• International Journal of CAD/CAM
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• v.8 no.1
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• pp.21-28
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• 2009

In the present work, an attempt has been made to construct branching surface from 2-D contours, which are given at different layers and may have branches. If a layer having more than one contour and corresponds to contour at adjacent layers, then it is termed as branching problem and approximated by adding additional points in between the layers. Firstly, the branching problem is converted to single contour case in which there is no branching at any layer and the final branching surface is obtained by skinning. Contours are constructed from the given input points at different layers by energy-based B-Spline approximation. 3-D curves are constructed after adding additional points into the contour points for all the layers having branching problem by using energy-based B-Spline formulation. Final 3-D surface is obtained by skinning 3-D curves and 2-D contours. There are three types of branching problems: (a) One-to-one, (b) One-to-many and (c) Many-to-many. Oneto-one problem has been done by plethora of researchers based on minimizations of twist and curvature and different tiling techniques. One-to-many problem is the one in which at least one plane must have more than one contour and have correspondence with the contour at adjacent layers. Many-to-many problem is stated as m contours at i-th layer and n contours at (i+1)th layer. This problem can be solved by combining one-to-many branching methodology. Branching problem is very important in CAD, medical imaging and geographical information system(GIS).

• Journal of the Society of Naval Architects of Korea
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• v.42 no.2 s.140
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• pp.113-123
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• 2005

A higher order panel method based on B-spline representation for both the geometry and the solution is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then shown to be evaluated using conventional numerical quadrature. By selecting a proper order for numerical quadrature, the accuracy of the present method can be increased to the machine limit. The far- and near-field influences are shown to be evaluated based on the same far-field approximation, but the near-field solution requires subdividing the panels into smaller subpanels continuously, which can be effectively implemented due to the B-spline representation of the geometry. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution on the blade surface, including very close to the tip and trailing edge regions, with far fewer panels than existing low order panel methods.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.733-751
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• 2011

In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

• East Asian mathematical journal
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• v.34 no.5
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• pp.661-681
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• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.11
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• pp.879-885
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• 1990

An intergral equation is derived for surface current distribution of cylinders with end cap using quasistatic approximation method. The moment method is applied for numerical solution. Point matching method using Cubic B-spline function as a basis function, delta function as a weighting function is applied for moment method. And also, the influencial relation in accordance with structural variation is analized in case of spheroidal end up cap type and flat type.

• Steel and Composite Structures
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• v.28 no.1
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• pp.25-37
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• 2018

For the first time, the parametric instability characteristics of tow-steered variable stiffness composite laminated (VSCL) cylindrical panels is investigated using B-spline finite strip method (FSM). The panel is considered containing geometrical defects including cutout and delamination. The material properties are assumed to vary along the panel axial length of any lamina according to a linear fiber-orientation variation. A uniformly distributed inplane longitudinal loading varies harmoni-cally with time is considered. The instability load frequency regions corresponding to the assumed in-plane parametric load-ing is derived using the Bolotin's first order approximation through an energy approach. In order to demonstrate the capabili-ties of the developed formulation in predicting stability behavior of the thin-walled VSCL structures, some representative results are obtained and compared with those in the literature wherever available. It is shown that the B-spline FSM is a proper tool for extracting the stability boundaries of perforated delaminated VSCL panels.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.11
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• pp.2106-2115
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• 1994

As a pre processing for an edge detection process. edge preserving smoothing algorithm is proposed. For this purpose we used the interpolation method using B-spline basis function and scaling of digital images. By approximation of continuous function from descrete data using B-spline basis function. undetermined data between two sample can be computed. so that they smooth the surfaces of objects. Some edges having mainly low frequency components are detected using down scaling of the images. Edge maps from proposed pre processed images are hardly affected by the varying space constants($\sigma$) and threshold values used in detecting zero-crossing.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.569-573
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• 2001

An approximate representation of discrete functions {f$_{i,j}\mid$｜i, j=-1, 0, 1, …, N+1}in two variables by a fuzzy system is described. We use the cubic B-splines as fuzzy sets for the input fuzzification and spike functions as the output fuzzy sets. The ordinal number of f$_{i,j}$ in the sorted list is taken to be the out put fuzzy set number in the (i, j) th entry of the fuzzy rule table. We show that the fuzzy system is an exact representation of the cubic spline function s(x, y)=$\sum_{N+1}^{{i,j}=-1}f_{i,j}B_i(x)B_j(y)$ and that the approximation error S(x, y)-f(x, y) is surprisingly O($h^2$) when f(x, y) is three times continuously differentiable. We prove that when f(x, y) is a gray scale image, then the fuzzy system is a smoothed representation of the image and the original image can be recovered exactly from its fuzzy system representation when it is a digitized image.e.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.719-724
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• 1994

This paper describes a hybrid surface-based method for smooth 3D surface approximation to a sequence of 2D cross sections. The resulting surface is a hybrid G $^{1}$ surface represented by a mesh of triangular and rectangular Bezier patches defined on skinning, branching, or capping regions. Each skinning region is approximated with a closed B_spline surface, which is transformed into a mesh of Bezier patches. Triangular G $^{1}$ surfaces are constructed over brabching and capping regions such that the transitions between each capping regions such that the transitions between each triangular surface and its neighboring skinning surfaces are G $^{1}$ continuous. Since each skinning region is represented by an approximated rectangular C $^{2}$ suface instead of an interpolated trctangular G $^{[-1000]}$ surface, the proposed method can provide more smooth surfaces and realize more efficient data reduction than triangular surfacebased method.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.465-480
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• 2019

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K^{\varphi}_wf)_{w>0}$. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in $C({\mathbb{R}})$, the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$ for the family $(K^{\varphi}_wf)_{w>0}$. Finally, we give some examples of kernels such as B-spline kernels and the Blackman-Harris kernel to which the theory can be applied.