• Polymer(Korea)
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• v.30 no.1
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• pp.45-49
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• 2006

In this study, it was investigated on the boron separation ken synthetically prepared seawater. ion exchange resin used in the experiments was Amberlite IRA 743, containing glucamine functional group. The experiments were carried out as a function of the conditions of the pH, boron initial concentration and temperature of seawater in a batch reactor. As a result, optimum conditions for boron adsorption were at pH 8.5 and 313 K, respectively. The adsorption rate was increased very fast with increasing the temperature, but decreased with increasing the initial concentration of boron. Also, the kinetics for boron adsorption applied the pseudo-second order model, as follows: $$\frac{X}{1-X}=780[C_0]^{-1.65}t^{1.48}\;exp\;({-\frac{17883}{RT}}\)\;;\;pH8.5$$

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 1993.10a
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• pp.443-452
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• 1993

Direct freezing tests of soybean seed by liquid nitrogen were carried out at various moisture contents and the following important conclusions were drawn from the results of temperature measurements of soybean seed and photographs of bubbles generated on its surface : 1) Assuming that the temperature gradient in a soybean seed is negligible because of its small seed size and the freezing ratio is followed the Heiss's formula, and a differential equation based on the heat energy balance was introduced . The equation was easily solved by the Runge-Kutta-Gill method and the predicted values of the temperature were in good agreement with the observed data. 2) The photographs of bubble generation during freezing showed the boiling mode was nucleate, and then the most suitable formula on the nucleate boiling heat transfer was introduced from many formulate proposed up to now by fitting the calculated values based on the formula to the observed data. The formula used for the predict on of the seed temperature was as follows: $\frac{{\partial}T_s}{\partial\theta}\;=\;-\frac{{\alpha}(T_s\;-\;T_L)^{3.3}}{W(C_s\;-\;\frac{{\delta}m(CT_s\;+\;{\sigma})}{T_s^2})}$ where C = difference of the specific heat between pure ice and water m=moisture content of soybean seed $T_s$ = seed temperature $T_L$ = Temperature of liquid nitrogen W = mass of soybean seed $\alpha$ = proportional constant $\delta$ = constant depends on variety or the type of seed $\theta$ = time $\sigma$ = latent heat of melting of pure ice This study will give important information in the hydro-freezing technique by liquid nitrogen, available as a new technique of processing agricultural products in the near future.

• Journal of Ecology and Environment
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• v.43 no.4
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• pp.376-384
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• 2019

Background: Nutrient release during litter decomposition was investigated in Vitex doniana, Terminalia avecinioides, Sarcocephallus latifolius, and Parinari curatellifolius in Makurdi, Benue State Nigeria (January 10 to March 10 and from June 10 to August 10, 2016). Leaf decomposition was measured as loss in mass of litter over time using the decay model W_t/W₀ = e-^{kd t}, while $Kd=-{\frac{1}{t}}In({\frac{Wt}{W0}})$ was used to evaluate decomposition rate. Time taken for half of litter to decompose was measured using T₅₀ = ln ²/k; while nutrient accumulation index was evaluated as $NAI=(\frac{{\omega}t\;Xt}{{\omega}oXo})$. Results: Average mass of litter remaining after exposure ranged from 96.15 g, (V. doniana) to 78.11 g, (S. lafolius) in dry (November to March) and wet (April to October) seasons. Decomposition rate was averagely faster in the wet season (0.0030) than in the dry season (0.0022) with P. curatellifolius (0.0028) and T. avecinioides (0.0039) having the fastest decomposition rates in dry and wet seasons. Mean residence time (days) ranged from 929 to 356, while the time (days) for half the original mass to decompose ranged from 622 to 201 (dry and wet seasons). ANOVA revealed highly significant differences (p < 0.01) in decomposition rates and exposure time (days) and a significant interaction (p < 0.05) between species and exposure time in both seasons. Conclusion: Slow decomposition in the plant leaves implied carbon retention in the ecosystem and slow release of CO₂ back to the atmosphere, while nitrogen was mineralized in both seasons. The plants therefore showed effectiveness in nutrient cycling and support productivity in the ecosystem.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.6-6
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• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1587-1598
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• 2013

In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $$\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$$ under general geometric flow on complete noncompact manifolds, where 0 < ${\sigma}$ < 1 is a real constant and $b(x,t)$ is a function which is $C^2$ in the $x$-variable and $C^1$ in the$t$-variable. As an application, we get an interesting Harnack inequality.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.753-765
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• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.105-116
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• 2013

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, then every positive solution blows up in finite time, but for $q$ > $q_c$, there exist both global and non-global solutions to the problem.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.515-526
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• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• Journal of Biosystems Engineering
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• v.37 no.3
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• pp.155-165
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• 2012

This study was performed to offer the data for design of the seedling bed transfer equipment to make the automation of working process in a plant factory. The seedling bed transfer equipment pushing the seedling bed with bearing wheels on the rail for interconnecting each working process by a pneumatic cylinder was made and examined. The examined transfer force to push the seedling bed with a weight of 178.9 N by the pneumatic cylinder with length of 60 cm and section area of 5 $cm^2$ was measured by experiments. The examined transfer forces was compared with theoretical ones calculated by the theoretical formula derived from dynamic system analysis according to the number of the seedling bed and pushing speed of the pneumatic cylinder head at no load. The transfer function of the equipment with the input variable as the pushing speed $V_{h0}$(m/s) and the output variable as the transfer force f(t)(N) was represented as $F(s)=(V_{h0}/k)(s+B/M)/(s(s^2+Bs/M+1/(kM))$ where M(kg), k(m/N) and B(Ns/m) are the mass of the bed, the compression coefficient of the pneumatic cylinder and the dynamic friction coefficient between the seedling bed and the rail, respectively. The examined transfer force curves and the theoretical ones were represented similar wave forms as to use the theoretical formular to design the device for the seedling bed transfer. The condition of no vibration of the transfer force curve was $kB^2>4M$. The condition of transferring the bed by the repeatable impact and vibration force according to difference of transfer distance of the pneumatic cylinder head from that of the bed was as $Ce^{-\frac{3{\pi}D}{2\omega}}<-1$, where ${\omega}=\sqrt{\frac{1}{kM}-\frac{B^2}{4M^2}}$, $C=\{\frac{\frac{B}{2M}-\frac{1}{kB}}{\omega}\}$, $D=\frac{B}{2M}$. The examined mean peak transfer force represented 4 times of the stead state transfer force. Therefore it seemed that the transfer force of the pneumatic cylinder required for design of the push device was 4Bv where v is the pushing speed.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.369-379
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• 2018

Let ${\mathbb{H}}_3$ be the 3-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we calculate the volumes of geodesic balls in ${\mathbb{H}}_3$. Let $B_e(R)$ be the geodesic ball with center e (the identity of ${\mathbb{H}}_3$) and radius R in ${\mathbb{H}}_3$. Then, the volume of $B_e(R)$ is given by $$Vol(B_e(R))={\frac{\pi}{6}}\{-16R+(R^2+6){\sin}\;R+(R^3+10R){\cos}\;R+(R^4+12R^2){\int\nolimits_0^R}\;{\frac{{\sin}\;t}{t}}dt\}$$.