• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.5
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• pp.695-702
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• 2002

Nonlinear dynamics of striped diffusion flames, by the diffusional-thermal instability with Lewis numbers sufficiently less than unity, is numerically investigated by examining various two-dimensional flame-structure solutions. The Lewis numbers for fuel and oxidizer are assumed to be identical and an overall single-step Arrhenius-type chemical reaction rate is employed in the model. Particular attention is focused on identifying the flame-stripe solution branches corresponding to each distinct stripe pattern and hysteresis encountered during the transition. At a Damkohler number slightly greater than the extinction Damkohler number, eight-stripe solution first emerges from one dimensional solution. The eight-stripe solution survives Damkohler numbers much smaller than the extinction Damkohler number until the transition to four-stripe solution occurs at the first forward transition Damkohler number. At the second forward transition Damkohler number, somewhat smaller than the first transition Damkohler number, the transition to two-stripe solution occurs. However, anu further transition from two-stripe solution to one-stripe solution is not always possible even if one-stripe solution can be independently accessed for particular initial conditions. The Damkohler number ranges for two-stripe and one-stripe solutions are found to be virtually identical because each stripe is an independent structure if distance between stripes is sufficiently large. By increasing the Damkohler number, the backward transition can be observed. In comparison with the forward transition Damkohler numbers, the corresponding backward transition Damkohler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.429-444
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• 2012

By using Mawhin continuation theorem and comparison theorem, the existence of periodic solution and persistence for a predator-prey system with diffusion and impulses are investigated in this paper. An example and simulation are given to show the effectiveness of the main results.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.295-309
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• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• Journal of the Korean Wood Science and Technology
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• v.19 no.4
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• pp.7-17
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• 1991

The feasibility of treating three softwood(Japanese larch pitch pine, and Korean pine) thinned logs by double-diffusion treatment processes was investigated. Some posts were incised before immersion, and others were imersed in hot copper sulfate solution. Comparison among species indicated that. in general, pitch pine was most treatable and Japanese larch least treatable. For all three species, almost all treatment schedules gave consistently good penetration and high net retention, but very steep gradient of preservative distribution. As expected, the treatability was increased by the extension of immersion time, increased concentration of treating solution, incising. and heating of the first solution. Of the variables tested, it appears that heating of the first solution is the most important. From the data in this paper, it may be concluded that, if the first solution is not heated, the best schedule is #3. If the first solution is healed. it appears the best schedules are #10 or #11. Since heating of the first solution improves the treatability. schedules # 10 or :#11 are recommended if the cost of heating might be justified. The data presented in this paper indicate that double-diffusion treatment processes seem to offer a promise as a comparatively effective and easy-operating method of treating thinned logs for the small-scale production of treated stock.

• Korean Membrane Journal
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• v.4 no.1
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• pp.36-40
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• 2002

The diffusion coefficients of ions in the reverse transport system using the carrier mediated membrane were estimated from the diffusional membrane permeabilities and the ion activity in membrane system. In the aqueous alkali metal ions-membrane system diffusional flux of alkali metal ions driven by coupled proton was analyzed. The aqueous phase I contained NaOH solution and the aqueous phase II also contained NaCl and HCl mixed solution. The concentration of Na ions of both phases were $10^{0},\;10^{-1},\;10^{-2},\;5{\times}10^{-1}\;and\;5{\times}10^{-2}\;mol{\cdot}dm^{-3}$ and the concentration of HCI in aqueous phase II was always kept at $1{\times}10^{-1}\;mol{\cdot}dm^{-3}$. Moreover, the carrier concentration in liquid membrane was $10^{-2}\;mol{\cdot}dm^{-3}$. The results indicated that the diffusion coefficients depend strongly on the concentration of both phases electrolyte solution equilibriated with the membrane. The points were interpreted in terms of the energy barrier theory. Furthermore, eliminating the potential terms from the membrane equation was derived.

• Korean Journal of Soil Science and Fertilizer
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• v.28 no.3
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• pp.233-240
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• 1995

Fick's diffusion equation was transformed into algebraic subsidiary equation with its initial and boundary conditions through Laplace transformation, and the subsidiary equation was transformed back on the basis of Burington's table of inverse transformations so that it became the solution of Fick's equation. The initial and boundary condition was for upward diffusion of salts into flooding water of constant depth from uniform polder soil of infinite depth containing constant concentration of salt. The derived solution was tested through comparison for its conformability with other solutions of simpler initial and boundary conditions. The importance of shallow transplanting of rice seedlings and salt removing by growing rice was mentioned on the basis of very slow desalting rate by diffusion calculated from the derived solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.31-40
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• 2009

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

• Applied Chemistry for Engineering
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• v.3 no.2
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• pp.349-359
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• 1992

Studies were carried out on the selective removal of inorganic salts such as NaCl and $Na_2SO_4$ from dye solution, using counter diffusion-reverse osmosis and nanofiltration, respectivey. For the dye solution used in the experiments, 1 to 30% of salts were removed by counter diffusion while the loss of dye molecules was less than 0.3%. The separation factors by one pass operation were 10-500 according to ionic species. In five successive operations, removals of anion($Cl^-$) increased but those of cation($Na^+$) decreased due to the Donnan effect. Effects of feed flow rate on removal efficiencies of various ions were also observed at constant flow rate of stripping water. Reverse osmosis of desalted dye solution by counter diffusion was conducted to prepare highly concentrated liquid dyes. The rejection efficiency of dye molecules was greater than 99%. For the rejection efficiency of chloride ion, experimental values were compared with theoretical ones based on solution-diffusion model. Two stage diafiltration was performed in nanofiltration. The rejection efficiency of chloride ion was continuously decreased due to the Donnan dialysis and even negative rejection was observed. The Donnan effect was more pronounced in the second diafiltration.