• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.743-760
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• 2024

In this paper, we are devoted to study a forth order curve flow for a smooth closed curve in centro-affine geometry. Firstly, a new evolutionary equation about this curve flow is proposed. Then the related geometric quantities and some meaningful conclusions are obtained through the equation. Next, we obtain finite order differential inequalities for energy by applying interpolation inequalities, Cauchy-Schwartz inequalities, etc. After using a completely new symbolic expression, the n-order differential inequality for energy is considered. Finally, by the means of energy estimation, we prove that the forth order curve flow has a smooth solution all the time for any closed smooth initial curve.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4307-4316
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• 2023

In this paper, modal effective mass for asymmetric fluid-structure interaction system is defined and equations for its calculation is derived. To establish consistency, modal effective mass in symmetric structure only system is briefly reviewed, followed by a definition of the modal effective mass in asymmetric system. The equations for calculating modal effective mass in asymmetric system are derived by utilizing the properties of left and right eigenvectors. To simplify the equations, the assumption is made that the mass matrix is only affected by the fluid. The simplified equation is then compared to the equation already used in ANSYS. Finally, the validity of the modal effective mass definition and derivation in this paper is demonstrated through a simple example.

• Journal of Energy Engineering
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• v.16 no.1 s.49
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• pp.46-52
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• 2007

The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.272-280
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• 2023

We study the numerical analysis for the Cahn-Hilliard (CH) equation using the decoupled projection (DP) method. The CH equation is a fourth order nonlinear partial differential equation that is hard to solve. Therefore, various of numerical schemes have been proposed to solve the CH equation. To verify the relation of each existing scheme for the CH equation, we consider the DP method for linear convex splitting schemes. We present the numerical experiments to demonstrate our analysis. Throughout this study, it is expected to construct a novel numerical scheme using the relation with existing numerical schemes.

• Bulletin of the Korean Chemical Society
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• v.32 no.12
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• pp.4341-4346
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• 2011

Impact sensitivity, one of the most important screening factors for novel high energy density materials (HEDMs), was predicted by use of quantitative structure-property relationship (QSPR) based on the electrostatic potential (ESP) values calculated on the van der Waals molecular surface (MSEP). Among various 3D descriptors derived from MSEP, we utilized total and positive variance of MSEP, and devised a new QSPR equation by combining three other parameters. We employed 37 HEDMs bearing a benzene scaffold and nitro substituents, which were also utilized by Rice and Hare. All the molecular structures were optimized at the B3LYP/6-31G(d) level of theory and confirmed as minima by the frequency calculations. Our new QSPR equation provided a good result to predict the impact sensitivities of the molecules in the training set including zwitterionic molecules.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.225-233
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• 2001

In this paper, we establish the energy inequalities for second order quasilinear hyperbolic mixed problems in the domain R_(sup)n.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.286-290
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• 2005

We consider the poisson equation where the functions involved are periodic including the solution function. Let $R=[0,1]{\times}[0,l]{\times}[0,1]$ be the region of interest and let $\phi$(x,y,z) be an arbitrary periodic function defined in the region R such that $\phi$(x,y,z) satisfies $\phi$(x+1, y, z)=$\phi$(x, y+1, z)=$\phi$(x, y, z+1)=$\phi$(x,y,z) for all x,y,z. We describe a very simple method for solving the equation ${\nabla}^2u(x, y, z)$ = $\phi$(x, y, z) based on the cubic spline interpolation of u(x, y, z); using the requirement that each interval [0,1] is a multiple of the period in the corresponding coordinates, the Laplacian operator applied to the cubic spline interpolation of u(x, y, z) can be replaced by a square matrix. The solution can then be computed simply by multiplying $\phi$(x, y, z) by the inverse of this matrix. A description on how the storage of nearly a Giga byte for $20{\times}20{\times}20$ nodes, equivalent to a $8000{\times}8000$ matrix is handled by using the fuzzy rule table method and a description on how the shape preserving property of the Laplacian operator will be affected by this approximation are included.

• Transactions of the Korean hydrogen and new energy society
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• v.34 no.2
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• pp.162-168
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• 2023

The fast refueling process of compressed hydrogen has an important impact on the filling efficiency and safety. With the development and use of hydrogen energy, the demand for precision measurement of filling hydrogen thermodynamic parameters is also increasing. In this paper, the compressibility factor calculation model of high-pressure hydrogen gas was studied, and the basic equation of state and thermo-physical parameters were calculated. The hydrogen density data provided by the National Institute of Standards and Technology was compared with the calculation results of each model. Results show that at a pressure of 0.1-100 MPa and a temperature of 233-363 K, the calculation accuracy of the Zheng-Li equation of state was less than 0.5%. In the range of 0.1-70 MPa, the accuracy of Redich-Kwong equation is less than 3%. The hydrogen pressure more influences on the compressibility factor than the hydrogen temperature does. Using the Zheng-Li equation of state to calculate the compressibility factor of on-board high pressure hydrogen can obtain high accuracy.

• Journal of Trauma and Injury
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• v.36 no.4
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• pp.337-342
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• 2023

Purpose: This study aimed to compare the resting energy expenditure (REE) measured using indirect calorimetry with that estimated using predictive equations in severe trauma patients to determine the appropriate caloric requirements. Methods: Patients admitted to the surgical intensive care unit between January 2020 and March 2023 were included in this study. Indirect calorimetry was used to measure the patients' REE values. These values were subsequently compared with those estimated using predictive equations: the weight-based equation (rule of thumb, 25 kcal/kg/day), Harris-Benedict, Ireton-Jones, and the Penn State 2003 equations. Results: A total of 27 severe trauma patients were included in this study, and 47 indirect calorimetric measurements were conducted. The weight-based equation (mean difference [MD], -28.96±303.58 kcal) and the Penn State 2003 equation (MD, - 3.56±270.39 kcal) showed the closest results to REE measured by indirect calorimetry. However, the REE values estimated using the Harris-Benedict equation (MD, 156.64±276.54 kcal) and Ireton-Jones equation (MD, 250.87±332.54 kcal) displayed significant differences from those measured using indirect calorimetry. The concordance rate, which the predictive REE differs from the measured REE value within 10%, was up to 36.2%. Conclusions: The REE values estimated using predictive equations exhibited substantial differences from those measured via indirect calorimetry. Therefore, it is necessary to measure the REE value through indirect calorimetry in severe trauma patients.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.06a
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• pp.549-550
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• 2007