• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1599-1619
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• 2018

In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity c tends to infinity in a pointwise sense.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.929-941
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• 2000

We study a parabolic system of chemotaxis introduced by E.F. Keler and L.A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the L$^1$norm of the initial value is less than 8$\pi$. Meanwhile a method of rearrangement is porposed toprove an inequality of Trudinger-Moser's type.

• Composites Research
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• v.35 no.3
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• pp.216-221
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• 2022

Recently, the worldwide demand for disposable masks has increased due to COVID-19 infections and severe air pollution. Personal masks should reduce breathe resistance while maintaining filtering performance. In this study, a solution blowing process is used to produce composite nanofiber filters to co-spin two polymers at once. The manufacture process of the various fiber diameter filter was designed, and the filtration performance and differential pressure of the prepared filter was investigated. Poly vinylidene fluoride-hexafluoropropylene (PVDF-HFP) and Polylactic acid (PLA) fibers were chosen to be entangled together in a layer with a diameter of 1.05 ㎛ and 0.33 ㎛. Composite nanofilters showed up to 87% filtration efficiency and 32 Pa differential pressure.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.37-56
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• 2013

This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration system $$\{u_t=(\mid(u^{m_1})_x{\mid}^{{p_1}^{-1}}(u^{m_1})_x)_x+u^{l_{11}}{{\int_0}^a}v^{l_{12}}({\xi},t)d{\xi},\;(x,t)\;in\;[0,a]{\times}(0,T),\\{v_t=(\mid(v^{m_2})_x{\mid}^{{p_2}^{-1}}(v^{m_2})_x)_x+v^{l_{22}}{{\int_0}^a}u^{l_{21}}({\xi},t)d{\xi},\;(x,t)\;in\;[0,a]{\times}(0,T)}$$ with nonlinear boundary conditions $u_x{\mid}{_{x=0}}=0$, $u_x{\mid}{_{x=a}}=u^{q_{11}}u^{q_{12}}{\mid}{_{x=a}}$, $v_x{\mid}{_{x=0}}=0$, $v_x|{_{x=a}}=u^{q21}v^{q22}|{_{x=a}}$ and the initial data ($u_0$, $v_0$), where $m_1$, $m_2{\geq}1$, $p_1$, $p_2$ > 1, $l_{11}$, $l_{12}$, $l_{21}$, $l_{22}$, $q_{11}$, $q_{12}$, $q_{21}$, $q_{22}$ > 0. Under appropriate hypotheses, the authors establish local theory of the solutions by a regularization method and prove that the solution either exists globally or blows up in finite time by using a comparison principle.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.721-736
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• 2014

We consider the equation ${\Delta}_mu=p(x)u^{\alpha}+q(x)u^{\beta}$ on $R^N(N{\geq}2)$, where p, q are nonnegative continuous functions and 0 < ${\alpha}{\leq}{\beta}$. Under several hypotheses on p(x) and q(x), we obtain existence and nonexistence of blow-up solutions both for the superlinear and sublinear cases. Existence and nonexistence of entire bounded solutions are established as well.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1003-1031
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• 2020

We consider the following Dirichlet initial boundary value problem with a gradient absorption and a nonlocal source $$\frac{{\partial}u}{{\partial}t}-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)={\lambda}u^k{\displaystyle\smashmargin{2}{\int\nolimits_{\Omega}}}u^sdx-{\mu}u^l{\mid}{\nabla}u{\mid}^q$$ in a bounded domain Ω ⊂ ℝ^N, where p > 1, the parameters k, s, l, q, λ > 0 and µ ≥ 0. Firstly, we establish local existence for weak solutions; the aim of this part is to prove a crucial priori estimate on |∇u|. Then, we give appropriate conditions in order to have existence and uniqueness or nonexistence of a global solution in time. Finally, depending on the choices of the initial data, ranges of the coefficients and exponents and measure of the domain, we show that the non-negative global weak solution, when it exists, must extinct after a finite time.

• Journal of Ship and Ocean Technology
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• v.1 no.2
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• pp.19-30
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• 1997

The accurate prediction of the flow and the pressure distribution near the tip of the blade is crucial in determining the tip vortex cavitation inception which usually occurs on the blade tip or inside the core of the tip vortex just downstream of the blade tip. An improved boundary element method is applied to the prediction of the flow around propeller blades, with emphasis at the tip region. In the method, the Blow adapted grid and a higher order panel method, which combines a hyperboloidal panel geometry with a hi-quadratic dipole distribution, are used in order to accurately model the trailing wake geometry and the highly rolled-up regions in the wake. The method is applied to several propeller geometries and the results have been found to agree well to the existing experimental data. Inviscid flow methods are able to predict the pressures at the tip as well as the shape of the trailing wake. On the other hand, they are unable to determine the flow inside the viscous core of the tip vortex, where cavitation inception often occurs. Thus, a method is presented that treats the flow inside the viscous core. The inner flow is treated with a 2-D Clavier-stokes solution without making any assumptions for axisymmetric flow and conicity of the flow along the tip trajectory. The method can thus allow the treatment of general propeller blade configurations. The velocity and pressure distributions inside the core are shown and compared to those from other numerical methods.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.6 no.1
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• pp.10-16
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• 1995

The E-polarized scattering problems by a perfect conductor strip grating are analyzed by the method of moments. For an E-polarization the induced surface current density is expected to blow up at the strip both edges. Then the induced surface current density on the strip is expanded in a series of multiplication of Ultraspherical ploynomials with zeroth order and functions with appropriate edge boundary condition. The numerical results for current density and reflection cofficient are compared with other functions, it is shown that numerical results better improves the convergence of the moment method soulutions with general incident angles than the existing several other functions. The sharp variation points in the magnitude of geometric-optical reflection coefficient can be moved by varying the incident angle, strip width, and strip spacing.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6C
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• pp.231-240
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• 2011

Various pile load tests were carried out at Gwangyang district for 10 different piles in order to analyze the characteristcs of steel pile using high strength steel and high driving energy. Pile drivability results showed that PHC piles needed highest total blow count even with the shortest pile length and high strength steel pipe piles showed smallest total blow count eventhough driven to a more hard ground condition with longer pile length. Pile dynamic analysis results showed that for PHC pile and general steel pipe pile the allowable pile design load was decided by the allowable material strength but for high strength steel pipe pile the design load can be decided according to the ground bearing capacity. Static load test and load transfer test results showed that the pile design efficiency could be improved over 80% allowing lesser number of piles necessary for a more economical solution. Set-up effects was analyzed and regression equation for the site ground condition was derived. Bearing capacity was checked with widely used design equation and the limitation of current design method and future technology development on this subject is dicussed in this paper.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.10
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• pp.20-28
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• 2007

Zigbee sensor network base on IEEE802.15.4 has local address of 2 byte on transmit packet data which is pick up the address for each sensor node. Sensor network is requested low power, low cost, many nodes at hues physical area. There for Zigbee is very good solution supporting for next Ubiquitous generation but the Zigbee sensor network has address allocation problem of each sensor node. Is established standard from Zigbee Alliance, to the address allocation method uses Cskip algorithm. The Cskip algorithm use the hazard which allocates an address must blow Hop of the maximum modification and child node number. There is to address allocation and from theoretically it will be able to compose a personal 65536 sensor nodes only actual with concept or space, only 500 degree will be able to compose expansion or the low Zigbee network. We proposed an address allocation method using coordinate value for Zigbee sensor network.