• Honam Mathematical Journal
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• v.44 no.1
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• pp.17-25
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• 2022

The Hermite-Hadamard integral inequality for F_h-convex functions on time scales is established. The applicability of our results ranges from Optimization problems to Calculus of Variations and to Economics. Application to the Calculus of Variations on time scales is discussed.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.85-92
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• 2024

In this work we give the necessary and sufficient conditions for f-biharmonic curves in three-dimensional generalized symmetric spaces.

• Smart Structures and Systems
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• v.25 no.2
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• pp.219-228
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• 2020

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.53 no.3
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• pp.129-134
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• 2004

To analyze the performance of the gas circuit breaker(GCB), the flow field variables such as temperature, pressure and density should be evaluated accurately In the puffer chamber of puffer type GCB, the pressure rise may Exceed 20 bar and in this range of high pressure, $SF_6$ gas deviates the ideal gas property. Therefore, the real gas property of $SF_6$ should be taken into consideration for the accurate analysis of flow field. This paper presents the analysis technique of cold gas flow in GCB employing the real gas state equation of SF6. The FVFLIC method is Employed to solve the axisymmetric Euler equation. To reduce the computational effort of real gas state equation, the relationship between density and pressure is approximated by the polynomial at the temperature of 300K. The proposed method is applied to the test GCB model and simulation results show good agreement with the experimental ones.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.193-207
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• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.496-500
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• 1993

This paper presents an end-point position control of 1-link flexible robot arm by the PID self-tuning fuzzy algorithm. The governing equation is derived by the extended Hamilton's principle and based on the Bernoullie-Euler beam theory. The governing equation is solved by applying the Laplace transform and the numerical inversion method. The arm is mounted on the translational mechanism driven by a ballscrew whose rotation is controlled by dcservomotor. Tip position is controlled by the PID self-tuning fuzzy algorithm so that it follows a desired position. This paper shows the experimental and theoretical results of tip dispalcement, and also shows the good effects reducing the residual vibration of the end-point.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.826-831
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• 2005

In this paper the effect of moving mass on dynamic behavior of cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The crack is assumed to be in the first mode of fracture. As the depth of the crack is increased, the tip displacement of the cantilever beam is increased. When the crack depth is constant the frequency of a cracked beam is proportional to the spring stiffness.