• East Asian mathematical journal
• /
• v.25 no.2
• /
• pp.159-169
• /
• 2009

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.13 no.1
• /
• pp.39-46
• /
• 1993

The need to develop method which can improve the shape design efficiency using high quality approximation is being brought up. In this study, to perform shape optimal design of three-dimensional continuum structures an efficient approximation method for stress constraints is proposed, based on expanding the nodal forces in Taylor series with respect to shape variables. Numerical examples are performed using the 3-D cantilever beam and fixed-fixed beam and compared with other method to demonstrate the efficiency and convergence rate of the Force Approximation method. It is shown that by taking advantage of this high quality approximation, the total number of finite element analysis required for shape optimization of 3-D continuum structures can be reduced significantly, resulting to the same level of efficiency achieved previously in sizing optimization problems. Also, shape representation by super curve technique applied to obtain optimal shape finds useful method.

• Journal of the Chungcheong Mathematical Society
• /
• v.18 no.1
• /
• pp.101-116
• /
• 2005

Using the iterative method, we derive an controller realization of the bilinear system, which is resulted from the system reformulation. We utilize Banach Fixed Point Theorem to support proposed controller, and the simulation results are also illustrated to verify usefulness of this technique.

• 한국전산유체공학회:학술대회논문집
• /
• 2006.10a
• /
• pp.28-29
• /
• 2006

Computational approaches for the aerodynamic design and optimization are introduced. In this paper the aerodynamic design methods and applications, which have been applied to various aerospace vehicles at Konkuk University, are introduced. It is shown that system approximation technique reduces computational cost for CFD analysis and improves efficiency for the design optimization process.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.8
• /
• pp.921-931
• /
• 2011

This paper presents a data-fitting technique in which a B-spline hypervolume is used to approximate a given data set of scattered data samples. We describe the implementation of the data structure of a B-spline hypervolume, and we measure its memory size to show that the representation is compact. The proposed technique includes two algorithms. One is for the determination of the knot vectors of a B-spline hypervolume. The other is for the control points, which are determined by solving a linear least-squares minimization problem where the solution is independent of the data-set complexity. The proposed approach is demonstrated with various data-set configurations to reveal its performance in terms of approximation accuracy, memory use, and running time. In addition, we compare our approach with existing methods and present unconstrained optimization examples to show the potential for various applications.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
• /
• 2002.05a
• /
• pp.359-364
• /
• 2002

In case of pn control chart often used in mass production system of plant industry and so on, we could evaluate it's performance by the approximation to normal distribution. It has many differences according to sample sizes and defective fraction, and have disadvantage that needs much samples to use the normal distribution approximation. Existent control charts can not detect the cause of process something wrong because it is taking the sampling intervals of fixed length about all times from the process. Therefore, to overcome this shortcoming we use VSI(variable sampling intervals) techniques in this paper. This technique takes a long sampling interval to have the next sampling point if the sample point is in stable state, and if the sample point is near control lines, it takes short sampling interval because the probability to escape control limit is high. To analyze performance of pn control charts that have existent fixed sampling intervals(FSI) and that use VSI technique, we compare ATS of two charts, and analyze the performance of each control chart by the sample sizes, process fraction defective and control limits that Ryan and Schwertman had proposed.

• Structural Engineering and Mechanics
• /
• v.45 no.1
• /
• pp.95-110
• /
• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Journal of Korean Association for Spatial Structures
• /
• v.4 no.3 s.13
• /
• pp.77-84
• /
• 2004

This study presents an effective stiffness-based optimal technique to control quantitatively lateral drift for tall frameworks using composit member subject to lateral loads. To this end, displacement sensitivity depending on behavior characteristics of tall frameworks is established and approximation concept that preserves the generality of the mathematical programming and can efficiently solve large scale problems is introduced. Specifically, under the 'constant-shape' assumption, resizing techniqe of composite member is developed. Two types of 50 story frameworks are presented to illustrate the features of the quantitative lateral drift control technique proposed in this study.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.2
• /
• pp.45-55
• /
• 1994

In this paper, a block based image approximation technique using the Self Affine System(SAS) from the fractal theory is suggested. Each block of an image is divided into 4 tiles and 4 affine mapping coefficients are found for each tile. To find the affine mapping cefficients that minimize the error between the affine transformed image block and the reconstructed image block, the matrix euation is solved by setting each partial differential coefficients to aero. And to ensure the convergence of coding block. 4 uniformly partitioned affine transformation is applied. Variable block size technique is employed in order to applynatural image reconstruction property of fractal image coding. Large blocks are used for encoding smooth backgrounds to yield high compression efficiency and texture and edge blocks are divided into smaller blocks to preserve the block detail. Affine mapping coefficinets are found for each block having 16$\times$16, 8$\times$8 or 4$\times$4 size. Each block is classified as shade, texture or edge. Average gray level is transmitted for shade bolcks, and coefficients are found for texture and edge blocks. Coefficients are quantized and only 16 bytes per block are transmitted. Using the proposed algorithm, the computational load increases linearly in proportion to image size. PSNR of 31.58dB is obtained as the result using 512$\times$512, 8 bits per pixel Lena image.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.277-302
• /
• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.