• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.515-525
• /
• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

• ETRI Journal
• /
• v.16 no.1
• /
• pp.1-15
• /
• 1994

A computationally-efficient approach to the calculation of the transient field of an acoustic radiator was developed. With this approach, a planar or curved source, radiating either continuous or pulsed waves, is divided into a finite number of shifted and/or rotated versions of an incremental source such that the Fraunhofer approximation holds at each field point. The acoustic field from the incremental source is given by a 2-D spatial Fourier transform. The diffraction transfer function of the entire source can be expressed as a sum of Fraunhofer diffraction pattern of the incremental sources with the appropriate coordinate transformations for the particular geometry of the radiator. For a given spectrum of radiator velocity, the transient field can be computed directly in the frequency domain using the diffraction transfer function. To determine the accuracy of the proposed approach, the impulse response was derived using the inverse Fourier transform. The results obtained agree well with published data obtained using the impulse response approach. The computational efficiency of the proposed method compares favorably to those of the point source method and the impulse response approach.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.6A
• /
• pp.794-801
• /
• 2000

In this paper, the efficient new performance evaluation method for digital communication channels is suggested and verified its efficiency in terms of simulation run-tim for the digital satellite broadcasting satellite TV channel. In order to solve the difficulties of the existing Importance Sampling(IS) Technics, we adopted the discrete probability mass function(PMF) in the new method for estimating the statistical characteristics of received signals from the measured Nth order central moments. From the discrete probability mass function obtained with less number of the received signal than the one required in the IS technic, continuous cumulative probability function and its inverse function are exactly estimated by using interpolation and extrapolation technic. And the overall channel is simplified with encoding block, inner channel performance degra-dation modeing block which is modeled with the Uniform Random Number Generator (URNG) and concatenated Inverse Cummulative Pr bility Distribution function, and decoding block. With the simplified channel model, the overall performance evaluation can be done within a drastically reduced time. The simulation results applied to the nonlinear digital satellite broadcasting TV channel showed the great efficiency of the alogrithm in the sense of computer run time, and demonstrated that the existing problems of IS for the nonlinear satellite channels with coding and M-dimensional memory can be completely solved.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.756-761
• /
• 2004

The effects of two important numerical procedures on the high precision structural analysis are investigated in this study. The two numerical procedures include continuous variable approximation and time integration. For the continuous variable approximation, polynomial mode functions generated by the Gram-Schmidt process are introduced and the numerical results obtained by employing the polynomial mode functions are compared to those obtained by classical beam mode functions. The effect of the time integration procedure on the analysis precision is also investigated. It is found that the two procedures affect the precision of structural analysis significantly.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2005.03a
• /
• pp.529-535
• /
• 2005

This paper presents a system identification (SI) scheme in time domain using measured acceleration data. The error function is defined as the time integral of the least squared errors between the measured acceleration and the calculated acceleration by a mathematical model. Damping parameters as well as stiffness properties of a structure are considered as system parameters. The structural damping is modeled by the Rayleigh damping. A new regularization function defined by the L1-norm of the first derivative of system parameters with respect to time is proposed to alleviate the ill-posed characteristics of inverse problems and to accommodate discontinuities of system parameters in time. The time window concept is proposed to trace variation of system parameters in time. Numerical simulation study is performed through a two-span continuous truss subject to ground motion.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.9
• /
• pp.806-811
• /
• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Journal of the Korean Institute of Navigation
• /
• v.21 no.1
• /
• pp.109-118
• /
• 1997

In this paper, applications of multilayer neural networks to control of flexible robot beam are considered. The multilayer nerual networks can be used to approximate any continuous function to a desired degree of accuracy and the weights are updated by Gradient Method. When a flexible beam is rotated by a motor through the fixed end, transverse vibration may occur. The motor torque should be controlled insuch a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible manipulators so that is arrested as soon as possbile at the end of rotation. Accurate control of lightweight beam during the large changes in configuration common to robotic tasks requires dynamic models that describe both rigid body motions, as well as the flexural vibrations. Therefore, a linear dynamic state-space model of for a single link flexible robot beam is derived and PD controller, LQP controller, and inverse dynamical neural networks controller are composed. The effectiveness the proposed control system is confirmed by computer simulation.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.39 no.2
• /
• pp.50-55
• /
• 2002

The standard approach of image resampling is to fit the original image with continuous model and resample the function at a desired rate. We used the B-spline function as the continuous model because it oscillates less than the others. The main purpose of this paper is the derivation of a nonuniform optimal resampling algorithm. To derive it, needing approximation can be computed in three steps: 1) determining the I-spline coefficients by matrix inverse process, 2) obtaining the transformed-spline coefficients by the optimal resampling algorithm derived from the orthogonal projection theorem, 3) converting of the result back into the signal domain by indirect B-spline transformation. With these methods, we can use B-spline in the non-uniform resampling, which is proved to be a good kernel in uniform resampling, and can also verify the applicability from our experiments.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.2
• /
• pp.323-342
• /
• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. 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 $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

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