• Journal of the Korean Chemical Society
• /
• v.32 no.4
• /
• pp.301-310
• /
• 1988

Reaction rates for mononuclear heterocyclic rearrangement of N-(5-phenyl-1,2,4-oxadiazol-3-yl)-N'-arylformamidines into 3-acylamino-1-aryl-1,2,4-triazoles were determined spectrophotometrically in dioxane/water (50 : 50, v/v). There are two different reaction paths according to pH. One is pH-independent path, the other is pH-dependent one. In pH-independent path, the result of substituent effect by IYT equation show that N-H bond breaking as well as new N-N bond formation controls the reaction rate. In pH-dependent path, concave-upward Hammett plot was observed. It can be concluded that new N-N bond formation is more advanced than N-H bond breaking in transition state for electron-donating substituents, but N-H bond breaking is more advanced than new N-N bond formation for electron-withdrawing substituents.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.437-448
• /
• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1117-1127
• /
• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Korean Journal of Mathematics
• /
• v.12 no.1
• /
• pp.67-75
• /
• 2004

Paul Turan observed that the Legendre polynomials satisfy the inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)$ > 0, $-1{\leq}x{\leq}1$. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved $P^{\alpha}_n(x)P^{\beta}_{n+1}(x)-P^{\alpha}_{n+1}(x)P{\beta}_n(x)$ > 0, $\frac{1}{2}{\leq}{\alpha}$ < ${\beta}{\leq}{\alpha}+2.0$ < $x$ < 1, for the ultraspherical polynomials (respectively, Laguerre ploynomials). The Bustoz-Savage inequalities hold for Laguerre and ultraspherical polynomials which are symmetric. In this paper, we prove some similar inequalities for non-symmetric Jacobi polynomials.

• Korean Journal of Crystallography
• /
• v.15 no.2
• /
• pp.83-87
• /
• 2004

An organometallic complex. $Me_2Pt(PPh_2CH_2C(t-Bu)=N-N=CMe(2-py)-\kappa^2N,P)$ was synthesized from phosphinohydrazone $Ph_2PCH_2C(t-Bu)=NNH_2$, 2-acetylpyridine, and $[PtMe2({\mu}-SMe_2)]_2$. The molecular structure of this complex has been determined by X-ray diffraction. Crystallographic data: monoclinic, space group $P2_1/n,\;a=11.6926(7)\;{\AA},\;b=15.6607(19)\;{\AA},\; c=14.6125(6)\;{\AA},\;\beta=93.018(4)^{\circ},\;Z=4,\;V=2672.0(4)\;{\AA}^3$. The structure was solved by direct methods and refined by full-matrix least-squares methods to give a model with a reliability factor R = 0.0363 for 5238 reflections.

• Journal of the Korea Society of Computer and Information
• /
• v.17 no.4
• /
• pp.139-145
• /
• 2012

Generally, Quicksort selects the pivot from leftmost, rightmost, middle, or random location in the array. This paper suggests Quicksort using middle range pivot $P_0$ and continually divides into 2. This method searches the minimum value $L$ and maximum value $H$ in the length n of list $A$. Then compute the initial pivot key $P_0=(H+L)/2$ and swaps $a[i]{\geq}P_0$,$a[j]<P_0$ until $i$=$j$ or $i$>$j$. After the swap, the length of list $A_0$ separates in two lists $a[1]{\leq}A_1{\leq}a[j]$ and $a[i]{\leq}A_2{\leq}a[n]$ and the pivot values are selected by $P_1=P_0/2$, $P_2=P_0+P_1$. This process repeated until the length of partial list is two. At the length of list is two and $a$[1]>$a$[2], swaps as $a[1]{\leftrightarrow}a[2]$. This method is simpler pivot key process than Quicksort and improved the worst-case computational complexity $O(n^2)$ to $O(n{\log}n)$.

• Journal of Life Science
• /
• v.19 no.1
• /
• pp.1-8
• /
• 2009

In this paper, to elucidate the further mechanisms of N-methyl-N'-nitro-N-nitrosoguanidine (MNNG)-induced growth arrest, we investigated the effect of MNNG on cell cycle and proliferation in U937 cells, a p53-null human myeloid leukemia cell line. It was found that MNNG causes an arrest at the G2/M phase of the cell cycle and induces apoptosis, which is closely correlated to inhibition of cyclin B1 and cyelin-dependent kinase (Cdk) 2-associated kinase activities. MNNG treatment in. creased protein and mRNA levels of the Cdk inhibitor p21(WAF1/CIP1), and activated the reporter construct of a p21 promoter. By using p21 promoter deletion constructs, the MNNG-responsive element was mapped to a region between 113 and 61 relative to the transcription start site. These data indicate that in U937 cells MNNG can circumvent the loss of wild-type p53 function and induce critical downstream regulatory events leading to transcriptional activation of p21. Present results indicate that the p53-independent up-regulation of p21 by MNNG is likely responsible for the inhibition of cyclin/Cdk complex kinase activity rather than the down-regulation of cyclins and Cdks expression. These novel phenomena have not been previously described and provide important new insights into the possible biological effects of MNNG.

• Journal of applied mathematics & informatics
• /
• v.33 no.3_4
• /
• pp.365-377
• /
• 2015

For a (molecular) graph, the first and second Zagreb indices (M₁ and M₂) are two well-known topological indices, first introduced in 1972 by Gutman and Trinajstić. The first Zagreb index M₁ is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M₂ is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let $K_{n_1,n_2}^{P}$ with n₁ $\leq$ n₂, n₁ + n₂ = n and p < n₁ be the set of bipartite graphs obtained by deleting p edges from complete bipartite graph K_n1,n2. In this paper, we determine sharp upper and lower bounds on Zagreb indices of graphs from $K_{n_1,n_2}^{P}$ and characterize the corresponding extremal graphs at which the upper and lower bounds on Zagreb indices are attained. As a corollary, we determine the extremal graph from $K_{n_1,n_2}^{P}$ with respect to Zagreb coindices. Moreover a problem has been proposed on the first and second Zagreb indices.

• Journal of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.307-330
• /
• 2013

If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.

• Journal of the Korean Chemical Society
• /
• v.22 no.3
• /
• pp.150-157
• /
• 1978

The rate constants for the hydrolysis of the derivatives of N-(p-nitrophenyl)-benzohydrazonyl azide (p-$CH_3,\;p-CH_3O,\;p-NO_2$, p-Cl, p-Br) have been determined by UV spectrophotometry in 50% dioxane-water at $25^{\cicr}C$ and a rate equation which can be applied over wide pH range was obtained. Below pH 5, the rate of hydrolysis of hydrazonyl azides is accelerated by electron-donating group ($\rho$ = -0.47), whereas at the pH values greater than 7, the $\rho$-value is 0.68. The effect of salt, solvent, substituent and azide ion on the rate of hydrolysis are rationalized in terms of $S_N1$ and $S_N2$ mechanism; below pH 5, the hydrolysis proceed through $S_N1$, however, above pH 7, the hydrolysis is started by the attack of hydroxide ion and in the range of pH 5∼7, these two reactions occur competitively.