• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Journal for History of Mathematics
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• v.34 no.2
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• pp.39-54
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• 2021

One of the topics in school mathematics is the relation between the roots and the coefficients of equations. It deals with the way to find the roots out of the coefficients of equations. One of the concepts derived from the theory of equations is symmetric functions. Symmetry is a kind of functionality of human cognition. It is, in mathematics, geometrically related to the congruence and the similarity of figures, and algebraically a kind of invariants. We look at stories on the appearance of symmetric functions through the development of the theory of equations.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.431-448
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• 2018

This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^*{\bar{X}}^{-1}A=Q$, where A, Q are given complex matrices with Q positive definite. We show that such a matrix equation always has a unique positive definite solution and if A is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^*{\bar{X}}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^*Y^{-1}B=Q$, where B, Q are uniquely determined by A. Then several effective numerical algorithms for the unique positive definite solution of $X-A^*{\bar{X}}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.

• East Asian mathematical journal
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• v.33 no.1
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• pp.1-9
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• 2017

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• Journal of Nutrition and Health
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• v.26 no.6
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• pp.793-803
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• 1993

This study was designed to measure viscosity, osmolality and in vitro flow rates via nasogastric tubes for 6 types of commercially available and 9 hospital-blenderized enteral solutions and to examine the effect of viscosity and osmolaility of enteral formula on the flow rates in gravity drip administration. Each solution was infused through 18, 16, 14, 12 French sizes of silicone rubber tube. Flow rates were measured six times at $25^{\circ}C$ using formula bags and drip sets hung at a uniform height on a intravenous drip stand with tube uniformly positioned in collecting container. Viscosity ranged widely from 16.0 to 195.5 cps with mean, 64.61$\pm$64.42 for hospital-blenderized formula while mean viscosity of commercial formula was 7.60$\pm$4.84 cps. Mean osmolality of commercial formula and hospital-blenderized formula were 370$\pm$100.80, 540.33$\pm$89.37 mOsm/kg respectively. There was negative relationship between viscosity of formula and flow rates through tubes but no significant relationship between flow rates and osmolalty. Some of hospital-blenderized formula was too viscous to be infused througth tube with gravity drip administration and the recipe of formula requires to be modiifed. On the other hand, commercial formula with the low viscosity flows too rapidly with large bore size tubes. Smaller size of tube must be selected for hyperosmolar solution to decrease possible side effects associated with tube feeding. Two kinds of regression equations for flow rates obtained according to viscosity and tube sizes were also presented for the purpose of practical uses. In conclusion, this study emphasizes that viscosity of fomula, osmolality, patient's tolerance and comfort, caloric density should be considered in the selection of tubes for gravify drip administration.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.329-338
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• 1997

In this paper a general analytical approach is proposed to analyse the nonlinear response of elastic cable under complex loads. The effect of temperature change on the cable is also considered. From the vertical equilibrium equations of cable, the general analytical formula of vertical displacement is derived. Based on the vertical displacement formula and on the compatibility condition of the cable, the dimensionless equation with respect to cable tension is established. By means of such analytical procedures, the exact solutions of various cable problems can be obtained quickly. The example given in this paper shows that the new procedure is efficient for practical analysis and can be easily implemented by a general computer program without the superposition problem which there has always been in traditional analytical methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1921-1930
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• 1993

In order to evaluate the inlet pressure correctly, the full Navier-Stokes equations are solved numerically for the computational domain which covers the cavity region between pads as well as the bearing film. A nonuiform grid system is adopted to reduce the number of grid points, and the numerical solutions are obtained for a wide range of Reynolds number in laminar regime with various values of the distance between pads. The numerical results show that the inlet pressure is significantly affected by Reynolds number and the distance between pads. An expression for the loss coefficient in terms of Reynolds number and non-dimensional distance between pads is obtained on the basis of the numerical results. It is found that the inlet pressure over the whole range of numerical solutions can be fairly accurately estimated by applying the formula for the loss coefficient to the extended Bernoulli equation.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.259-274
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• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.