• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.379-385
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• 2008

Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.393-401
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• 2007

In the present paper we introduce the subclass $S^{\lambda}_{a,c}(p,A,B)$ of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5].

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.119-122
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• 1988

In recent years, several authors have dealt with the fraction derivative [1], in special functions [2], convolution integral equation [5], differintegral equation [4], the derivative of H-function [6], and some other applications. The present paper considers the fraction derivatve in the form of differential eqiation.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.545-565
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• 2016

In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = and ${\Omega}$ = stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1579-1588
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• 2003

In this paper, the finite element equations for the transient linear viscoelastic stress analysis are presented in time domain, whose variational formulation is derived by using the Galerkin's method based on the equations of motion in time integral. Since the inertia terms are not included in the variational formulation, the time integration schemes such as the Newmark's method widely used in the classical dynamic analysis based on the equations of motion in time differential are not required in the development of that formulation, resulting in a computationally simple and stable numerical algorithm. The viscoelastic material is assumed to behave as a standard linear solid in shear and an elastic solid in dilatation. To show the validity of the presented method, two numerical examples are solved nuder plane strain and plane stress conditions and good results are obtained.

• Journal of KSNVE
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• v.9 no.4
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• pp.778-784
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• 1999

A method for obtaining the motion of an impact system whose primary and secondary system are composed of lumped masses, springs and dampers, and all the contacts are made through spring and damping elements is presented. The frequency response functions derived from the equations of motion and the impulse response functions obtained from the inverse Fourier transform of the derived frequency response functions are used for the calculation of the system responses. The procedure developed for the calculation of displacements and force time-histories was based on the convolution integrals of impulse response functions and forces applied to the systems. Time histories of displacements and contact forces are obtained for the case where a random excitation is applied to a point in the system. Impact statistics such as contact forces and the time between impacts calculated from those time histories is presented.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.288-295
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• 1993

Three dimensional linear transient wave propagation over a constant depth due to bottom disturbances is presented. Present solution based on Seo(1993) is expressed in terms of a convolution integral of source function. For three cases of different source functions, each solution is proved to satisfy the corresponding initial condition. The general feature of wave height attenuation resulted from the dispersion effect is shown and discussed by numerical results of the solutions.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.5
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• pp.18-22
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• 1989

We calculate the distribution of the induced current on the strip by the TE waves on the infinite conducting strip. The boundary equations represented as the spatial domain function becomevery complicated equations including convolution integral. As we transform it to the spectral domain, we have a very simple equation expressed by some algebraic multiplication of the current density function and Green's function. It is shown that the computation result of the induced current distribution gives the optimum value, when the stop condition of iteration presented in this paper are satisfied.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.69-78
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• 1995

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine(SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the onlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increament. The method is applied to a nonlinear generic model of the high pressure oxygen turthods, the convolution approach proved to be more accurate and highly more efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance(IHB) method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic(subsynchronous) responses of the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-totor models to their coordinates at the bearing clearances.