• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.327-344
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• 2009

In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale $\mathbb{T}$ $$\{{{{{{x^{\bigtriangleup\bigtriangleup}(t)+f(t,\;y(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}\atop{y^{\bigtriangleup\bigtriangleup}(t)+g(t,\;x(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}}\atop{\alpha_1x(a)-\beta_1x^{\bigtriangleup}(a)=\gamma_1x(\sigma(b))+\delta_1x^{\bigtriangleup}(\sigma(b))=0,}}\atop{\alpha_2y(a)-\beta_2y^{\bigtriangleup}(a)=\gamma_2y(\sigma(b))+\delta_2y^{\bigtriangleup}(\sigma(b))=0,}}$$ where $\alpha_i$, $\beta_i$, $\gamma_i\;{\geq}\;0$ and $\rho_i=\alpha_i\gamma_i(\sigma(b)-a)+\alpha_i\delta_i+\gamma_i\beta_i$ > 0(i = 1, 2), f(t, y) may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems $x^{\bigtriangledown\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangledown}(t)$ + g(t, x(t)) = 0, $x^{\bigtriangleup\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangleup\bigtriangledown}(t)$ + g(t, x(t)) = 0, and $x^{\bigtriangledown\bigtriangleup}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangleup}(t)$ + g(t, x(t)) = 0 satisfying similar boundary conditions.

• Journal of Animal Science and Technology
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• v.52 no.2
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• pp.149-156
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• 2010

This study was carried out to investigate the effect of dietary supplementation of whole grain barley cracked feed on eating behaviors of Hanwoo steers during finish fattening period. Thirty Hanwoo steers (28 months old) were assigned to five dietary treatments: control (C: normal concentrate as a basal diet), and four feeding groups [T1: 10% addition of whole grain barley cracked (WGBC) feed, T2: 20% addition of WGBC, T3: 30% addition of WGBC and T4: 40% WGBC during the finish fattening period, respectively]. The results of eating behaviors for 48 hours are summarized as follows: Total intake (roughage + concentrate) was higher in the order of T4 > T1 > C > T3 > T2 (P<0.05). Eating time was higher in the order of T4 > T3 > C > T1 > T2 (P<0.01). Ruminating time was higher in the order of T4 > T1 > C > T3 > T2 (P<0.05). But resting time was higher in the order of T2 > T1 > C > T3 > T4. The chewing time including eating and ruminating time was higher in the order of T4 > T3 > C > T1 > T2 (P<0.01). Number of bolus, number of total chews, number of chews/bolus and feed value index were highest in T4 (P<0.05). Ruminating time per bolus was highest in C, and T3 was the lowest (P<0.05) as compared to others. Number of bolus per minute was highest in T3, and C is the lowest (P<0.05). Eating rate and chewing efficiency were highest in T2 (P<0.01, 0.05), but ruminating efficiency was higher in T1 than others. The group behavior was higher in the order of resting(78.5%) > ruminating(11.4%) > eating(10.1%). The stand resting of group behavior was higher in the order of T3 > C > T2 > T1 > T4.

• Journal of Animal Science and Technology
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• v.44 no.4
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• pp.407-418
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• 2002

This study was conducted to evaluate the efficacy of wheat and wheat bran  as the source of phytase in a 5 week broiler feeding trial. One thousand day-old broiler chickens(Ross$^{(R)}$) were divided into 20 pens of 50 broilers(25 male and 25 female) each. Four pens were randomly arranged to one of the five dietary treatments: T1, control diet containing normal nonphytate P(NPP) ;  T2, T1 － 0.1% NPP; T3, T2 ＋ 600IU microbial phytase(NOVO$^{(R)}$) per kg diet; T4, T2 ＋ 600IU plant phytase from wheat and wheat bran; T5, T2 ＋ 600IU plant phytase from wheat and hydrothermally treated wheat bran. Reduction of NPP level by 0.1%(T2) reduced weight gain and feed intake but plant phytase treatments(T4 and T5) recovered the lost performance. Plant phytase treatments showed better (p<0.05) weight gain and intake than the microbial phytase treatment(T3). There was no difference between regular wheat bran treatment(T4) and hydrothermally treated wheat bran treatment(T5). Mortality was the highest by low NPP diet(T2). Availability of ether extract and crude ash of grower diet was the highest(p<0.05) in normal wheat bran diet(T4). Availability of Ca and P of grower diet was the highest(p<0.05) in T4 followed by T3 and T5. Availability of Mg, Fe and Zn was drastically improved by phytase treatments(T3, T4 and T5). Excretion of Ca, P, Mg, Fe and Zn was the lowest(p<0.05) with microbial phytase treatment(T3). Serum level of Ca and Mg was the highest(p<0.05) with the low NPP treatment(T2). Tibial ash content of T2 and T3 was lower(p<0.05) than that of T1, T4 and T5. However, tibial Ca content was higher(p<0.05) in T1 and T2 than other treatments. Tibial P and Mg contents were the highest(p<0.05) in T1. It was concluded that plant phytase from wheat bran can be effectively used to improve P utilization. Hydrothermal treatment of wheat bran prior to inclusion in the diet had no beneficial effects.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.475-484
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• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.401-409
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• 2010

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${\nabla}_{\alpha}\;[x(t)\;-\;r(t)x(t\;-\;k)]\;+\;p(t)x(t\;-\;{\tau})\;-\;q(t)x(t\;-\;{\sigma})\;=\;0$, $t\;{\geq}\;t_0$, where $t_0\;{\in}\;\mathbb{R}$, t varies in the real interval ($t_0,\;{\infty}$), $\alpha$ > 0, $\kappa$, $\tau$, ${\sigma}\;{\geq}\;0$, $r\;{\in}\;C\;([t_0-{\alpha},\;{\infty}),\;\mathbb{R}^+$, p, $q\;{\in}\;C\;([t_0,\;{\infty}),\;\mathbb{R}^+)$ and ${\nabla}_{\alpha}x(t)\;=\;x(t)\;-\;x(t\;-\;{\alpha})$ for $t\;{\geq}\;t_0$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.203-215
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• 2009

In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t); Tu(t); Su(t)), $0{\leq}t{\leq}T_0$, $t{\neq}t_i$, u(0) + g(u) = $u_0$, ${\Delta}u(t_i)=I_i(u(t_i))$, i = 1,2,${\ldots}$p, 0<$t_1$<$t_2$<$\cdots$<$t_p$<$T_0$, in a Banach space X, where A is the infinitesimal generator of a $C_0$ semigroup, g constitutes a nonlocal conditions, and ${\Delta}u(t_i)=u(t_i^+)-u(t_i^-)$ represents an impulsive conditions.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.