• Journal of Korean Physical Therapy Science
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• v.8 no.2
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• pp.997-1003
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• 2001

The purpose of this study is to know the average of pint range of motion and difference according to the aging for the elderly, This study consisted of elder male(n=75) and elder female(n=l09), The result of assessment and analysis in shoulder pint range of motion are as follows: 1) The average shoulder flexion pint range of motion in 60-69(from sixty to sixty-nine)years old are 163.04(Left-Male), 162.91(Right-Male), 158.74 (Left-Female), 158.74 (Right-Female). 70-79years old are 149.40(L-M), 152.38(R-M), 153,37(L-F), 153.37(R-F). 80-89 years old are 149.57(L-M), 147.93(R-M), 151.17(L-F), 150.33(R-F). There was no significant difference among group, 2) The average shoulder extension pint range of motion in 60-69years old are 48.15(L-M), 47.20(R-M), 45.16(L-F), 44.23(R-F), 70-79years old are 37.l1(L-M), 38.70(R-M), 35.17(L-F), 36.71(R-F), 80-89 years old are 34.46(L-M). 36.71(R-M), 33.90(L-F), 33.09(R-F). There was significant difference among group(p<.05). 3) The average shoulder abduction pint range of motion in 60-69years old are 164.22(L-M), 165.96(R-M), 159.34(L-F), 159.97(R-F), 70-79years old are 152.27(L-M), 155.05(R-M), 152.32(L-F), 53.66(R-F), 80-89 years old are 152.17(L-M), 153.76(R-M), 147.53(L-F), 147.37(R-F). There was significant difference in right shoulder abduction among group(p<05). 4) The average shoulder internal rotation pint range of motion in 60-69years old are 63.52(L-M), 65.70(R-M), 64.16(L-F), 64.61(R-F), 70-79years old are 64.50(L-M), 65.81(R-M) 61.10(L-F), 61.83(R-F). 80-89 years old are 61.60(L-M), 61.66(R-M), 57.53(L-F), 57.53(R-F). There was no significant difference among group. 5) The average shoulder external rotation pint range of motion in 60-69years old are 50.87(L-M), 50.22(R-M), 51.03(L-F), 50.42(R-F), 70-79years old are 50.91(L-M), 50.20(R-M) 48.37(L-F), 50.20(R-F). 80-89 years old are 46.83(L-M), 47.93(R-M), 43.43(L-F), 43.72(R-F).There was significant difference in left shoulder external rotation among group(p<.05).

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.487-496
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• 1996

Let f(z) be an entire function. Then the order $\rho(f)$ of f is defined by $$ \rho(f) = \overline{lim}_r\to\infty \frac{log r}{log^+ T(r,f)} = \overline{lim}_r\to\infty \frac{log r}{log^+ log^+ M(r,f)}, $$ where T(r,f) is the Nevanlinna characteristic of f (see [4]), $M(r,f) = max_{$\mid$z$\mid$=r} $\mid$f(z)$\mid$$ and $log^+ t = max(log t, 0)$.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.1-11
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• 2019

Let R be a prime ring with involution of the second kind and centre Z(R). Suppose R admits a generalized derivation $F:R{\rightarrow}R$ associated with a derivation $d:R{\rightarrow}R$. The purpose of this paper is to study the commutativity of a prime ring R satisfying any one of the following identities: (i) $F(x){\circ}x^*{\in}Z(R)$ (ii) $F([x,x^*]){\pm}x{\circ}x^*{\in}Z(R)$ (iii) $F(x{\circ}x^*){\pm}[x,x^*]{\in}Z(R)$ (iv) $F(x){\circ}d(x^*){\pm}x{\circ}x^*{\in}Z(R)$ (v) $[F(x),d(x^*)]{\pm}x{\circ}x^*{\in}Z(R)$ (vi) $F(x){\pm}x{\circ}x^*{\in}Z(R)$ (vii) $F(x){\pm}[x,x^*]{\in}Z(R)$ (viii) $[F(x),x^*]{\mp}F(x){\circ}x^*{\in}Z(R)$ (ix) $F(x{\circ}x^*){\in}Z(R)$ for all $x{\in}R$.

• Journal of Bio-Environment Control
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• v.24 no.3
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• pp.153-160
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• 2015

The objectives of this study were to determine optimal length of off-time between irrigation cycles to improve irrigation efficiency using a frequency domain reflectometry (FDR) sensor-automated irrigation (FAI) system for tomato (Solanum lycopersicum L.) cultivation aimed at minimizing effluent from coir substrate hydroponics. For treatments, the 5-minute off-time length between 3-minute run-times (defined as 3R5F), 10-minute off-time length between 3-minute run-times (defined as 3R10F), or 15-minute off-time length between 5-minute run-times (defined as 5R15F) were set. During the 3-minute or 5-minute run-time, a 60mL or 80mL of nutrient solution was irrigated to each plant, respectively. Until 62 days after transplant (DAT) during the autumn to winter cultivation, daily irrigation volume was in the order of 3R5F (858mL) > 5R15F (409mL) > 3R10F (306mL) treatment, and daily drainage ratio was in the order of 3R5F (44%) > 5R15F (23%) > 3R10F (14%). Between 63 and 102 DAT, daily irrigated volume was in the order of 5R15F (888mL) > 3R5F (695mL) > 3R10F (524mL) with the highest drainage ratio, 19% (${\pm}2.6$), at the 5R15F treatment. During the spring to summer cultivation, daily irrigation volume and drainage ratio per plant was higher in the 3R5F treatment than that of the 3R10F treatment. For both cultivations, a higher water use efficiency (WUE) was observed under the 3R10F treatment. Integrated all the data suggest that the optimal off-time length is 10 minutes.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.573-586
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• 2018

Let R be a noncommutative prime ring of characteristic different from 2, Q be its maximal right ring of quotients and C be its extended centroid. Suppose that $f(x_1,{\ldots},x_n)$ be a noncentral multilinear polynomial over $C,b{\in}Q,F$ a b-generalized derivation of R and d is a nonzero derivation of R such that d([F(f(r)), f(r)]) = 0 for all $r=(r_1,{\ldots},r_n){\in}R^n$. Then one of the following holds: (1) there exists ${\lambda}{\in}C$ such that $F(x)={\lambda}x$ for all $x{\in}R$; (2) there exist ${\lambda}{\in}C$ and $p{\in}Q$ such that $F(x)={\lambda}x+px+xp$ for all $x{\in}R$ with $f(x_1,{\ldots},x_n)^2$ is central valued in R.