• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.247-262
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• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• Journal of the Korean Chemical Society
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• v.18 no.4
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• pp.244-250
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• 1974

The mechanisms of the electrode reaction of chlorate ion were investigated, using Pt-electrode, by means of the technique of galvanostatic double pulses. For double current pulses (a cathodic pulse followed by an anodic pulse), the mechanism of the electrode reaction of chlorate ion over a current density range from 20 ma/cm2 to 25 ma/cm2 was suggested as the following: $CIO_3^-\;{\longrightarrow^{I}_{n_{1c}}\;CIO_2^-\;{\longrightarrow^{II}_{n_{2a}}\;CIO^-\;{\longrightarrow^{I'}_{n_{1a}}\;CIO_2^-\;{\longrightarrow^{II'}_{n_{2a}}\;CIO_4^-$ For a higher current density from 40 ma/cm2, it was suggested as the following: $CIO_3^-\;{\longrightarrow^{III}_{n_c}}\;CIO^-\;{\longrightarrow^{I'}_{n_{1a}}\;CIO_2^-\;{\longrightarrow^{II'}_{n_{2a}}\;CIO_4^-$ or $CIO_3^-\;{\longrightarrow_{n_c}}\;CIO^-\;{\longrightarrow_{n_a}}\;CIO_4^-$

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.117-122
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• 1994

In this paper we show that if {$H_n$} is a continuous strong higher derivation of order n on an ultraprime Banach algebra with a constant c, then $c||H_1||^2{\leq}4||H_2||$ and for each $1{\leq}l$ < n $$c^2||H_1||\;||H_{n-l}{\leq}6||H_n||+\frac{3}{2}\sum_{\array{i+j+k=n\\i,j,k{\geq}1}}||H_i||\;||H_j||\;||H_k||+\frac{3}{2}\sum_{\array{i+k=n\\i{\neq}l,\;n-1}}||H_i||\;||H_k|| $$ and for a strong higher derivation {$H_n$} of order n on a prime ring A we also show that if [$H_n$(x),x]=0 for all $x{\in}A$ and for every $n{\geq}1$, then A is commutative or $H_n=0$ for every $n{\geq}1$.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Korean Journal of Crystallography
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• v.2 no.1
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• pp.12-16
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• 1991

C18H22N4OS, Mr=342.47, monoclinic, P2₁/c,a=11.802(2), b=31.962(2), c=9.829(2)A, β=100.12(1)˚, V=3694.8A3,F(000)=1472, Z=8, Dx=1.246 Mg m-3, Dm=1.17Mg m-3,λ=0.71073 A, μ=0.15mm-1, T=294 K. final R=0.0856 for 3718 observed reflection (Fo>3σ(Fo)) There are two molecules in an asymmetric unit and a major difference between these molecules is in the C(9)-N(1)-C(6)-C(7) torsion angles [58.8(8)˚and 1(1)˚]. Both molecules have intramolecular N(1)-H(10)'N(3) hydrogen bonds [ 2.613(7) and 2.566(7) A] and assume V-shaped conformation with N(2) atoms at the verices. The two independent molecules are linked by the two N(2)-H(11)'S' hydrogen bonds[3.367(5) A and 3.421(4)A] and the dimergen are held together by van der Waals forces.

• Bulletin of the Korean Chemical Society
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• v.13 no.6
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• pp.676-680
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• 1992

Irradiation of N-t-butyl-N-chloro-3-phenylpropanesulfonamide (1a) in benzene at $20^{\circ}C$ using 450 W high pressure mercury arc lamp in the presence of oxygen affored N-t-butyl-3-phenylpropanesulfonamide (2), N-t-butyl-3-chloro-3-phenylpropanesulfonamide (3), and N-t-butyl-3-oxo-3-phenylpropanesulfonamide (4). Similarly, N-t-butyl-4- (5), N-t-butyl-4-chloro-4- (6), and N-t-butyl-4-phenylbutanesulfonamides (7) were obtained from N-t-butyl-N-chloro-4-phenylbutanesulfonamide (1b). However, irradiation of N-t-butyl-N-chloro-5-phenylpentanesulfonamide (1c) under the same conditions gave complex mixtures. These results indicate that sulfonamidyl radical generated from each of 1a and 1b can abstract intramolecularly a hydrogen atom from the benzylic position only by forming six and seven-membered transition states, respectively.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.409-431
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• 2022

In this paper, we deal with the existence of solutions of the following system of nonlinear rational difference equations with order five $x_{n+1}=\frac{y_{n-3}x_{n-4}}{y_n(a+by_{n-3}x_{n-4})}$, $y_{n+1}=\frac{x_{n-3}y_{n-4}}{x_n(c+dx_{n-3}y_{n-4})}$, n = 0, 1, ⋯, where parameters a, b, c and d are not executed at the same time and initial conditions x_-4, x_-3, x_-2, x_-1, x₀, y_-4, y_-3, y_-2, y_-1 and y₀ are non zero real numbers.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.6
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• pp.553-557
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• 1999

In order to investigate the optical properties of the $Al_XGa_{1-X}N/GaN$ thin film grown by metalorganic chemical vapor deposition (MOCVD) method, the photoluminescene (PL), photocurrent (PC) and persistent photoconductivity (PPC) measurements were carried out at room temperature. The band gap of the $A1_x$$Ga_{1-x}$N/GaN was determined to 3.70 eV by the PL and PC measurements. The PC measurement on the light illumination from the top of the $A1_x$$Ga_{1-x}$N/GaN thin film provides peaks at 3.70, 3.43, and around 2.2 eV. The PC spectrum by the illumination passing through from the substrate of the sample can be shown at 3.43 eV together with a broad tail band from the GaN band edge to around 2.23 eV. The photocurrent quenching and anomalous PPC decay observed in PPC measurements indicate that metastable electron states are fomed in the band gap of GaN layer to trap electrons which can be tunneled the potential barrier for long recovery time.