• Industrial Engineering and Management Systems
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• v.7 no.1
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• pp.9-22
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• 2008

As an extension of a previous work by the authors (Song and Esogbue, 2006), a new algorithm for automated modeling of nonstationary seasonal time series is presented in this paper. Issues relative to the methodology for building automatically seasonal time series models and periodic time series models are addressed. This is achieved by inspecting the trend, estimating the seasonality, determining the orders of the model, and estimating the parameters. As in our previous work, the major instruments used in the model identification process are correlograms of the modeling errors while the least square method is used for parameter estimation. We provide numerical illustrations of the performance of the new algorithms with respect to building both seasonal time series and periodic time series models. Additionally, we consider forecasting and exercise the models on some sample time series problems found in the literature as well as real life problems drawn from the retail industry. In each instance, the models are built automatically avoiding the necessity of any human intervention.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Childhood Kidney Diseases
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• v.20 no.2
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• pp.50-56
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• 2016

Purpose: Nocturnal enuresis (NE) is one of the most common problems in childhood. NE has a multifactorial etiology and is influenced by sleep and arousal mechanisms. The aim of the present study was to prospectively evaluate sleep problems and patterns in children with NE compared with normal healthy controls. Methods: Twenty-eight children with NE and 16 healthy controls were included in the study. To evaluate sleep habits and disturbances, parents and children filled out a questionnaire that included items about sleep patterns and sleep-related behaviors prior to treatment for NE. Demographic factors and other data were compared for the two groups based on the responses to the sleep questionnaire. Results: Night awakening, sleepwalking, and periodic limb movements were more prevalent in children with NE, but symptoms of sleep-disordered breathing were not increased in this group. There were statistically significant differences in periodic limb movements and daytime sleepiness between the two groups. Conclusion: Children with NE seemed to have more sleep problems such as night awakening, sleepwalking, and periodic limb movements. In addition, a higher level of daytime sleepiness and hyperactivity in patients with NE suggested a relationship between NE and sleep disorders.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.353-361
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• 2007

In this paper, we prove the existence of multiple solutions for Neumann and periodic problems. Our main tools are recent general multiplicity theorems proposed by B. Ricceri.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.665-685
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• 2000

The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.107-127
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• 2014

The goal of this note is to describe the asymptotic behaviour of problems set in cylinders when the size of them is becoming infinite. This leads to consider problems in unbounded domains as well as new singular perturbations issues.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.215-230
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• 2001

In this paper, an asymptotic two-scale method is developed for solving vibration problem of long periodic structures. Such eigenmodes appear as a slow modulations of a periodic one. For those, the present method splits the vibration problem into two small problems at each order. The first one is a periodic problem and is posed on a few basic cells. The second is an amplitude equation to be satisfied by the envelope of the eigenmode. In this way, one can avoid the discretisation of the whole structure. Applying the Floquet method, the boundary conditions of the global problem are determined for any order of the asymptotic expansions.

• Journal of Aerospace System Engineering
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• v.14 no.3
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• pp.17-23
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• 2020

In this paper, the efficient periodic unsteady flow analysis is developed by using a Chebyshev collocation operator applied to the time differential term of the governing equations. The partial implicit time integration method was also applied in the governing equation for a fluid, which means flux terms were implicitly processed for a time integration and the time derivative terms were applied explicitly in the form of the source term by applying the Chebyshev collocation operator. To verify this method, we applied the 1D unsteady Burgers equation and the 2D oscillating airfoil. The results were compared with the existing unsteady flow frequency analysis technique, the Harmonic Balance Method, and the experimental data. The Chebyshev collocation operator can manage time derivatives for periodic and non-periodic problems, so it can be applied to non-periodic problems later.