• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.33-45
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• 2002

An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.491-502
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• 2019

This paper explores the analytical buckling solution of rectangular thin plates by the finite integral transform method. Although several analytical and numerical developments have been made, a benchmark analytical solution is still very few due to the mathematical complexity of solving high order partial differential equations. In solution procedure, the governing high order partial differential equation with specified boundary conditions is converted into a system of linear algebraic equations and the analytical solution is obtained classically. The primary advantage of the present method is its simplicity and generality and does not need to pre-determine the deflection function which makes the solving procedure much reasonable. Another advantage of the method is that the analytical solutions obtained converge rapidly due to utilization of the sum functions. The application of the method is extensive and can also handle moderately thick and thick elastic plates as well as bending and vibration problems. The present results are validated by extensive numerical comparison with the FEA using (ABAQUS) software and the existing analytical solutions which show satisfactory agreement.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1193-1202
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• 2020

We consider the integral ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$ as a function of the positive integer n. We show that there exists an asymptotic series in ${\frac{1}{n}}$ and compute the first terms of this series together with an explicit error bound.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.485-494
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• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.73-85
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• 2005

In this paper a criterion for $L^1-convergence$ of a new modified sine sums is obtained by using $Ces{\grave{a}}ro$ means of integral and non-integral orders.

• Coupled systems mechanics
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• v.8 no.1
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• pp.1-17
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• 2019

The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.667-677
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• 2013

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

• Journal of Power Electronics
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• v.14 no.1
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• pp.82-91
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• 2014

This paper proposes a compensation algorithm for the analog rotor position errors caused by nonideal sinusoidal encoder output signals including offset and gain errors. In order to achieve a much higher resolution, position sensors such as resolvers or incremental encoders can be replaced by sinusoidal encoders. In practice, however, the periodic ripples related to the analog rotor position are generated by the offset and gain errors between the sine and cosine output signals of sinusoidal encoders. In this paper, the effects of offset and gain errors are easily analyzed by applying the concept of a rotating coordinate system based on the dq transformation method. The synchronous d-axis signal component is used directly to detect the amplitude of the offset and gain errors for the proposed compensator. As a result, the offset and gain errors can be well corrected by three integrators located on the synchronous d-axis component. In addition, the proposed algorithm does not require any additional hardware and can be easily implemented by a simple integral operation. The effectiveness of the proposed algorithm is verified through several experimental results.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.64-71
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• 2006

In this paper, a uniform speed controller for an ultrasonic rotary motor is developed using the phase-difference method. The phase difference method uses traveling waves to drive the ultrasonic motor. The traveling waves are obtained by adding two standing waves that have a different phase to each other. A compact phase-difference driver system is designed and integrated by combining VCO(Voltage Controlled Oscillator) and phase shifter. Theoretically the relationship between the phase difference in time and the rotational speed of the ultrasonic motor is sine function, which is verified by experiments. Then a series of experiments under various loading conditions are conducted to characterize the motor's performance that is the relationship between the speed and torque. Proportional-integral control is adopted for the uniform speed control. The proportional control unit calculates the compensating phase-difference using the rotating speed which is measured by an encoder and fed back. Integral control is used to eliminate steady-state errors. Differential control for reducing overshoot is not used since the response of ultrasonic motor is prompt due to its low inertia and friction-driving characteristics. The developed controller demonstrates reasonable performance overcoming disturbing torque and the changes in material properties due to continuous usage.