• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• 한국환경과학회지
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• 제8권4호
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• pp.443-449
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• 1999

This paper describe the working of algal culture system under batch and continuous feeding effluents in biological treatment process. The main objective of this study was the determination of fundamental opeating parameters such as dilution rates, light intensity, biomass concentration, nutrients contents, which engender an effective nutrient and organic waste removal process. The results of this research indicate that the algae system will remove effectively nutrient and organic waste. In batch cultures, 91.8% dissolved orthophosphate and 83.3% ammonia nitrogen were removed from the sewage in ten days. In continuous flow systems, a detention time of 2.5 days was found adequate to remove 91% T-P, 87% T-N and 95% $NH_3-N$. At 22-28$^{\circ}C$, 60 rpm, with an intensity of 3500 Lux, the specific growth rate, k was 0.59/day in batch experiments. The optimal growth temperature and nutrients rate (N/P) were respectively $25^{\circ}C$ and 3~5. With an abundant supply of untrients, it was possible to sustain substantial population densities in the temperature range of 22~28$^{\circ}C$.

• 대한수학회지
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• 제54권4호
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• pp.1175-1187
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• 2017

The spectral problem $$-y^{{\prime}{\prime}}+q(x)y={\lambda}y,\;0 < x < 1, \atop y(0)cos{\beta}=y^{\prime}(0)sin{\beta},\;0{\leq}{\beta}<{\pi};\;{\frac{y^{\prime}(1)}{y(1)}}=h({\lambda})$$ is considered, where ${\lambda}$ is a spectral parameter, q(x) is real-valued continuous function on [0, 1] and $$h({\lambda})=a{\lambda}+b-\sum\limits_{k=1}^{N}{\frac{b_k}{{\lambda}-c_k}},$$ with the real coefficients and $a{\geq}0$, $b_k$ > 0, $c_1$ < $c_2$ < ${\cdots}$ < $c_N$, $N{\geq}0$. The sharpened asymptotic formulae for eigenvalues and eigenfunctions of above-mentioned spectral problem are obtained and the uniform convergence of the spectral expansions of the continuous functions in terms of eigenfunctions are presented.

• 대한수학회지
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• 제49권3호
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• pp.641-658
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• 2012

The goal of this paper is to develop a nonlinear observer-based control strategy for a multi-variables continuous stirred tank reactor (CSTR). A new robust nonlinear observer is constructed to estimate the whole process state variables. The observer is coupled with a nonlinear controller, designed based on the input-output linearization for controlling the concentration and reactor temperature. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Finally, computer simulations are developed for showing the performance of the proposed controller.

• 대한수학회논문집
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• 제10권1호
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• 대한수학회지
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• 제43권2호
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• pp.373-382
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• 2006

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.

• 한국환경보건학회지
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• 제21권4호
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• pp.17-23
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• 1995

As a basic experiment to develope biological pretreatment proces~ in water treatment, the experiments on biodegradability and isothermal adsorption of activated carbon were performed on refractories such as humic acid, $NH_3-N$, phenol and ABS which caused the problems in drinking water treatment. Also, the treatabilities on humic acid were examined in the continuous flow type reactors. The removal efficiencies of humic acid, $NH_3-N$, phenol and ABS in the biodegradable experiments for 5 days were 20.1%, 73.4%, 91.7% and 97.5%, respectively. In the isothermal adsorption test of refractories on activated carbon to be used as a media in the continuous flow type reactors, ABS and phenol are adsorbed easily, but humic acid and $NH_3-N$ are difficult to be done. The removal efficiencies of humic acid in granular activated carbon(GAC) reactor were about 7-8% higher than in biological activated carbon(BAC) reactor. The removal efficiencies of humic acid in biological fluidized bed(BFB) reactor were about 30% in GAC media, but were almost zero in sea sand media.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• 한국안전학회지
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• 제15권4호
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• pp.35-40
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• 2000

The influence of cyclic loading history on the creep behavior of the 30 vol% hot-pressed $SiC_f/Si_3N_4copmposite was experimentally investigated at $1200^{\circ}C$. The duration of loading/unloading had great effects on the creep behaviors. The short term duration cyclic loading history test results showed significant reduction in the primary and steady-state creep rates. For example, 300sec loading/300sec unloading history resulted in 70% lower steady-state creep rate than that of the continuous loading. However the long term duration cyclic loading history test results showed little change in creep rates compared to those of the continuous one. The reason for the significant change in the short term duration cycles was estimated due to the change in the stress redistribution between the fiber and matrix during the creep recovery in the primary stage.

• 대한수학회논문집
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• 제9권3호
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.