• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1157-1169
• /
• 2010

This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.647-654
• /
• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.2
• /
• pp.337-346
• /
• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.303-316
• /
• 2000

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

• Journal of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.113-138
• /
• 2012

We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.

• Journal of the Korean Society of Environmental Restoration Technology
• /
• v.13 no.2
• /
• pp.42-51
• /
• 2010

Herbs and shrubs are employed for environmental restoration purposes. Among common herbs and shrubs, few species with low germination rates were selected and studied for enhanced germination rates and decreased germination times via soaking treatment. Rhus chinensis, incubator grown samples treated with the bacterial solution for 72hrs followed by immediate seeding showed the highest germination rate of 26.7% and germination period of 5.7 days, 3 days decrease from the control. Treatment of distilled water (t=3.79, p<0.01), nutrient broth (t=4.44, p<0.00) and bacterial solution (t=4.42, p<0.00) showed highly significant difference. In the case of soil tests, treating in the nutrient broth for 72 hrs followed by immediate seeding yielded the the highest germination rate of 23.3% with 7.3 days to initial germination, a decrease of 14.7 days with respect to the control. All the samples followed by immediate seeding showed significant difference (t=2.13, p<0.05). Incubator grown samples of Lespedeza cyrtobotrya showed different results. The incubator samples suspended for 48 hrs in distilled water followed by immediate seeding and 1 day drying displayed the highest germination rate of 96.7%, surpassing that of the control by 33.4%. The incubator samples treated with the distilled water and nutrient broth showed enhanced germination. But only the samples treated with distilled water and nutrient broth for 48hrs showed the increased germination in soil tests. All the sample treated for 24 hrs followed by immediate seeding or dried for 1 day showed initial germination as early as 1 day in incubator. The initial germinations were shortened in the samples treated with distilled water and nutrient broth for 48hrs in soil tests. Lespedeza cuneata incubator sample treated with nutrient broth for 24 hrs and dried for 1 day exhibited the highest germination rate of 83.3%, a 31.1% improvement over the control. The incubator samples treated with distilled water for 48 hrs (t=4.20, p<0.01) showed effective increase of germination. The treatment of distilled water (t=2.96, p<0.05) and bacterial solution (t=2.24, p<0.05) showed significant difference. The germination rates in soil were less than those of incubator and the control. The incubator samples treated with distilled water and bacterial solution displayed 1 day germination period, shortened by 1.3 days compared to the control. For soil grown samples, the samples treated with distilled water showed delayed initial germination and those treated with nutrient broth for 48hrs and bacterial solution for 72hrs shortened initial germination.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.16 no.2
• /
• pp.21-27
• /
• 2008

An inverse method is introduced to construct the problem for the error analysis of the numerical solution of initial value problem. These problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The process leading to the exact solution makes use of an initially available approximate numerical solution. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. Using this special case exact solution, it is possible to investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution.

• Journal of Electrochemical Science and Technology
• /
• v.10 no.1
• /
• pp.14-21
• /
• 2019

Supported liquid membrane process usually is used for recovering or enrichment of valuable metals in the industrial wastewater. But, even if the metals in the wastewater was separated with high chemical selectivity, it cannot be enough concentrated since separation performance of supported liquid membrane (SLM) process is limited by concentration gradient between feed solution and stripping solution. If metal concentration in the stripping solution to be enough low, transport of metal through membrane can be accomplishment constantly. Therefore, Electrodialysis (ED) has been placed after SLM process and the stripping solution of SLM was used as the feed solution for the ED process. Transport of ions in the solutions is successfully performed by ED process. Thus, the metal concentration in the stripping solution does not rise as to stop ion transport. Besides, valuable metals easily are concentrated by ED process for re-use. In this study, effects of operation parameters like initial Cd(II) concentration, HCl concentration in the feed solution of SLM and applied voltage are investigated on separation efficiency, flux and permeability of the both processes. As the feed solution concentration increased, all performance values has increased. When initial concentration of 100 mg/L is used, separation performances (SP) are 55% and 70%, for SLM and consecutive process, respectively. The best HCl concentration in the feed solution of SLM has determined as 2 M, in this conditions SP are 64% and 72%, for SLM and consecutive process, respectively. With increased of applied voltage on ED process, SP of the consecutive process has been raised from 72% to 83%. According to the obtained experimental data, consecutive process has better separation performance than SLM. When the separation performances of both processes were compared for the same operating conditions, it was determined higher the separation efficiency, permeability and flux values of the consecutive process, 8%, 9% and %10.6, respectively. Consequently, the use of the consecutive process increases the performance efficiency of both processes. The consecutive process studied has quite a good chemical separation efficiency, and enrichment capability. Moreover, this process requires few water and energy.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.13 no.2
• /
• pp.93-102
• /
• 2013

This paper proposes an algorithm designed to obtain the optimal solution for transportation problem. The transportation problem could be classified into balanced transportation where supply meets demand, and unbalanced transportation where supply and demand do not converge. The archetypal TSM (Transportation Simplex Method) for this optimal solution firstly converts the unbalanced problem into the balanced problem by adding dummy columns or rows. Then it obtains an initial solution through employment of various methods, including NCM, LCM, VAM, etc. Lastly, it verifies whether or not the initial solution is optimal by employing MODI. The abovementioned algorithm therefore carries out a handful of complicated steps to acquire the optimal solution. The proposed algorithm, on the other hand, skips the conversion stage for unbalanced transportation problem. It does not verify initial solution, either. The suggested algorithm firstly allocates resources so that supply meets demand, in the descending order of its loss cost. Secondly, it optimizes any surplus quantity (the amount by which the initially allocated quantity exceeds demand) in such a way that the loss cost could be minimized Once the above reallocation is terminated, an additional arrangement is carried out by transferring the allocated quantity in columns with the maximum cost to the rows with the minimum transportation cost. Upon application to 2 unbalanced transportation data and 13 balanced transportation data, the proposed algorithm has successfully obtained the optimal solution. Additionally, it generated the optimal solution for 4 data, whose solution the existing methods have failed to obtain. Consequently, the suggested algorithm could be universally applied to the transportation problem.

• Journal of Korean Society of Water and Wastewater
• /
• v.18 no.2
• /
• pp.174-180
• /
• 2004

This study is a fundamental research to test the applicability of abandoned eggshell as seed material for crystallization reaction. Eggshell was calcinated at $850^{\circ}C$ and ground to lesser than 0.42mm. The calcination characteristics of eggshell were examined by X-ray diffraction (XRD). The effect of initial calcium concentration, alkalinity, reaction temperature condition, seed dosage were studied by batch test. For the low concentration sample(P concentration is under 50mg/L), more than 90% of P can be removed. The effect of initial calcium concentration(0~120mg/L) was performed. At the result of the test, more than 50mg/L calcium concentration has high removal efficiency. Alkalinity effect was studied for synthetic solution(100mg/L initial P, 50mg/L calcium, 0.025% seed dosage) with 0~300mg/L bicarbonate alkalinities. For synthetic solution(100mg/L initial P, 50mg/L calcium, 100mg/L bicarbonate alkalinity, 0.025% seed dosage), the phosphorus concentration was examined with $10{\sim}35^{\circ}C$. In addition, calcinated eggshell was injected to swine wastewater to test the applicability to actual wastewater.