• 대한수학회보
• /
• 제49권4호
• /
• pp.885-898
• /
• 2012

Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

• 한국응용과학기술학회지
• /
• 제18권2호
• /
• pp.111-117
• /
• 2001

Density, viscosity, conductance, dye solubility and carbon-13 nmr studies were performed in aqueous solution of three disodium 4-n-alkyl-3-sulfonatosuccinate anionic surfactant at $20^{\circ}C$. The cmc values were 0.14 mol/l for the disodium-4-n-octyl-3-sulfonatosuccinate($R_{8)S$), 0.041mol/l for the disodium-4-n-decyl-3-sulfonatosuccinate($R_{10}S$), and 0.018mol/l for the disodium-n-dodecyl-3-sulfonatosuccinate <$R_{12}S$). The aggregation numbers determined viscometrically and conductimetrically were 28 for $R_{8}S$, 48 for $R_{10}S$, and 67 for $R_{12}S$. The volume changes upon micellization were $8.9cm^{3}/mol$ for $R_{8}S$, $9.5cm^{3}/mol$ for $R_{10}S$, and $10.1cm^{3}/mol$ for $R_{12}S$. Binding constants for the dye pada to the micelles and the fractions of unbound counter-ion were also obtained. The two polar heads with their carbon linkage were likely in an aqueous environment in the $R_{8}S$ micelles with the micelles themselves being spherical.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.397-408
• /
• 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.

• 대한수학회보
• /
• 제47권5호
• /
• pp.961-971
• /
• 2010

As an application of 'reverse engineering' technique introduced by R. Fintushel, D. Park and R. Stern [9], we present a simple way to construct an infinite family of exotic (2n+2l-1)$\mathbb{CP}^2#$(2n+4l-1)$\overline{\mathbb{CP}}^2$'s for all $n\;{\geq}\;0$, $l\;{\geq}\;1$.

• Journal of applied mathematics & informatics
• /
• 제10권1_2호
• /
• pp.167-174
• /
• 2002

A group G is said to be (l, n, n)-generated if it is a quotient group of the triangle group T(p,q,r)=(x,y,z|x$\^$p/=y$\^$q/=z$\^$r/=xyz=1). In [15], the question of finding all triples (l, m, n) such that non-abelian finite simple groups are (l , m, n)-generated was posed. In this paper we partially answer this question for the sporadic group He. We continue the study of (p, q, r) -generations of the sporadic simple groups, where p, q, r are distinct primes. The problem is resolved for the Held group He.

• 대한수학회지
• /
• 제55권3호
• /
• pp.671-694
• /
• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• 대한수학회보
• /
• 제53권3호
• /
• pp.885-902
• /
• 2016

In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere ${\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}$ for $k{\geq}1$ Let ${\psi}:M^3{\rightarrow}{\mathbb{S}}^4$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is a Clifford tori ${\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)$, $r^2_1+r^2_2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius r around the Veronese embedding of the real projective plane ${\mathbb{R}}P^2({\sqrt{3}})$.

• 한국자기학회:학술대회 개요집
• /
• 한국자기학회 2007년도 The 1st International Symposium on Advanced Magnetic Materials
• /
• pp.211.1-211.1
• /
• 2007

• 대한수학회지
• /
• 제48권6호
• /
• pp.1171-1187
• /
• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• Bulletin of the Korean Chemical Society
• /
• 제26권9호
• /
• pp.1359-1365
• /
• 2005

A series of new chiral [iminophosphoranyl]ferrocenes, {${\eta}^5-C_5H_4-(PPh_2=N-2,6-R_2-C_6H_3)$}Fe{${\eta}^5-C_5H_3-1-PPh^2-2-CH(Me)NMe_2$} (1: R = Me, $^iPr$), {${\eta}^5{-C_5H_4-(PPh_2=N-2,6-R_2}^1-C_6H_3)$}Fe{${\eta}^5-C_5H_3-1-(PPh_2=N-2,6-R_2-C_6H_3)-2-CH(Me)R_2$} (2: $R^1\;=\;Me,\;^iPr;\;R^2\;=\;NMe_2$, OMe), and $({\eta}^5-C_5H_5)Fe${${\eta}^5-C_5H_4-1-PR_2-2-CH(Me)N=PPh_3$} (3:R = Ph, $C_6H_{11}$) have been prepared from the reaction of [1,1'-diphenylphosphino-2-(N,N-dimethylamino) ethyl]ferrocene with arylazides (1 & 2) and the reaction of phosphine dichlorides ($R_3PCl_{2}$) with [1,1'-diphenylphosphino-2-aminoethyl]ferrocene (3), respectively. They form palladium complexes of the type $[Pd(C_3H_5)(L)]BF_4$ (4-6: L = 1-3), where the ligand (L) adopts an ${\eta}^2-N,N\;(2)\;or\;{\eta}^2$-P,N (3) as expected. In the case of 1, a potential terdentate, an ${\eta}^2$-P,N mode is realized with the exclusion of the –=NAr group from the coordination sphere. Complexes 4-6 were employed as catalysts for allylic alkylation of 1,3-diphenylallyl acetate leading to an almost stoichiometric product yield with modest enantiomeric excess (up to 74% ee). Rh(I)-complexes incorporating 1-3 were also prepared in situ for allylic alkylation of cinnamyl acetate as a probe for both regio- and enantioselectivities of the reaction. The reaction exhibited high regiocontrol in favor of a linear achiral isomer regardless of the ligand employed.