• Coupled systems mechanics
• /
• v.1 no.4
• /
• pp.345-360
• /
• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.683-699
• /
• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.21 no.4
• /
• pp.1-10
• /
• 2013

This paper addresses the derivation of 6-DOF equation of Tanker and Receiver's aircraft for aerial refueling. The new set of nonlinear equations are derived in terms of the relative translational and rotational motion of receiver aircraft respect to the tanker aircraft body frame. Further the wind effect terms due to the tanker's turbulence are included. The derivation of absolute dynamic equation for tanker aircraft written in the inertial frame is calculated from the relative dynamics equations of receiver. The derived relative and absolute equations are implemented the simulation in the same flight conditions to verify the relative motion and compare the trim results by using the MATLAB/SIMULINK program.

• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.881-890
• /
• 1998

Sufficient conditions for forced oscillations of the solutions of impulsive nonlinear parabolic differential-difference equations are obtained.

• Korean Journal of Community Nutrition
• /
• v.14 no.4
• /
• pp.462-473
• /
• 2009

The purpose of this study is to analyze the accuracy of predictive equations for resting metabolic rate (RMR) in Korean college students. Subjects were 60 healthy Korean college students (30 males, 30 females) aged 18-25 years. RMR was measured by indirect calorimetry. Predicted RMRs were calculated using the Harris-Benedict, Schofield (W)/(WH), FAO/ WHO/UNU(W)/(WH), Owen, Mifflin, Cunningham, Liu, IMNA and Henry (W)/(WH) equations. The accuracy of the equations was evaluated on basis of accurate prediction (the percentage of subjects whose RMR was predicted within 90% to 110% of the RMR measured), mean difference, RMSPE, mean % difference, limits of agreement of Bland- Altman method between predicted and measured RMR. Measured RMR of male and female students were $1833.4{\pm}307.4kcal/day$ and $1454.3{\pm}208.0kcal/day$, respectively. All predictive equations underestimated measured RMR. Of the predictive equations tested, the Harris-Benedict equation (mean difference: -80.4 kcal/day, RMSPE: 236 kcal/day, mean % difference: -3.1%) was the most accurate and precise, but accurate prediction of the equation was only 42%. Thus, this study suggests that the ethnicity-specific predictive equation from Korean people should be developed to improve the accuracy of predicted RMR for Koreans. (Korean J Community Nutrition 14(4) : 462${\sim}$473, 2009)

• Animal Bioscience
• /
• v.34 no.4
• /
• pp.558-566
• /
• 2021

Objective: Objectives were to estimate energy and protein requirements of dairy crossbred steers, as well as to evaluate equations previously described in the literature (HH46 and CS16) to predict the carcass and empty body chemical composition of crossbred dairy cattle. Methods: Thirty-three Holstein×Zebu steers, aged 19±1 months old, with an initial shrunk body weight (BW) of 324±7.7 kg, were randomly divided into three groups: reference group (n = 5), maintenance level (1.17% BW; n = 4), and the remaining 24 steers were randomly allocated to 1 of 4 treatments. Treatments were: intake restricted to 85% of ad libitum feed intake for either 0, 28, 42, or 84 d of an 84-d finishing period. Results: The net energy and the metabolizable protein requirements for maintenance were 0.083 Mcal/EBW0.75/d and 4.40 g/EBW0.75, respectively. The net energy (NEG) and protein (NPG) requirements for growth can be estimated with the following equations: NEG (Mcal/kg EBG) = $0.2973_{({\pm}0.1212)}{\times}EBW^{0.4336_{({\pm}0.1002)}$ and NPG (g/d) = 183.6(±22.5333)×EBG-2.0693(±4.7254)×RE, where EBW, empty BW; EBG, empty body gain; and RE, retained energy. Crude protein (CP) and ether extract (EE) chemical contents in carcass, and all the chemical components in the empty body were precisely and accurately estimated by CS16 equations. However, water content in carcass was better predicted by HH46 equation. Conclusion: The equations proposed in this study can be used for estimating the energy and protein requirements of crossbred dairy steers. The CS16 equations were the best estimator for CP and EE chemical contents in carcass, and all chemical components in the empty body of crossbred dairy steers, whereas water in carcass was better estimated using the HH46 equations.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.841-857
• /
• 1997

We present analysis and some computational methods for boundary optimal and feedback control problems for Navier-Stokes equations. We use one example to illustrate our methodology and ideas which are applicable to general control problems for Navier-Stokes equations. First, we discuss the existence of optimal solutions and derive an optimality system of equations from which an optimal solution may be computed. Then we present a gradient type iterative method. Finally, we present some numerical results.

• Journal of applied mathematics & informatics
• /
• v.36 no.3_4
• /
• pp.271-283
• /
• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.581-589
• /
• 2009

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term and forcing term: $$(r(t)k_1(x(t),x'(t)))'+p(t)k_2(x(t),x'(t))x'(t)+q(t)f(x(t))=0$$. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity. And, as a consequence, our results apply to wider classes of nonlinear differential equations. Some illustrative examples are considered.

• The Korean Journal of Quaternary Research
• /
• v.10 no.1
• /
• pp.19-26
• /
• 1996

This review gives an information on the oxygen isotopic composition of car-bonate and utility of paleotemperature equations to reconstruct the paleoenvironment in the late Quaternary paleoclimatic studies. The introduc-tion of various paleotemperature equations is described with respect to the de-velopment and usefulness. In addition the calculation of paleotemperature in the paleoceanographic and paleoclimatic research is constrained to provide more precise and correct approach in the interpretation of paleotemperature.