• Tribology and Lubricants
• /
• v.29 no.5
• /
• pp.275-285
• /
• 2013

The Reynolds equation is commonly used to investigate the lubrication characteristics of a spool valve. However, the applicability of the Reynolds equation is questionable for analyzing a spool valve because cavitation often occurs in the grooves of the valve and the depth of a groove is much higher than the clearance in most cases. In this study, the validity of the Reynolds equation in the spool valve analysis is investigated by comparing the results obtained from the Reynolds equation and those obtained from the Navier-Stokes equation. The results are compared in terms of the lateral forces, friction forces, and volume flow rates (leakages). A significant difference of more than 20% is found in the lateral forces in cases where cavitation occurs and there are many grooves. Therefore, the Navier-Stokes equation should be used to investigate the lubrication characteristics of a spool valve when cavitation occurs and when the spool valve contains many grooves.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.645-651
• /
• 2010

In this note we study positive solutions of the mth order rational difference equation $x_n=(a_0+\sum{{m\atop{i=1}}a_ix_{n-i}/(b_0+\sum{{m\atop{i=1}}b_ix_{n-i}$, where n = m,m+1,m+2, $\ldots$ and $x_0,\ldots,x_{m-1}$ > 0. We describe a sufficient condition on nonnegative real numbers $a_0,a_1,\ldots,a_m,b_0,b_1,\ldots,b_m$ under which every solution $x_n$ of the above equation tends to the limit $(A-b_0+\sqrt{(A-b_0)^2+4_{a_0}B}$/2B as $n{\rightarrow}{\infty}$, where $A=\sum{{m\atop{i=1}}\;a_i$ and $B=\sum{{m\atop{i=1}}\;b_i$.

• Journal of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.255-268
• /
• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Korea-Australia Rheology Journal
• /
• v.11 no.3
• /
• pp.225-232
• /
• 1999

This study presents 1-dimensional simple model for sheet casting or rectangular fiber spinning process. In order to achieve this goal, we introduce the concept of force flux balance at the die exit, which assigns for the extensional flow outside the die the initial condition containing the information of shear flow history inside the die. With the Leonov constitutive equation that predicts non-vanishing second normal stress difference in shear flow, we are able to describe the anisotropic swelling behavior of the extrudate at least qualitatively. In other words, the negative value of the second normal stress difference causes thickness swelling much higher than width of extrudate. This result implies the importance of choosing the rheological model in the analysis of polymer processing operations, since the constitutive equation with the vanishing second normal stress difference is shown to exhibit the characteristic of isotropic swelling, that is, the thickness swell ratio always equal to the ratio in width direction.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.689-706
• /
• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.27 no.7
• /
• pp.52-58
• /
• 2013

The two-dimensional finite difference time domain algorithm is used to numerically reconstruct the electron density profile in O-mode ultrashort pulse reflectometry. A Gaussian pulse is employed as the source of a probing electromagnetic wave. The Gaussian pulse duration is chosen in such a manner as to have its frequency spectrum cover the whole range of the plasma frequency. By using a number of numerical band-pass filters, it is possible to compute the time delays of the frequency components of the reflected signal from the plasma. The electron density profile is reconstructed by substituting the time delays into the Abel integral equation. As a result of simulation, the reconstructed electron density profile agrees well with the assumed profile.

• Proceedings of the KIEE Conference
• /
• 2000.07b
• /
• pp.903-905
• /
• 2000

For an accurate analysis of three dimensional linear magnetostatic problems, a new boundary integral equation formulation is presented. This formulation adopts difference magnetic field concept and uses single layer magnetic surface charge as unknown. The proposed method is capable of eliminating numerical cancellation errors inside ferromagnetic materials. In additions, computing time and storage memory are reduced by 75% in comparison with the reduced and total scalar potential formulation. Two examples are given to show its efficiency and accuracy.

• Kyungpook Mathematical Journal
• /
• v.48 no.2
• /
• pp.173-181
• /
• 2008

We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation $x_{n+1}\;-\;a^2x_{n-1}\;+\;bx_{n-k}\;=\;0$, n = 0, 1,$\cdots$, where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions.

• International Journal of Advanced Culture Technology
• /
• v.6 no.4
• /
• pp.29-38
• /
• 2018

The purpose of this study was to analyze the direct and indirect effects of residential satisfaction on the quality of life and to analyze the difference according to the residence type. The subjects of this study were 422 elderly people aged 65 or older residing in two metropolitan municipalities. The data were analyzed by using structural equation model by multi-group analysis. The results showed that the degree of satisfaction with the residential environment indirectly affected not only the quality of life of the elderly but also social participation activities. As a result of verifying the difference of the residential satisfaction and quality of life path according to the residence type, there was a difference in the route between groups according to the type of residence. This study is significant in that the elderly who have not been interested in the elderly housing policy have been investigated and the relationship between the residential satisfaction and quality of life of the elderly by residence type has been investigated .

• Journal of the Korea Safety Management & Science
• /
• v.23 no.4
• /
• pp.43-48
• /
• 2021

In this study, the experiment was conducted on a fire door(W × H = 0.98 m × 2.19 m) installed on the vestibule. The effective leakage area for each opening angles and closing forces derived from the impulse-momentum equation was compared and analyzed with the experimental results. As a result of the experiment, the major factors affecting the door closing forces were the pressure difference and the area of the door. The difference of door closing forces between measured and calculated values by the impulse-momentum equation showed a deviation of less than ±15% at the opening angles of 5°to 10°. At the door opening angle of 2.5°, the dynamic pressure was much higher than the measured static pressure, and this pressure difference is estimated to be air resistance acting to prevent the door from being completely closed.