• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.157-175
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• 2019

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.4
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• Journal of KSNVE
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• v.11 no.1
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• pp.156-166
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• 2001

This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous, isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle surface. The relationships are combined to yield equations of motion in terms of orthogonal displacement components taken in the meridional, normal and circumferential directions. Strain energy and kinetic energy functionals are also presented. The equations of motion and energy functionals may be used to determine the static or dynamic displacements and stresses in shells of revolution, including free and forced vibration and wave propagation.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.299-312
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• 2008

In this paper, we establish some oscillation criteria for nonautonomous second order neutral delay dynamic equations $(x(t){\pm}r(t)x({\tau}(t)))^{{\Delta}{\Delta}}+H(t,\;x(h_1(t)),\;x^{\Delta}(h_2(t)))=0$ on a time scale ${\mathbb{T}}$. Oscillatory behavior of such equations is not studied before. This is a first paper concerning these equations. The results are not only can be applied on neutral differential equations when ${\mathbb{T}}={\mathbb{R}}$, neutral delay difference equations when ${\mathbb{T}}={\mathbb{N}}$ and for neutral delay q-difference equations when ${\mathbb{T}}=q^{\mathbb{N}}$ for q>1, but also improved most previous results. Finally, we give some examples to illustrate our main results. These examples arc [lot discussed before and there is no previous theorems determine the oscillatory behavior of such equations.

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.715-726
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• 2016

In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.5
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• pp.86-92
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• 1999

Effluent concentration estimation equations for wetland system were developed throught statistical analysis of treatment wetland experimental data. Existin g empirical equations were reviewed for thier accuracy with experimental data, and compared with the estimatin equations. About 70 experimental data sets were used for multiple regression, and variables include influent concentration, hydraulic loading rate, average daily air temperature , and plant coverage. The estimatin equations developed for BOD5 , SS ,T-P, and T-N predicted effluent concentrations moderately well, and coefficient fo determination ($R^2$) for them was 0.74 , 0.60, 0.59 and 0.58 respectively. The equations obtained from same data but excluding plant coverage showed relatively lower $R^2$ than the former case, and it was 0.66, 0.52, 0.41 and 0.57 respectively. The EPA, WPCF , and Kadlec and Knight equations worked poorly and $R^2$ for them was significantly lower than the estimation equation developed in the study. The reason might be that the existing equations were oversimplified that they did ot include important parameters such as air temperature and plant coverage. Therefore, developing reasonable estimation equations from experiment under realistic condition is highly recommended rather than using exiting estimation equations.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.6
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• pp.326-334
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• 2017

We obtain height of waves overtopping on a porous breakwater using both the one-layer and two-layer Boussinesq equations. The one-layer Boussinesq equations of Lee et al. (2014) are used and the two-layer Boussinesq equations are derived following Cruz et al. (1997). For solitary waves overtopping on a porous breakwater, we find through numerical experiments that the height of waves overtopping on a low-crested breakwater (obtained by the Navier-Stokes equations) are smaller than the height of waves passing through a high-crest breakwater (obtained by the one-layer Boussinesq equations) and larger than the height of waves passing through a submerged breakwater (obtained by the two-layer Boussinesq equations). As the wave nonlinearity becomes smaller or the porous breakwater width becomes narrower, the heights of transmitting waves obtained by the one-layer and two-layer Boussinesq equations become closer to the height of overtopping waves obtained by the Navier-Stokes equations.

• Nutrition Research and Practice
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• v.13 no.3
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• pp.256-262
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• 2019

BACKGROUND/OBJECTIVES: The objectives of this study were to evaluate the accuracy of the Dietary Reference Intakes (DRI) for estimating the energy requirements of older adults, and to develop and validate new equations for predicting the energy requirements of this population group. MATERIALS/METHODS: The study subjects were 25 men and 23 women with a mean age of $72.2{\pm}3.9\;years$ and $70.0{\pm}3.3\;years$, and mean BMI of $24.0{\pm}2.1$ and $23.9{\pm}2.7$, respectively. The total energy expenditure (TEE) was measured by using the doubly labeled water (DLW) method, and used to validate the DRI predictive equations for estimated energy requirements (EER) and to develop new EER predictive equations. These developed equations were cross-validated by using the leave-one-out technique. RESULTS: In men, the DRI equation had a -7.2% bias and accurately predicted the EER (meaning EER values within ${\pm}10%$ of the measured TEE) for 64% of the subjects, whereas our developed equation had a bias of -0.1% and an accuracy rate of 84%. In women, the bias was -6.6% for the DRI equation and 0.2% for our developed equation, and the accuracy rate was 74% and 83%, respectively. The predicted EER was strongly correlated with the measured TEE, for both the DRI equations and our developed equations (Pearson's r = 0.915 and 0.908, respectively). CONCLUSIONS: The DRI equations provided an acceptable prediction of EER in older adults and these study results therefore support the use of these equations in this population group. Our developed equations had a better predictive accuracy than the DRI equations, but more studies need to be performed to assess the performance of these new equations when applied to an independent sample of older adults.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.2
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• pp.41-49
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• 2019

We approximately obtain heights of cnoidal waves overtopping on a porous breakwater using both the one-layer Boussinesq equations (Vu et al., 2018) and the two-layer Boussinesq equations (Huynh et al., 2017). For cnoidal waves overtopping on a porous breakwater, we find through numerical experiments that the heights of cnoidal waves overtopping on a low-crested breakwater (obtained by the Navier-Stokes equations) are smaller than the heights of waves passing through a high-crested breakwater (obtained by the one-layer Boussinesq equations) and larger than the heights of waves passing through a submerged breakwater (obtained by the two-layer Boussinesq equations). As the cnoidal wave nonlinearity becomes smaller or the porous breakwater width becomes narrower, the heights of transmitting waves obtained by the one-layer and two-layer Boussinesq equations become closer to the height of overtopping waves obtained by the Navier-Stokes equations.