• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.819-827
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• 2001

An algorithmic approach to degree reduction of B-spline curves is presented. The new algorithms are based on the blossoming spline curves are obtained by the generalized least square method. The computations are carried out by minimizing the $L_2$ distamce between the two curves.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.679-682
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• 1988

From the viewpoint of general recognition system, B-spline is introduced for the approximation and recognition of human profile contours. Profile contour is approximated to the cublic B-spline curve by least square fitting so that B-Spline nodes nearly correspond with the curvature extrema of the contour. This method is designed for the spline to be good features in recognition, and also showed good approximation compared with the variants of B-spline appraximation.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.12 no.2
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• pp.79-85
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• 2003

An algorithm for fitting with Least Square is a traditional and an effective method in processing with experimental data. Due to the lack of definite representation, it is difficult to fit measured data with free curves or surfaces. B-Spline is usefully utilized to express free curves and surfaces with a few parameters. This paper presents the combination of these two techniques to process the point data measured from CMM and other similar instruments. This research shows tests and comparison of the simulation results from two techniques.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.349-363
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• 2020

Penalized spline is a suitable nonparametric approach in estimating mean model in small area. However, application of the approach in informative sampling in a published article is uncommon. We propose a semiparametric mixed-model using penalized spline under informative sampling to estimate mean of small area. The response variable is explained in terms of mean model, informative sample effect, area random effect and unit error. We approach the mean model by penalized spline and utilize a penalized spline function of the inclusion probability to account for the informative sample effect. We determine the best and unbiased estimators for coefficient model and derive the restricted maximum likelihood estimators for the variance components. A simulation study shows a decrease in the average absolute bias produced by the proposed model. A decrease in the root mean square error also occurred except in some quadratic cases. The use of linear and quadratic penalized spline to approach the function of the inclusion probability provides no significant difference distribution of root mean square error, except for few smaller samples.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.281-294
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• 2016

The paper is devoted to study a mesh-free analysis method of structural elements of engineering structures based on B-spline Wavelet Basis Function. First, by employing the moving-least square method and the weighted residual method to solve the structural displacement field, the control equations and the stiffness equations are obtained. And then constructs the displacement field of the structure by using the m-order B-spline wavelet basis function as a weight function. In the end, the paper selects the plane beam structure and the structure with opening hole to carry out numerical analysis of deformation and stress. The Finite Element Method calculation results are compared with the results of the method proposed, and the calculation results of the relative error norm is compared with Gauss weight function as weight function. Therefore, the clarification verified the validity and accuracy of the proposed method.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• Journal of Advanced Navigation Technology
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• v.9 no.1
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• pp.41-47
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• 2005

In this paper, the performances of various channel estimation schemes for DVB-H system are investigated. The linear interpolation, the second order interpolation, the cubic spline interpolation, and the time-domain interpolation, which are used in frequency domain, are chosen as the channel estimation schemes. We derived the performances of Mean Square Error (MSE), Bit Error Rate (BER), and the complexity of calculation in Rayleigh and Rician fading channel through computer simulations. From the simulation results, the cubic spline interpolation shows the best performance under high $E_b/N_0$ environments.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.102-112
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• 1997

This paper describes the method that can construct kinematically admissible velocity fields for forging of gear-like components which have tooth shape around the cylinder. The kinematically admissible velo- city fields for the various gear-like components, involute spur gear, trapezoidal spline, square spline, ser- ration and trochoidal gear, were constructed by pilling up the velocity components according to the shape of tooth and billet. The billets, of hollow and solid, were Al 2218 and 2024. To verify the method, the analyses and experiments were carried out and compared with each other. For analyses, the half pitches of com- ponents were divided into several deformation regions based on their tooth profile. A neutral surface was used to represent the inner flow of material during forging. Its location varied with the energy optimazation and its contour varied with the number of teeth. In experiment, the contour of material filling up the tooth zone is hyperbolic curve caused by the frictional drag on the interface of die-wall/workpiece but, in the analysis, it is an arc which retains the same contour during all forging operation.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.37-47
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• 1995

Forging of trapezoidal spline, serration and square spline with solid cylindrical billets and hollow one has been investigated by means of upper bound method. Kinematically admissible velocity fields for forging of splines have been proposed in this study. The half pitch of splines has been divided into deformation regons. The neutral surface is introduced into forging of splines with flat punch and, for each step, it is assumed as a circle with its radius rn upper bound solutions obtained obtained by proposed kinematically admissible velocity fields are useful to predict the loads for forging of splines.