• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.24-33
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• 2000

This paper investigates the relationship between J-integral and crack tip opening displacement, ${\delta}_t$ using Gordens results of numerical analysis. Estimation were carried out for several strength levels such as ultimate, flow, yield, ultimate-flow, flow-yield stress to determine the influence of strain hardening and the ratio of crack length to width on the $J-{\delta}_t$ relationship. It was found that for SE(B) specimens, the $J-{\delta}_t$ relationship can be applied to relate J to ${\delta}_t$ as follows $J=m_j{\times}{\sigma}_i{\times}{\delta}_t$ where $m_j=1.27773+0.8307({\alpha}/W)$, ${\sigma}_i:{\sigma}_U$, ${\sigma}_{U-F}={\frac{1}{2}} ({\sigma}_U+{\sigma}_F$), ${\sigma}_F$, ${\sigma}_F}$ $Y=({\sigma}_F+{\sigma}_Y)$, ${\sigma}_Y$

• Korean Journal of Fisheries and Aquatic Sciences
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• v.15 no.3
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• pp.226-232
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• 1982

The measurements of the jerking force and the tail beat by hooked carp were carried out using a strain gauge at a fish pond from July to August 1981. The maximum jerking force was sustained for a while in the initial state after a carp was hooked, but the jerking force was gradually decreased as a function of the time elapsed until the fish was utterly exhausted, and it converged to the body weight at last. The results are as follows : 1. The maximum jerking force $F_m(g)$ can be expressed with empirical formula : $$F_m=3.23W+105$$ where W (g) is the body weight. 2. Dynamic change of the maximum jerking force $F_n(g)$ by one tail beat with time $t_{n}(-10T/2{\leq}\;t_n{\leq}10T/2)$ can he induced with the equation as follows : $$F_n=(0.27W-6.52)(|t_n|+C)^{-2.10}$$ where the period T (sec) is given by the following equation with the body weight : T=0.000385W+0.193 3. The jerking force at each of the peak points $F_p$ (g) varies with the time elapsed t (sec) as following equation : $$F_{p}=(2.23W+105)e^{-{\beta}t}+W$$. The value of durability index $\beta$ was nearly zero in the initial state and about 1.7 in the exhausted state at last. 4. It was clearly shown that the change of jerking force by hooked carp was closely related to the tail beat from a paired difference T-test.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.1-12
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• 2019

For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.551-563
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• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

• Korean Journal of Poultry Science
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• v.30 no.2
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• pp.95-99
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• 2003

A total of 112 male and 1208 female Ross broiler breeders (30-wk-old) were used in this study to investigate whether a male to female (M/F) ratio of broiler breeder chickens may influence fertility and hatchability of hatching eggs. There were three treatments, each consisting of four pens with a size of 3.2 m ${\times}$ 6.4 m. Each pen housed approx. 100 females and 10 males to give the M/F ratio as follows: T1, 1/9; T2, 1/11; and T3, 1/13, respectively. The fertility of broiler breeder eggs ranged between 93 to 94％ at 30 wk of age. At 35 wk of age, breeder eggs from T3 tended to be less fertile (P>0.05) than those from T1 and T2. The low fertility observed in T3 at 35 wk of age further reduced to reach a statistical significance at 46 wk of age (P<0.05) when compared to those of T1 and T2. Hatchability of breeder eggs among treatments tended to follow a similar trend as shown in fertility, keeping hatchability of breeder eggs from T3 low when compared to the groups of T1 and T2. Our results indicated that the M/F ratio influenced fertility and consequently hatchability of breeder eggs. Furthermore, our study suggests that either 1/9 or 1/11 M/F ratio, but not 1/13 M/F ratio, seems suitable to sustain reproductive performance of broiler breeders throughout the laying periods.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.13-30
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• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• Journal of the korean academy of Pediatric Dentistry
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• v.11 no.1
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• pp.181-189
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• 1984

1,840 school children aged 6 to 13 years who live in inland area in CHOONG CHUNG BUK DO were surveyed epidemiologically on the dental caries prevalence. The results were as follows; 1. The prevalence of dental carries was 76.35 percentage in male, 76.15 percentage in female, and 76.25 percentage in both sexes. 2. d.m.f rate was 77.72 percentage in male, 80.07 percentage in female, and 78.86 percentage in both sexes. D.M.F rate was 30.73 percentage in male, 38.52 percentage in female, and 34.51 percentage in both sexes. 3. d.m.f.t. rate and index was 27.94 percentage,2.55T, and d.m.f.s. rate & index was 13.62 percentage, 6.22T. 4. D.M.F.T rate & index in permanent teeth was 4.86 percentage,0.72T, and D.M.F.S. rate & index was 1.20 percentage,0.89T. 5. The filling rate was 3.90 percentage in decidious teeth, 2,00 percentage in permanent teeth.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.335-342
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• 1996

Suppose $k$ is a field and $M$ is the set of all $m \times n$ matrices over $k$. If T is a linear operator on $M$ and f is a function defined on $M$, then T preserves f if f(T(A)) = f(A) for all $A \in M$.