• Korean Journal of Mathematics
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• v.19 no.3
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• pp.309-319
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• 2011

We give sufficient conditions that the homogeneous differential equations : for $t{\geq}t_0$(> 0), $$x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+p(t)x(t)=0,\\x^{{\prime}{\prime}}(t)+q(t)x^{\prime}(t)+F(t,x({\phi}(t)))=0$$, are oscillatory where $0{\leq}{\phi}(t)$, 0 < ${\phi}^{\prime}(t)$, $\lim_{t\to{\infty}}{\phi}(t)={\infty}$. and $F(t,u){\cdot}sgn$ $u{\leq}p(t)|u|$. We obtain comparison theorems.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.173-181
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• 1995

Our objective is to investigate approximate controllability of a class of partial integrodifferential systems. This work continuous the investigations of [8]. As a model for this class one may take the equation $\frac{\partialy(t,\;\xi)}{\partialt}\;=\;\frac{\partial}{\partial\xi}(a(t,\;\xi\frac{\partialy(t,\;\xi)}{\partial\xi})\;+\;F(t,\;y(t\;-\;r,\;\xi),\;{{\int_0}^t}\;k(t,\;s,\;y(s\;-\;r,\;\xi))ds)\;+\;b(\xi)u(t),\;0\;\leq\;\xi\;\leq\;1,\;\leq\;t\;\leq\;T$ with initial-boundary conditions y(t,\;0)\;=\;y(t,\;1)\;=\;0,\;0\;\leq\;t\;\leq\;T,\;y(t,\;\xi)\;=\;\phi(t,\;\xi),\;0\;\leq\;1,\;-r\;\leq\;t\;\leq\;0$.(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.273-284
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• 2017

In this paper, we study that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have uniformly Lipschitz stability by imposing conditions on the perturbed part ${\int_{t0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using integral inequalities.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.103-116
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• 2017

In this paper, we show that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have asymptotic property by imposing conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Journal of Animal Science and Technology
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• v.52 no.5
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• pp.441-448
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• 2010

This study was carried out to investigate the effects of the seeding dates and growth periods on the growth characteristics, dry matter yield and feed value of corn for silage in paddy field. The experimental design was arranged in a randomized block design with three replications. Treatments consisted of five seeding dates, 1 May (T1), 8 May (T2), 15 May (T3), 22 May (T4) and 29 May (T5). And harvesting time homologized by August 24. Therefore, growing periods were 115 days (T1), 108 days (T2), 101 days (T3), 94 days (T4) and 87 days (T5), respectively. In maturities at harvest time, T1, T2, T3, T4 and T5 were full dent, early dent, late dough, dough and early dough stage, respectively. Plant height and numbers of root system were highest in T5 (p<0.01), but leaf length was higher in T4 than others (p<0.05). Dead leaf, tip filling degree and ear circle were higher in T1 than others (p<0.05, 0.01). Leaf width, ear height, leaf number, ear length, stem diameter, stem hardness and brix were not significantly different among the treatments. Dry matter yield and TDN yield were higher in the order of T1 > T2 > T3 > T4 > T5 (p<0.01). Crude protein, crude ash, NDF, ADF and crude fiber were significantly higher in T4 (p<0.05, 0.01). But crude fat was the highest in T1, T3 was the lowest as compared to other treatments (p<0.01). Total EAA(essential amino acids) were higher in order of T4 > T3 > T1 > T2 > T5, and total NEAA (nonessential amino acids) were higher in order of T1 > T4 > T2 > T3 > T5, and total amino acids were higher in order of T4 > T1 > T3 > T2 > T5. But no significant differences were found among the treatments. TUFA (total unsaturated fatty acid) and TSFA (total saturated fatty acid) were in order of T1 > T2 > T3 > T5 > T4 (p<0.01). Minerals were the highest in T4 (4,721.25 mg/kg), and T2 (2,970.80 mg/kg) was the lowest as compared to other treatments (p<0.05). Based on the above results, seeding dates could be recommended as early May, and harvest times is yellow ripe stage for qualitative and quantitative production of corn for silage in rice paddy field soil.

• Korean Journal of Poultry Science
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• v.34 no.3
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• pp.165-172
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• 2007

We investigated the effects of dietary supplements of probiotics, illite, active carbon and hardwood vinegar on growth performance, feed intake, and pH, shear force, sensory evaluation, meat color and fatty acid composition of meat in broilers. Two hundred broilers were fed diets for five weeks containing 0.2% of probiotics (T1), and 1% of Illite (T2), 1% active carbon (T3), or 1% hardwood vinegar (T4). Body weight gain was higher in T1 and T4 groups fed the starter diet but was the lowest in C and T4 for finishing period (P<0.05). Feed efficiency was not significantly different. In proximate composition, crude fat content of chicken meat were decreased lower in all treatment groups than control, but moisture, crude protein and crude ash were not significantly different. Cooking loss was decreased in T3 and T4 and WHC (water holing capacity) was increased in T3 and T4 groups compared to the other groups. In sensory evaluation, T4 tended to improve the hardness. Redness $(a^*)$ and yellowness $(b^*)$ were no difference between the all treatment groups, lightness $(L^*)$ were higher in T1, T2, T3 and T4 groups than control group (P<0.05). Stearic acid content was lower in T1, T2, T3 and T4 groups, but oleic acid contents were higher in T1, T2, T3 and T4 groups (P<0.05). These results showed that supplementing broiler diets with 1.0% hardwood vinegar may noticeably improve the meat quality of broiler.

• Investigative Magnetic Resonance Imaging
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• v.12 no.1
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• pp.20-26
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• 2008

Purpose : To present the T1 and T2 relaxation times of the major cerebral metabolites at 1.5T and 3.0T and compare those between 1.5T and 3.0T. Materials and Methods : Using the phantom containing N-acetyl aspartate (NAA), Choline (Cho), and Creatine (Cr) at both 1.5T and 3.0T MRI, the T1 relaxation times were calculated from the spectral data obtained with 5000 ms repetition time (TR), 20 ms echo time (TE), and 11 different mixing time (TM)s using STEAM (STimulated Echo-Acquisition Mode) method. The T2 relaxation times were obtained from the spectral data obtained with 3000 ms TR and 5 different TEs using PRESS (Point-RESolved Spectroscopy) method. The T1 and T2 relaxation times obtained at 1.5T were compared with those of 3.0T. Results : The T1 relaxation times of NAA were $2293\;{\pm}\;48\;ms$ at 1.5T and $2559\;{\pm}\;124\;ms$ at 3.0T (11.6% increase at 3.0T). The T1 relaxation times of Cho were $2540\;{\pm}\;57\;ms$ at 1.5T and $2644\;{\pm}\;76\;ms$ at 3.0T (4.1% increase at 3.0T). The T1 relaxation times of Cr were $2543\;{\pm}\;75\;ms$ at 1.5T and $2665\;{\pm}\;94\;ms$ at 3.0T (4.8% increase). The T2 relaxation times of NAA were $526\;{\pm}\;81\;ms$ at 1.5T and $468\;{\pm}\;74\;ms$ at 3.0T (11.0% decrease at 3.0T). The T2 relaxation times of Cho were $220\;{\pm}\;44ms$ at 1.5T and $182\;{\pm}\;35\;ms$ at 3.0T (17.3% decrease at 3.0T). The T2 relaxation times of Cr were $289\;{\pm}\;47\;ms$ at 1.5T and $275\;{\pm}\;57\;ms$ at 3.0T (4.8% decrease at 3.0T). Conclusion : The T1 relaxation times of the major cerebral metabolites (NAA, Cr, Cho), which were measured at the phantom, were 4.1%-11.6% longer at 3.0T than at 1.5T. The T2 relaxation times of them were 4.8%-17.3% shorter at 3.0T than at 1.5T. To optimize MR spectroscopy at 3.0T, TR should be lengthened and TE should be shortened.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

• Applied Biological Chemistry
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• v.13 no.3
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• pp.193-195
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• 1970

The cultural conditions of the osmophilic yeasts for higher concentration of NaCl selected in the previous report were examined and the results obtained were as follows. 1) The strain $T_3\;and\;T_8$ were grown exceedingly well on the media containing 15 percent of NaCl and $T_5\;and\;T_9,\;T_{10}\;and\;T_{11}$ on the media containing 5 percent of NaCl. 2) The optimum temperature for growth of the strain $T_3\;and\;T_5$ was $30^{\circ}C,\;T_8\;T_{10}$ and $T_{11}\;was\;25^{\circ}C\;and\;T_9\;was\;35^{\circ}C.$ 3) Their lethal temperature was $60^{\circ}C$ (treatment for 10 minutes). 4) The optimum pH for growth of the strain $T_3\;and\;T_8$ was pH 4.0, $T_5$ was pH 6.0 and $T_9\;T_9\;and\;T_{11}$ was pH 5.0, respectively.