Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling by Muhammad USMAN, Muhammad ABBAS, Kenjiro T. MIURA

Subjects: “…bernstein polynomials…”
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Functions operating on several multivariate distribution functions by Ressel Paul

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Rough statistical convergence on triple sequence of the Bernstein operator of random variables in probability by Nagarajan Subramanian, Ayhan Esi, Mustafa Kemal Ozdemir

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Two Photon Processes in an Atom Confined in Gaussian Potential by Sonia Lumb, Shalini Lumb, Vinod Prasad

“…Transitions of an atom under the effect of a Gaussian potential and loose spherical confinement are studied. An accurate Bernstein-polynomial (B-polynomial) method has been applied for the calculation of the energy levels and radial matrix elements. …”
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Free-form 3D modelling by Wee, Tobie Feng Sheng

“…This report covers the development of a 3D free form deformation software using the trivariate Bernstein polynomial equation as suggested by Sederberrg and Parry, and looks at the results and limitations of such a program, suggesting future developments.…”
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Optimization of the Progressive Image Mosaicing Algorithm in Fine Art Image Fusion for Virtual Reality by Bin Song

“…The fade-in and fade-out algorithm based on the Bernstein polynomial has certain limitations in image fusion. …”
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Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations. by Azmat Ullah, Suheel Abdullah Malik, Khurram Saleem Alimgeer

“…Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. …”
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Isogeometric treatment of large deformation contact and debonding problems with T-splines: a review by Dimitri Rossana

“…The isogeometric discretizations are here incorporated into an existing finite element framework by using Bézier extraction, i.e. a linear operator which maps the Bernstein polynomial basis on Bézier elements to the global isogeometric basis. …”
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Intuitionistic fuzzy piecewise Bézier curve modeling with C1 and G1 continuities for complex data by Zulkifly, Mohammad Izat Emir, Wahab, Abd. Fatah, Bidin, Mohd. Syafiq, Embong, Ahmad Fadillah, Hoe, Yeak Su

“…Later, the control point in cubic case is blended with the Bernstein polynomial to produce a single piece of curve. …”

Numerical solutions of 2D Fredholm integral equation of first kind by discretization technique by Faheem Khan, Tayyaba Arshad, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar

“…This technique is based on the discretization of 2DFIEs by replacing the unknown function with two-dimensional Bernstein polynomial basis functions. We formulate the convergence analysis which shows the fast converges of this technique to the actual solution. …”
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Numerical Methods on the Triple Informative Prior Distribution for the Failure Rate Basic Gompertz Model by Nadia Al-Obedy, Amal Mohammed, Sudad Abraheem

“…A comparison was made about the performance of these estimators with the numerical solution that was found using expansion methods (Bernstein polynomial and power function) which was applied to find the failure rate function numerically. …”
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Fractional Bernstein Series Solution of Fractional Diffusion Equations with Error Estimate by Mohammed Hamed Alshbool, Osman Isik, Ishak Hashim

“…In the present paper, we introduce the fractional Bernstein series solution (FBSS) to solve the fractional diffusion equation, which is a generalization of the classical diffusion equation. The Bernstein polynomial method is a promising one and can be generalized to more complicated problems in fractional partial differential equations. …”
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Interactive mesh visualisation and deformation by Ong, Elysia Wei Xi

“…Through the implementation, the project sheds light on the mathematical complexities behind the FFD algorithm, principally the tensor product trivariate Bernstein polynomial. The results obtained proved that FFD could indeed be achieved in real-time. …”
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Generalized Shifted Chebyshev Koornwinder’s Type Polynomials: Basis Transformations by Mohammad A. AlQudah, Maalee N. AlMheidat

“…In addition, explicit formulas of conversion matrices between generalized shifted Chebyshev Koornwinder’s type polynomials and Bernstein polynomial bases were given.…”
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Efficient Aerodynamic Shape Optimization of the Hypersonic Lifting Body Based on Free Form Deformation Technique by Bin Zhang, Zhiwei Feng, Boting Xu, Tao Yang

“…Some commonly used basis functions are researched in FFD modeling of the windward side of a typical lifting body, including the Bernstein polynomial, the B-spline function, and the non-uniform rational B-spline (NURBS) function. …”
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Transient Nonlinear Heat Conduction in Concrete Structures: A Semi-Analytical Approach by Hui Wang, Xi Chen, Eduardus Koenders, Ying Dai, Xingchun Huang, Qing Ai, Yong Yuan

“…Thereafter, it was extended to the whole domain by utilizing the Bernstein polynomial. The semi-analytical approach was validated by comparing it with the numerical results of two independent Finite Element simulations of nonlinear heat conduction along concrete plates, subjected to either moderate or fierce thermal loading. …”
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DoreBer: Document-Level Relation Extraction Method Based on BernNet by Boya Yuan, Liwen Xu

“…Specifically, DoreBer performs estimation of filter over the normalized Laplacian spectrum of a graph by leveraging an order-K Bernstein polynomial approximation, and designs its spectral property by setting the coefficients of the Bernstein basis. …”
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A Shape Preserving Class of Two-Frequency Trigonometric B-Spline Curves by Gudrun Albrecht, Esmeralda Mainar, Juan Manuel Peña, Beatriz Rubio

“…In fact, the normalized B-basis functions converge to the Bernstein polynomials as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>. …”
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Application of Bernstein collocation method for solving the generalized regularized long wave equations by D.A. Hammad

“…A general form for any m derivative of any Bernstein polynomials is constructed. A general matrix form for the vector of any m derivative of any Bernstein polynomials is also constructed. …”
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A Study on the <inline-formula><graphic file="1687-1847-2010-163217-i1.gif"/></inline-formula>-Adic Integral Representation on <inline-formula><graphic file="1687-1847-2010-163217-... by Kim Won-Joo, Simsek Yilmaz, Jang Lee-Chae

“…<p/> <p>We consider the Bernstein polynomials on <inline-formula><graphic file="1687-1847-2010-163217-i3.gif"/></inline-formula> and investigate some interesting properties of Bernstein polynomials related to Stirling numbers and Bernoulli numbers.…”
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