• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.437-448
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• 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.

• East Asian mathematical journal
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• 제25권2호
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• 대한수학회지
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• 제41권3호
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• 한국결정학회지
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• 제5권2호
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• pp.78-84
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• 1994

N-[1-(benzotriazol-1-yl)butyl]-P-nitroaniline ( BBN, C6H7N502) 의 분자 및 결정구조를 반-선 회절 법Abstract으로 연구하였다. 이 결정은 단사정계이고 공간군은 P21/n이다. 단위세포 길이는 a=17.542(2)A, b= 10.755(3)A, c=8.891(1)A 이며 a=b=r=90˚,b=104.58(1)˚,Z=4 이다.구조해석에 사용한 X-선은 CuKa선(λ:1.5418A )을 사용하였다. 분자구조는 직접법으로 풀었으며 최소자승법으로 정밀화하였 다. 최종 신뢰도 R값은 255개 파라메터, F≥4o(F)인 2248개의 회절반점에 대하여 R= 0.0411 이었다. 분자간 결합은 1개의 수소결합인 N(11)-Hll(Nll)‥‥N(3)로 결합되어 있으며, N(11)‥‥N(3)=3.136(2).1, N(11)-Hl 1 (Nl 1) ‥‥N(3) =164.1(15)˚이다.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.381-403
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• 2021

Consider the three-dimensional system of difference equations $x_{n+1}=\frac{{\prod_{j=0}^{k}}z_n-3j}{{\prod_{j=1}^{k}}x_n-(3j-1)\;\(a_n+b_n{\prod_{j=0}^{k}}z_n-3j\)}$, $y_{n+1}=\frac{{\prod_{j=0}^{k}}x_n-3j}{{\prod_{j=1}^{k}}y_n-(3j-1)\;\(c_n+d_n{\prod_{j=0}^{k}}x_n-3j\)}$, $z_{n+1}=\frac{{\prod_{j=0}^{k}}y_n-3j}{{\prod_{j=1}^{k}}z_n-(3j-1)\;\(e_n+f_n{\prod_{j=0}^{k}}y_n-3j\)}$, n ∈ ℕ₀, where k ∈ ℕ₀, the sequences $(a_n)_{n{\in}{\mathbb{N}}_0$, $(b_n)_{n{\in}{\mathbb{N}}_0$, $(c_n)_{n{\in}{\mathbb{N}}_0$, $(d_n)_{n{\in}{\mathbb{N}}_0$, $(e_n)_{n{\in}{\mathbb{N}}_0$, $(f_n)_{n{\in}{\mathbb{N}}_0$ and the initial values x_-3k, x_-3k+1, …, x₀, y_-3k, y_-3k+1, …, y₀, z_-3k, z_-3k+1, …, z₀ are real numbers. In this work, we give explicit formulas for the well defined solutions of the above system. Also, the forbidden set of solution of the system is found. For the constant case, a result on the existence of periodic solutions is provided and the asymptotic behavior of the solutions is investigated in detail.

• 한국환경농학회지
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• 제42권4호
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• pp.389-395
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• 2023

This study evaluated the effects of gibberellic acid (GA₃) on the growth and quality of creeping bentgrass (Agrostis palustris Huds.). Experimental treatments included a No application of fertilizer and GA₃ (NFG) Control [3 N active ingredient (a.i.) g/m²], 0.3GA₃ (GA₃ 0.3 a.i. mg/m²/200 mL), 0.6GA₃ (GA₃ 0.6 a.i. mg/m²/200 mL), 1.2GA₃ (GA₃ 1.2 a.i. mg/m²/200 mL), and 2.4GA₃ (GA₃ 2.4 a.i. mg/m²/200 mL). Additionally, the study included a 1.5N+GA₃ experiment with similar GA₃ treatments combined with 1.5N a.i. g/m² : NFG, Control (3N a.i. g/m²), 1.5N+ 0.3GA₃ (1.5N a.i. g/m²+GA₃ 0.3 a.i. mg/m²/200 mL), 1.5N+0.6GA₃ (1.5N a.i. g/m²+GA₃ 0.6 a.i. mg/m²/200 mL), 1.5N+1.2GA₃ (1.5N a.i. g/m²+GA₃ 1.2 a.i. mg/m²/ 200 mL), and 1.5N+2.4GA₃ (1.5N a.i. g/m²+GA₃ 2.4 a.i. mg/m²/200 mL). Compared to the NFG, turf color index chlorophyll content was not significantly different (p< 0.05). However, shoot length in 1.2GA₃, 2.4GA₃, 1.5N+0.3GA₃, 1.5N+0.6GA₃, 1.5N+1.2GA₃, and 1.5N+2.4GA₃ treatments increased by 0.8%, 10.6%, 5.15%, 8.3%, 13.5 %, and 21.6%, respectively, compared to the control. As compared to the control, clipping yield in 1.5N+1.2GA₃ and 1.5N+2.4GA₃ treatments increased by 7.1% and 14.3 %, respectively. These results indicated that GA₃ application increased shoot length, with the 1.2GA₃ treatment showing shoot length similar to the control (3N a.i. g /m² ).

• 대한수학회지
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• 제46권5호
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• pp.895-905
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• 2009

Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.

• 한국분말재료학회지
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• 제6권1호
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• pp.18-35
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• 1999

Phase equilibria in the system Si3N4-TiC-TiCxN1-x-C-N were determined by thermodynamic calculations (CALPHAD-method). The reaction peaction paths for Si3N4-TiC and SiC-TiC composites in the Ti-Si-C-n system were simulated at I bar N2-pressure and varying terpreatures. At a temperature of 1923 K two tie-triangles (TiC0.34N0.66+SiC+C and TiC0.13N0.87+SiC+Si3N4) and two 2-phase fieds (TiCxN1-x+SiC; 0.13

• 정보처리학회논문지A
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• 제11A권7호
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• pp.571-576
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• 2004

비선형 클라인 고든 방정식의 수치해를 구하기 위해 라그란제 보간을 사용하는데 비선형 항을 계산하기위해 보간식의 차이가 거의 없는 변형된 식을 사용하여 해의 .안정성과 해의 수렴성을 밝히고 오차를 분석하였다. 즉 $I(x)^{3}$ 대신에 $f(x_i)^{3}I_i(x)$을 사용하였으며 오차는 $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ 이하임을 보였고 석기서 N은 다항식의 차수이다.