• Tunnel and Underground Space
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• v.11 no.1
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• pp.20-29
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• 2001

Final convergence of tunnel crown due to excavation have been well predicted by regression analysis which is expressed as a function of convergence curve on a time and distance dependent. In this study, the validity of the equations for shallow, wide tunnel was investigated by measurement and numerical analysis. Studied tunnel(Sansoo Tunnel) is located at the boundary of downtown and mountain park. Exponential predictions equation was better coincided with measured data than fractional equation for studied tunnel, although the ground was expected to be elasto-plastic. This is because weathered rock ground is changed elasto-plastic ground into elastic ground by multi-steel grouting and forepoling.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.329-341
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• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.109-124
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• 2009

Based on the observed data for Clarithromycin released, three commonly used inflow models: the power, the exponential, and the logarithmic models are considered. Among them, the power model is used most in practice for simplicity. Using the numerical parameter estimation techniques, the parameters appeared in the model equations are estimated. Through the numerical estimation results using the several experimental data sets, the exponential model turns out to be best among the three models. More specifically, the sum of squares of absolute errors and the sum of squares of relative errors for the exponential model are reduced by 80-95 % for the experimental data sets and 60-90 % for the noise added data sets compared with those for the power and logarithmic models. A typical experimental data set is used in this paper to show the estimation method and its numerical results. The proposed numerical method and its algorithm are designed for estimating the parameters appeared in the model differential equations for which the exact form of the solution is unknown in general. The methodology developed can be applied to more general cases such as the nonlinear ordinary differential equations or the partial differential equations.

• Journal of Intelligence and Information Systems
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• v.22 no.2
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• pp.115-125
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• 2016

The Bollinger Band indicating the current price position in the recent price action range is obtained by adding/substracting the simple standard deviation (SSD) to/from the simple moving average (SMA). In this paper, we first compare the characteristics of the SMA and the exponential moving average (EMA) in the operator's point of view. A basic equation is obtained between the interval length N of the SMA operator and the weighting factor ${\rho}$ of the EMA operator, that makes the centers of the 1st order momentums of each operator impulse respoinse identical. For equivalent N and ${\rho}$, frequency response examples are obtained and compared by using the discrete time Fourier transform. Based on observation that the SMA operator reacts more excessively than the EMA operator, we propose a novel exponential standard deviation (ESD) band centered at the EMA and derive an auto recursive formula for the proposed ESD band. Practical examples for the ESD band show that it has a smoother bound on the price action range than the Bollinger Band. Comparisons are also made for the gap corrected chart to show the advantageous feature of the ESD band even in the case of gap occurrence. Trading techniques developed for the Bollinger Band can be straight forwardly applied to those for the ESD band.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.10b
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• pp.217-218
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• 2002

An integrated adhesive wear model was proposed to determine the transient wear and steady-state wear of aluminium alloy matrix composites. The transient wear volume was described by an exponential equation, while the steady-state wear was governed by a revised Archard equation, in which both the transient wear volume and transient sliding distance were excluded. A mathematical method was developed to determine both the transient distance and the net steady-state wear coefficient. Experimental wear tests were carried out on three types of commercial A6061 aluminum alloy matrix composites reinforced with 10%, 15% and 20% alumina particles. More accurate wear coefficient values were obtained with the proposed model. The average standard wear coefficient, as determined by the original Archard equation, was found to be about 51% higher.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.131-138
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• 2016

We determine the general solutions $f:\mathbb{R}^2{\rightarrow}\mathbb{R}$ of the functional equation f(ux-vy, uy+v(x+y)) = f(x, y)f(u, v) for all x, y, u, $v{\in}\mathbb{R}$. We also investigate both bounded and unbounded solutions of the functional inequality ${\mid}f(ux-vy,uy+v(x+y))-f(x,y)f(u,v){\mid}{\leq}{\phi}(u,v)$ for all x, y, u, $v{\in}\mathbb{R}$, where ${\ph}:\mathbb{R}^2{\rightarrow}\mathbb{R}_+$ is a given function.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.509-512
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• 2001

In this study, pollutant load from paddy field was estimated by regression equation from 5 to 8 in 2001. During study period, total rainfall was 511.3mm and runoff discharge was 968.71mm. Regression equation between flow rate(m3/s) and pollutant loading rate(g/s) is exponential relationship. For site 1, coefficient of determination (R2) for $COD_{cr}$, T-P, T-N were 0.7068, 0.8441, 0.6806 respectively and site 2, 0.9369, 0.8855, 0.4262 respectively. Considering unit loads, Jun was the highest valus as 13.85 $COD_{c}kg/km2/day$, 0.24 T-Pkg/km2/day, 1.22 T-Nkg/km2/day. Until study period, total $COD_{cr}$ load estimated regression equation is 19.32kg/km2/day and, T-P, T-N were 0.264, 1.88 respectively

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.29 no.7
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• pp.387-393
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• 2016

Threshold voltage shift has been observed from many thin-film transistors (TFTs) and the time evolution of the shift can be modeled as the stretched-exponential and -hyperbola function. These analytic models are derived from the kinetic equation for defect-creation or charge-trapping and the equation consists of only reversible reactions. In reality TFT's a shift is permanent due to an irreversible reaction and, as a result, it is reasonable to consider that both reversible and irreversible reactions exist in a TFT. In this paper the case when both reactions exist in parallel and make a combined threshold voltage shift is modeled and simulated. The results show that a combined threshold voltage shift observed from a TFT may agrees with the analytic models and, thus, the analytic models don't guarantee whether the cause of the shift is defection-creation or charge-trapping.

• East Asian mathematical journal
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• v.32 no.5
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• pp.659-675
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• 2016

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history $$\large u_{tt}-M(x,t,{\tau},\;{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\\hspace{25}-{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{-{\infty}}}^t}\;k(t-{\tau}){\Delta}u(x,t)d{\tau}+{\mid}u{\mid}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.6
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• pp.362-366
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• 2002

A mathematical model has been developed for describing the oxygen concentration during the exponential growth of microorganisms, in a static solid substrate bed supported on a tray fermentor. The model equations comprise of one partial differential equation for mass transfer and an ordinary differential equation of growth. After nondimensionlisation, analytical solution tn the model has been obtained by the method of Laplace transforms. An expression for critical thickness of bed is deduced from the model equation. The significance of the model in the design of tray fermentors is discussed. The validity of the discussion is verified by taking an illustration from the literature.