P$|P $\in$ $*_w$-Max(D) and htP $\geq$2}. We show that $D\;\subseteq\;\tilde{D}\;\subseteq\;D^{*g}$ and study some properties of $\tilde{D}$ and $D^{*g}$.

• Bulletin of the Korean Chemical Society
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• v.34 no.12
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• pp.3690-3694
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• 2013

The $H_2Ge=Ge:$ and its derivatives ($X_2Ge=Ge:$, X = H, Me, F, Cl, Br, Ph, Ar${\ldots}{\ldots}$) is a new species. Its cycloaddition reactions is a new area for the study of germylene chemistry. The mechanism of the cycloaddition reaction between singlet state Cl2Ge=Ge: and formaldehyde has been investigated with CCSD(T)//MP2/$6-31G^*$ method. From the potential energy profile, it could be predicted that the reaction has only one dominant reaction pathway. The reaction rule presented is that the two reactants first form a fourmembered Ge-heterocyclic ring germylene through the [2+2] cycloaddition reaction. Because of the 4p unoccupied orbital of Ge: atom in the four-membered Ge-heterocyclic ring germylene and the ${\pi}$ orbital of formaldehyde forming a ${\pi}{\rightarrow}p$ donor-acceptor bond, the four-membered Ge-heterocyclic ring germylene further combines with formaldehyde to form an intermediate. Because the Ge: atom in intermediate hybridizes to an $sp^3$ hybrid orbital after transition state, then, intermediate isomerizes to a spiro-Ge-heterocyclic ring compound via a transition state. The research result indicates the laws of cycloaddition reaction between $H_2Ge=Ge:$ and formaldehyde, and laid the theory foundation of the cycloaddition reaction between $H_2Ge=Ge:$ and its derivatives ($X_2Ge=Ge:$, X = H, Me, F, Cl, Br, Ph, Ar${\ldots}{\ldots}$) and asymmetric ${\pi}$-bonded compounds, which is significant for the synthesis of small-ring and spiro-Ge-heterocyclic compounds. The study extends research area and enriches the research content of germylene chemistry.