• Honam Mathematical Journal
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• v.31 no.4
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• pp.515-527
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• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Journal of the Korean Chemical Society
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• v.10 no.1
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• pp.11-14
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• 1966

The thermodynamic parameters for the solvolysis of the p-nitrobenzyl chloride which take place in the ethanol-water mixture media were determined. From the application of this data to the formula ${\delta}_M{\Delta}H^{\neq} = a'Y + b{\delta}_M{\Delta}S^{\leq}$ the following conclusion was obtained. The substrate constant a' for this reaction was not varied in the media which contain more than 50% alcohol and less than 50% alcohol. From this, it is clear that the mechanism of this reaction is the same both in the water-rich solvent and in the alcohol-rich solvent.

• Bulletin of the Korean Chemical Society
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• v.32 no.3
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• pp.889-893
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• 2011

The energetics and transition state (TS) structures of the reactions of six substrates, $R_1R_2P$(=O or S)Cl-type where $R_1=R_2$=Me and/or MeO, with ammonia in acetonitrile are theoretically investigated at the level of CPCM-MP2/6-31+G(d) and CPCM-MP2/6-311+G(3df,2p). The degrees of distortion of TS from the ideal trigonal bipyramidal pentacoordinate, ${\Delta}{{\delta}}_{{\neq}b}$ for a backside and ${\Delta}{{\delta}}_{{\neq}f}$ for a frontside attack, are calculated. The results of calculation suggest that the feasibility of a frontside attack for P=S is greater than that for P=O system when the two ligands, $R_1$ and $R_2$, becomes larger. The experimental and calculated results of anilinolyses of $R_1R_2P$(=O or S)Cl-type show the consistent tendencies.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.113-128
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• 2011

Let f : ${\mathbb{R}}{\rightarrow}{\mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$ in the half planes {(x, y) : $kx+sy{\geq}d$} for fixed d, k, $s{\in}{\mathbb{R}}$ with $k{\neq}0$ or $s{\neq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$ as $kx+sy{\rightarrow}{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.69-74
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• 1989

Recently one of the present authors [2] asserted that a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of cyclic parallel if and only if AJ=JA and he showed also a complete and connected cyclic-parallel real hypersurface of M$^{n}$ (c), is congruent to type $A_{1}$, $A_{2}$ or A according as c>0 or c<0. A real hypersurface of a complex space form M$^{n}$ (c) is said to be covariantly cyclic constant if the cyclic sum of covariant derivative of the second fundamental form is constant. The purpose of the present paper is to extend theorem 3 and 4 in [2] when the hypersurfaces are of coveriantly cyclic constant, that is a real hypersurface of a complex space form M$^{n}$ (c), c.neq.0, is of covariantly cyclic constant if an only if AJ=JA, and a complete and connected covariantly cyclic constant real hypersurface of M$^{n}$ (c) is congruent to type $A_{1}$, $A_{2}$ or a according as c>0 or c<0.

• Bulletin of the Korean Chemical Society
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• v.17 no.2
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• pp.138-142
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• 1996

The transition metal carbonylate, PPN+(${\eta}^5-MeCp)Mn(CO)_2Cl^-$ undergoes a novel ligand substitution reaction with PR3 (R=Me, Et, OEt, $C_6H_5$ in THF at elevated temperatures (40 $^{\circ}C$ up to 60 $^{\circ}C)$ under the pseudo-first-order reaction conditions (usually 20-fold excess of PR3 with respect to metal carbonylate concentrations) where chloride is displaced by PR3. The reaction follows overall first order dependence on [(${\eta}^5-MeCp)Mn(CO)_2Cl^-$]; however, the negative entropy changes of activation (${\Delta}S^{\neq}$=-19.3 e.u. for $P(OEt)_3$; ${\Delta}S^{\neq}$=-16.4 e.u. for $PPh_3$) suggest the existence of the intermediate, ((η3-MeCp)Mn(CO)2(THF)Cl-, which eventually transforms to the product (${\eta}^5-MeCp)Mn(CO)_2(PR_3)$.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.731-739
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• 2010

In this paper, we prove stability of the reciprocal difference functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)-r\(\sum_{i=1}^{m}x_i\)=\frac{(m-1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ and the reciprocal adjoint functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)+r\(\sum_{i=1}^{m}x_i\)=\frac{(m+1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ in m-variables. Stability of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables were proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar [13]. We extend their result to m-variables in similar types.

• Bulletin of the Korean Chemical Society
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• v.31 no.7
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• pp.1988-1992
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• 2010

4-Amino-1,2,4-triazole copper complex (4-ATzCu) was synthesized, and its thermal behaviors, nonisothermal decomposition reaction kinetics were studied by DSC and TG-DTG techniques. The thermal decomposition reaction kinetic equation was obtained as: $d\alpha$ / dt =$10^{22.01}$ (1-$\alpha$)[-ln(1-$\alpha$)]$^{1/3}$ exp($-2.75\times10^4$ /T). The standard mole specific heat capacity of the complex was determined and the standard molar heat capacity is 305.66 $J{\cdot}mol^{-1}{\cdot}K^{-1}$ at 298.15 K. The entropy of activation $({\Delta}S^{\neq})$, enthalpy of activation $({\Delta}H^{\neq})$, and Gibbs free energy of activation $({\Delta}G^{\neq})$ are calculated as 171.88 $J{\cdot}mol^{-1}{\cdot}K^{-1}$ 225.81 $kJ{\cdot}mol^{-1}$ and 141.18 $kJ{\cdot}mol^{-1}$, and the adiabatic time-to-explosion of the complex was obtained as 389.20 s.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.393-410
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• 2013

Let $R{\subseteq}T$ be an extension of integral domains, X be an indeterminate over T, and R[X] and T[X] be polynomial rings. Then $R{\subseteq}T$ is said to be LCM-stable if $(aR{\cap}bR)T=aT{\cap}bT$ for all $0{\neq}a,b{\in}R$. Let $w_A$ be the so-called $w$-operation on an integral domain A. In this paper, we introduce the notions of $w(e)$- and $w$-LCM-stable extensions: (i) $R{\subseteq}T$ is $w(e)$-LCM-stable if $((aR{\cap}bR)T)_{w_T}=aT{\cap}bT$ for all $0{\neq}a,b{\in}R$ and (ii) $R{\subseteq}T$ is $w$-LCM-stable if $((aR{\cap}bR)T)_{w_R}=(aT{\cap}bT)_{w_R}$ for all $0{\neq}a,b{\in}R$. We prove that LCM-stable extensions are both $w(e)$-LCM-stable and $w$-LCM-stable. We also generalize some results on LCM-stable extensions. Among other things, we show that if R is a Krull domain (resp., $P{\upsilon}MD$), then $R{\subseteq}T$ is $w(e)$-LCM-stable (resp., $w$-LCM-stable) if and only if $R[X]{\subseteq}T[X]$ is $w(e)$-LCM-stable (resp., $w$-LCM-stable).

• Journal of the Korean Society of Radiology
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• v.5 no.6
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• pp.421-426
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• 2011

This research was accomplished to assess dose effects on image quality at computed radiography (CR). The ultimate target of the research was finding optimized exposure that provides necessary image quality for the clinical chest diagnosis. Modulation transfer function (MTF), normalized noise power spectrum (NNPS), and Noise equivalent quanta (NEQ) corresponding to the different doses were measured for the assessment of image quality. The preparation of "edge test device" used in MTF measurement and experimental geometry setup were followed by the recommendations of International Electrotechnical Commission (IEC). The experimental results show the necessary image quality can be achieved even at a half of the automatic exposure control (AEC) setting dose for chest diagnosis. It means that the patient exposure can be reduced dramatically by using optimized dose.