• Korean Journal of Mathematics
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• 제30권2호
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• pp.403-412
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• 2022

In this paper, we introduce the following cubic-quartic functional equation of the form $$f(x+4y)+f(x-4y)=16[f(x+y)+f(x-y)]{\pm}30f(-x)+\frac{5}{2}[f(4y)-64f(y)]$$. Further, we investigate the general solution and the Ulam stability for the above functional equation in non-Archimedean spaces by using the direct method.

• 약학회지
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• 제23권3_4호
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• pp.147-152
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• 1979

Experiments were carried out to investigate for the interaction between FAD solution and synthetic resin containers made of polyvinylchloride(PVC), polyethylene(PE), and polycarbonate(PC), and for the effect of glycyrrhizine or malic acid on stabilization of FAD in aqueous solution by accelerated stability analysis. Analysis of FAD was determined by means of spectrometer and by separating by paper chromatography and metal ions were detected by atomic absorption spectrophotometer, which were extracted from containers by means of Food and Additive Regulation Standard. The thermal decomposition of FAD in aqueous solution was pseudo first order reaction and it was inhibited by adding glycyrrhizine or malic into the solution. PVC, PE and PC containers accelerated the decomposition of FAD in solution. It is assumed that bivalent heavy metals in resin containers may catalize the hydrolysis of FAD. The metals detected from the containers were Ca, Zn, Cu, Fe, Pb and Cd. And the total amounts of detected metals from PVC were 6.2mcg/cm$^{2}$, PE, 5.5mcg/cm$^{2}$, and PC, 2.7mcg/cm$^{2}$ which were proportional to the rate constant of FAD decomposition in aqueous solution.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1993년도 봄 학술회 논문집
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• pp.9-14
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• 1993

Practical solutions that are available today for assessing stability of tunnel working face are largely based on the concept of critical stability ratio. The accuracy of a prediction of the soil behavior in the working face, thus, depends on the ability of the solution to completely and accurately describe the stress fields or kinematics generated by the excavation and the accuracy of the undrained shear strength of the soil introduced in the computation. This paper reviews the selected solutions describing stability of the tunnel heading in squeezing ground, and suggests a reference solution which is established based on comparison of the solutions and field data on stability of tunnel headings in clays. Although dealing with the shear strength determination is an important companion part of the geotechnical prediction for stability of the tunnel heading in clays, this part is beyond the scope of this paper at this time.

• 한국수소및신에너지학회논문집
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• 제33권4호
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• pp.330-336
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• 2022

In order to evaluate the possibility as a separator in alkaline water electrolysis, the high temperature characteristics were evaluated by measuring the membrane resistance and durability of 5 types of commercial anion exchange membranes in 7 M KOH solution and at 80℃. The membrane resistance of AEM membrane measured in 7 M KOH solution and at 80℃ had a lower value of about 8-24 times compared to the other membranes. The durability of AEM membrane tested with the soaking time in 7 M KOH solution and at 80℃ showed a very good stability and that of FAAM40 and FAAM75-PK showed secondly a good stability. The thermal stability with the soaking time in 7 M KOH solution and at 80℃ of FAAM40 and FAAM75-PK membrane analyzed by thermo-gravimetric analysis showed a good stability compared to the other membranes.

• 충청수학회지
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• 제20권2호
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• 호남수학학술지
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• 제30권2호
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• pp.219-225
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• 2008

In this paper, we obtain the general solution and the stability of the 2-dimensional vector variable quadratic functional equation f( x + y, z - w) + f(x - y, z + w) = 2f(x, z ) + 2f(y, ${\omega}$). The quadratic form f( x, y) = $ax^2$ + $by^2$ without cross product terms is a solution of the above functional equation.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.513-519
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Jensen's functional equation $$2f(\frac{x_1+y_1}{2},\;\cdots,\;\frac{x_n+y_n}{2})=f(x_1,\;\cdots,\;x_n)+f(y_1,\;\cdots,\;y_n)$$. The function f given by $f(x_1,\;\cdots,\;x_n)=a_1x_1+{\cdots}+a_nx_n+b$ is a solution of the above functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.103-110
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• 2008

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form $f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$ is a solution of the above functional equation.

• 대한수학회지
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• 제59권2호
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• pp.279-298
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• 2022

In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.