• 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.

• East Asian mathematical journal
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• v.36 no.3
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• pp.417-424
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• 2020

Huang et al. proved that the n by n upper triangular matrix ring over a domain is weakly reversible-over-center by using the property of regular matrices. In this article we provide a concrete proof which is able to be available in the related study of centers. Next we extend an example of weakly reversible-over-center, which was argued by Huang et al., to the general case.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• YAKHAK HOEJI
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• v.28 no.2
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• pp.97-100
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• 1984

We have investigated the feasibility of using cyclic ambident nucleophiles in s-triazine ring transformation reaction and found that they can replace the $N_{1}-C_{2-N_{3}$ fragment of s-triazine directly in basic conditions, yielding the corresponding bicyclic products. In this paper, we described the reaction and mechanistic aspects of s-triazine to pyrimidopyrimidine transformation by 6-aminouracil derivatives. This type of ring transformation is supposed to be first attempt that deals with the successful s-triazine to bicyclic heterocycle transformation.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.210-214
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• 1994

The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.655-663
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• 2014

Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1333-1338
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• 2018

A ${\ast}-ring$ R is called ${\ast}-regular$ if every principal one-sided ideal of R is generated by a projection. In this note, several characterizations of ${\ast}-regular$ rings are provided. In particular, it is shown that a matrix ring $M_n(R)$ is ${\ast}-regular$ if and only if R is regular and $1+x^*_1x_1+{\cdots}+x^*_{n-1}x_{n-1}$ is a unit for all $x_i$ of R; which answers a question raised in the literature recently.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.155-162
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• 2016

This study attempts to reveal structures of two-dimensional ring polymer solutions in various polymer concentrations ranging from dilute to concentrated regime. Polymer sizes, single molecule structure factors, bond correlation functions and monomer density distribution functions from center of mass are given in order to clarify the polymer structures. Our study shows that a ring in dilute solution maintain pseudo-circular structure with self-avoiding walk (SAW) statistics, and it seems to be composed of two connecting SAW linear chains. In semidilute solutions, ring polymers are not entangled with each other and adopt collapsed configurations. Such assumption of collapsed structures in the semidilute regime gives an overlap concentration of ${\varphi}^*{\sim}N^{-1/2}$ where N is degree of polymerization. By normalizing the polymer concentration by these overlap concentration, we find universal behaviors of polymer sizes and structure factors regardless of N.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• Archives of Pharmacal Research
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• v.2 no.2
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• pp.99-110
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• 1979

The crystal structure of sulfapyridine, $C_{11}H_{11}N_{3}O_{2}S$, has been determined by X-ray diffraction method. The compound crystallizees in the monoclinic space group C2/c with a = 12, 80(4), b= 11.72(4), $c= 15.36(5){\AA}, {\beta}= 94(3)^{\circ}$and Z = 8. A total of 1133 observed reflections were collected by the Weissenberg method with CuKaradiation. Structure was solved by the heavy atom method and refined by isostropic block-diagonal least-squares method to the R value of 0.14. The nitrogen in the pyridine ring of sulfapyridine is associated with an extra-annular hydrogen. The C (benzene ring) S-N-C (pyridine ring) group adopts the gauche form with a fonformational angle of $71^{\circ}$. The benzene ring are inclined at angle of $84^{\circ}.to the pyridine ring plane. Sulfapyridine shows three different hydrogen bonding in the crystal. They are two N-H...O hydrogen bonds with the distance of 2.90 and 2.98${\AA}$ respectively, and on N-H...N with the distance of 3.06 ${\AA}$.