• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.501-516
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• 2013

The well-known Vlasov-Poisson equation describes plasma physics as nonlinear first-order partial differential equations. Because of the nonlinear condition from the self consistency of the Vlasov-Poisson equation, many problems occur: the existence, the numerical solution, the convergence of the numerical solution, and so on. To solve the problems, a viscosity term (a second-order partial differential equation) is added. In a viscosity term, the Vlasov-Poisson equation changes into a parabolic equation like the Fokker-Planck equation. Therefore, the Schauder fixed point theorem and the classical results on parabolic equations can be used for analyzing the Vlasov-Poisson equation. The sequence and the convergence results are obtained from linearizing the Vlasove-Poisson equation by using a fixed point theorem and Gronwall's inequality. In numerical experiments, an implicit first-order scheme is used. The numerical results are tested using the changed viscosity terms.

• Perinatology
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• v.29 no.4
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• pp.159-164
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• 2018

Objective: To compare neonatal respiratory morbidity of twins according to birth order related to gestational age and mode of delivery. Methods: We performed the retrospective research of the medical records of 3,224 neonates (1,612 twin pairs) born in a single center from January 2011 to December 2015. Subjects were classified into four gestational age groups: very (<32 weeks), moderate (32-33 weeks), late (34-36 weeks) preterm, and term (${\geq}37weeks$) groups. We investigated clinical characteristics and respiratory morbidity according to birth order related to gestational age group and mode of delivery. Results: We found increased risk of respiratory morbidity in second-born twin than first-born twin (P=0.039). Second-born twin was associated with increased risk of respiratory distress syndrome (RDS) in late preterm group (odds ratio [OR] 2.8, 95% confidence interval [CI] 1.30-5.95), and transient tachypnea of newborn in term group (OR 1.4, 95% CI 1.03-1.81). In vaginal delivery mode, there was no difference of respiratory morbidity between first and second-born twin in each group, but in cases of Cesarean delivery, second-born twin was related with a greater risk of RDS in late preterm group (OR 2.3, 95% CI 1.07-5.09). Birth order and Cesarean section independently increased the risk of RDS (adjusted OR [aOR] 1.69, 95% CI 1.12-2.54; aOR 2.14, 95% CI 1.25-3.66, respectively). Conclusion: Second-born twin and Cesarean delivery are associated with increased risk of RDS, especially in late preterm twins.

• Journal of Astronomy and Space Sciences
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• v.20 no.1
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• pp.11-20
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• 2003

A method for estimating the NORAD SGP4 atmospheric drag term from minimum osculating orbit states, i.e., two osculating orbits, is developed. The first osculating orbit state is converted into the NORAD TLE-type mean orbit state by iterative procedure. Then the converted TLE is propagated to the second orbit state using the SGP4 model with the incremental SGP4 drag term. The iterative orbit propagation procedure is finished when the difference of the two osculating semi-major axes between the propagated orbit and the given second orbit is minimized. In order to minimize the effect of the short-term variations of the osculating semi-major axis, the osculating argument of latitude of the second orbit is propagated to the same argument of latitude of the first orbit. The method is applied to the estimation of the NORAD-type TLE for the KOMPSAT-1 spacecraft. The SGP4 drag terms are estimated from both NORAD SGP4 orbit propagation and the numerical orbit propagation results. Variations of the estimated drag terms are analyzed for the KOMPSAT-1 satellite orbit determination results.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.608-615
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• 1998

In this paper a second-order iterative learning control algorithm with feedback is proposed for the trajectory-tracking control of nonlinear dynamic systems with unidentified parameters. In contrast to other known methods, the proposed teaming control scheme utilize more than one past error history contained in the trajectories generated at prior iterations, and a feedback term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances or system parameter variations. The convergence proof of the proposed algorithm is given in detail, and the sufficient condition for the convergence of the algorithm is provided. We also discuss the convergence performance of the algorithm when the initial condition at the beginning of each iteration differs from the previous value of the initial condition. The effectiveness of the proposed algorithm is shown by computer simulation result. It is shown that, by adding a feedback term in teaming control algorithm, convergence speed, robustness to disturbances and robustness to unmatched initial conditions can be improved.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.765-774
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• 2005

The orthogonality of polynomials plays an important role in many areas and in many cases only finite orthogonalities are used. Concerning this fact we find characterizations of a finite orthogonal polynomial system satisfying a second order differential equation and then give several examples.

• Journal of Korea Water Resources Association
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• v.44 no.2
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• pp.145-156
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• 2011

Two dimensional numerical model of high-order accuracy is developed to analyze complex flow including transition flow, discontinuous flow, and wave propagation to dry bed emerging at natural river flow. The bed slope term of two dimensional shallow water equation consisting of integral conservation law is treated efficiently by applying quasi-steady wave propagation scheme. In order to apply Finite Volume Method using Fractional Step Method, MUSCL scheme is applied based on HLL Riemann solver, which is second-order accurate in time and space. The TVD method is applied to prevent numerical oscillations in the second-order accurate scheme. The developed model is verified by comparing observed data of two dimenstional levee breach experiment and dam breach experiment containing structure at lower section of channel. Also effect of the source term is verified by applying to dam breach experiment considering the adverse slope channel.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1644-1651
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• 2022

This paper focuses on the power-level control of nuclear power plants (NPPs) in the presence of lumped disturbances. An adaptive second-order nonsingular terminal sliding mode control (ASONTSMC) scheme is proposed by resorting to the second-order nonsingular terminal sliding mode. The pre-existing mathematical model of the nuclear reactor system is firstly described based on point-reactor kinetics equations with six delayed neutron groups. Then, a second-order sliding mode control approach is proposed by integrating a proportional-derivative sliding mode (PDSM) manifold with a nonsingular terminal sliding mode (NTSM) manifold. An adaptive mechanism is designed to estimate the unknown upper bound of a lumped uncertain term that is composed of lumped disturbances and system states real-timely. The estimated values are then added to the controller, resulting in the control system capable of compensating the adverse effects of the lumped disturbances efficiently. Since the sign function is contained in the first time derivative of the real control law, the continuous input signal is obtained after integration so that the chattering effects of the conventional sliding mode control are suppressed. The robust stability of the overall control system is demonstrated through Lyapunov stability theory. Finally, the proposed control scheme is validated through simulations and comparisons with a proportional-integral-derivative (PID) controller, a super twisting sliding mode controller (STSMC), and a disturbance observer-based adaptive sliding mode controller (DO-ASMC).

• International Journal of Computer Science & Network Security
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• v.21 no.2
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• pp.77-87
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• 2021

In this study, a novel improved second order Radial Basis Function Neural Network based method with excellent scheduling capabilities is used for the dynamic prediction of short and long-term energy required applications. The effectiveness and the reliability of the algorithm are evaluated using training operations with New England-ISO database. The dynamic prediction algorithm is implemented in Matlab and the computation of mean absolute error and mean absolute percent error, and training time for the forecasted load, are determined. The results show the impact of temperature and other input parameters on the accuracy of solar Photovoltaic load forecasting. The mean absolute percent error is found to be between 1% to 3% and the training time is evaluated from 3s to 10s. The results are also compared with the previous studies, which show that this new method predicts short and long-term load better than sigmoidal neural network and bagged regression trees. The forecasted energy is found to be the nearest to the correct values as given by England ISO database, which shows that the method can be used reliably for short and long-term load forecasting of any electrical system.