• 대한수학회보
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• 제50권1호
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• 약학회지
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• 제40권1호
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• pp.72-77
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• 1996

Penicillin sensor was manufactured by immobillizing penicillinase with glutaraldehyde on the $H^+$-selective membrane based on PVC-COOH-TDDA. This membrane was not inter fered by $K^+$ ion in Pc-G potassium salt. When enzyme was immobilized with glutaraldehyde, the PVC-COOH matrix was more effective than PVC matrix. Calibration curve calculated from Nernst equation was not linear. But potential was relative to concentration of Pc-G. And maximal potentiometric velocity was also relative to concentration of Pc-G. Therefore, it may be applied to Michaelis-Menten equation. The penicillin sensor was useful for determination of Pc-G at concentration of 0.1~10mM level.

• 대한수학회보
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• 제37권4호
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 약학회지
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• 제40권6호
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• pp.625-631
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• 1996

The $H^+$-selective membrane consists of tridodecylamine, 2-nitrophenyl octyl ether and a little amount of additive in carboxylated PVC matrix, where penicillinase(Pcase ) and glutaraldehyde may be covalently attached to the matrix. When the $H^+$-selective electrode was used as a detector of biosensor, calibration curve calculated from Nernst equation was not linear. So we investigated the characteristic responses of the $H^+$-selective electrode to the product H+ from hydrolysis of penicillin-G(Pc-G) and plotted calibration curve correlating potential to concentration of Pc-G linearly. The optimal concentration of buffer solution was theoretically calculated and was also experimented. We tried to explain the linear curve of potential to concentration of Pc-G by using Henderson-Hasselbach equation. This method is more effective in calibration curve plotting than any other previous methods. The results obtained may help in further developing pH electrodes with improved analytical preformance.

• 대한수학회보
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• 제42권4호
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).

• 대한수학회지
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• 제58권3호
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• pp.703-722
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• 2021

Let G = (V, E) be a connected locally finite and weighted graph, ∆_p be the p-th graph Laplacian. Consider the p-th nonlinear equation -∆_pu + h|u|^p-2u = f(x, u) on G, where p > 2, h, f satisfy certain assumptions. Grigor'yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V. In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m-order differential operator 𝓛_m,p, we also prove the existence of the nontrivial solution to the analogous nonlinear equation.

• 한국연초학회지
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• 제35권1호
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• pp.1-6
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• 2013

Near InfraRed Spectroscopy(NIRS) is a quick and accurate analytical method to measure multiple components in tobacco manufacturing process. This study was carried out to develop calibration equation of near infrared spectroscopy for the prediction of the amount of chemical components and hot water solubles(HWS) of reconstituted tobacco leaf. Calibration samples of reconstituted tobacco leaf were collected from every lot produced during one year. The calibration equation was formulated as modified partial least square regression method (MPLS) by analyzing laboratory actual values and mathematically pre-treated spectra. The accuracy of the acquired equation was confirmed with the standard error of prediction(SEP) of chemical components in reconstituted tobacco leaf samples, indicated as coefficient of determination($R^2$) and prediction error of sample unacquainted, followed by the verification of model equation of laboratory actual values and these predicted results. As a result of monitoring, the standard error of prediction(SEP) were 0.25 % for total sugar, 0.03 % for nicotine, 0.03 % for chlorine, 0.16 % for nitrate, and 0.38 % for hot water solubles. The coefficient of determination($R^2$) were 0.98 for total sugar, 0.97 for nicotine, 0.96 for chlorine, 0.98 for nitrate and 0.92 for hot water solubles. Therefore, the NIRS calibration equation can be applicable and reliable for determination of chemical components of reconstituted tobacco leaf, and NIRS analytical method could be used as a rapid and accurate quality control method.

• 충청수학회지
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• 제20권4호
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• pp.465-476
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• 2007

The aim of this paper is to investigate the stability problem bounded by function for the generalized sine functional equations as follow: $f(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2\\g(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2$. As a consequence, we have generalized the superstability of the sine type functional equations.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.