• The Pure and Applied Mathematics
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• 제16권2호
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• pp.199-212
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• 2009

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.137-155
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• 2021

In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Finally, we give some applications of our results in discrete and functional fractional economic systems.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.131-143
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• 2019

In this study, the nonlinear vibration analysis of the composite nanoplate is studied. The composite nanoplate is fabricated by the functional graded (FG) core and lipid face sheets. The material properties in the FG core vary in three directions. The Kelvin-Voigt model is used to study the viscoelastic effect of the lipid layers. By using the Von-Karman assumptions, the nonlinear differential equation of the vibration analysis of the composite nanoplate is obtained. The foundation of the system is modeled by the nonlinear Pasternak foundation. The Bubnov-Galerkin method and the multiple scale method are used to solve the nonlinear differential equation of the composite nanoplate. The free and force vibration analysis of the composite nanoplate are studied. A comparison between the presented results and the reported results is done and good achievement is obtained. The reported results are verified by the results which are obtained by the Runge-Kutta method. The effects of different parameters on the nonlinear vibration frequencies, the primary, the super harmonic and subharmonic resonance cases are investigated. This work will be useful to design the nanosensors with high biocompatibility.

• Macromolecular Research
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• 제15권6호
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• pp.506-512
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• 2007

2,3-Di-(2'-hydroxyethoxy)-4'-nitrostilbene (3) was prepared and condensed with terephthaloyl chloride, adipoyl chloride, and sebacoyl chloride to yield novel Y-type polyesters (4-6) containing the NLO-chromophores 2,3-dioxynitrostilbenyl groups, which constituted parts of the polymer backbones. Polymers 4-6 were soluble in common organic solvents such as acetone and N,N-dimethylformamide. Polymers 4-5 showed thermal stability up to $300^{\circ}C$ in thermogravimetric analysis with glass transition temperatures $(T_g)$, obtained from differential scanning calorimetry, in the range $81-95^{\circ}C$. The second harmonic generation (SHG) coefficients $(d_{33})$ of the poled polymer films at the 1064 nm fundamental wavelength were around $3.68{\times}10^{-9}$ esu. The dipole alignment exhibited high thermal stability up to $T_g$, and there was no SHG decay below $T_g$ due to the partial main-chain character of the polymer structure.

• The Transactions of the Korean Institute of Electrical Engineers A
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• 제48권8호
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• pp.1046-1053
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• 1999

The musculotendon model is presented to show the declines in muscle force and shortening velocity during muscle fatigue due to the repeated functional electrical stimulation (FES). It consists of the nonlinear activation and contraction dynamics including physiological concepts of muscle fatigue. The activation dynamics represents $Ca^{2+}$ binding and unbinding mechanism with troponins of cross-bridges in sarcoplasm. It has the constant binding rate or activation time constant and two step nonlinear unbinding rate or inactivation time constant. The contraction dynamics is the modified Hill type model to represent muscle force - length and muscle force - velocity relations. A muscle fatigue profile as a function of the intracellular acidification, pH is applied into the contraction dynamics to represent the force decline. The computer simulation shows that muscle force and shortening velocity decline in stimulation time. And we validate the model. The model can predicts the proper muscle force without changing its parameters even when existing the estimation errors of the optimal fiber length. The change in the estimate of the optimal fiber length has an effect only on muscle time constant in transient period not on the tetanic force in the steady-state and relaxation periods.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.921-925
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• 2022

In this paper, we completely describe the automorphism group of the bounded Kohn-Nirenberg domain in [5].

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.14-19
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• 1993

In this paper, we proposed an indirect learning and direct adaptive control schemes using neural networks, i.e., composite adaptive neural control, for a class of continuous nonlinear systems. With the indirect learning method, the neural network learns the nonlinear basis of the system inverse dynamics by a modified backpropagation learning rule. The basis spans the local vector space of inverse dynamics with the direct adaptation method when the indirect learning result is within a prescribed error tolerance, as such this method is closely related to the adaptive control methods. Also hash addressing technique, similar to the CMAC functional architecture, is introduced for partitioning network hidden nodes according to the system states, so global neuro control properties can be organized by the local ones. For uniform stability, the sliding mode control is introduced when the neural network has not sufficiently learned the system dynamics. With proper assumptions on the controlled system, global stability and tracking error convergence proof can be given. The performance of the proposed control scheme is demonstrated with the simulation results of a nonlinear system.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Journal of Ship and Ocean Technology
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• 제12권2호
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.