A Geometric Modeling Method Based on TH-Type Uniform B-Splines

Abstract

A geometric modeling method based on TH-type uniform B-splines which are composed of trigonometric and hyperbolic polynomial with parameters is introduced in this paper. The new splines possess many important properties of quadratic and cubic B-splines. Taking different values of the parameters, one can not only locally adjust the shape of the curves, but also change the type of some segments of a curve between trigonometric and hyperbolic functions as well. The given curves can also interpolate directly control polygon locally by selecting special parameters. Moreover, the introduced splines can represent some quadratic curves and transcendental curves with selecting proper control points and parameters.

Enhancing Side Chain Rotamer Sampling Using Nonequilibrium Candidate Monte Carlo

“…6,8,9,[39][40][41][42] A cursory search of the RCSB PDB 43 for T4 lysozyme L99A returns over 120 structures containing nearly more than 90 distinct ligands and recently, absolute binding free energy calculations were calculated between T4 lysozyme L99A and 141 distinct ligands, using results from a more careful search. 44 Previously it has been observed that a valine sidechain in the binding pocket of T4 lysozyme L99A remodels its rotamer state in the presence of p-xylene, as compared with other ligands like toluene. 6,8,9 With benzene and toluene bound, valine 111 (Val111) adopts a trans conformation (χ 1 =180°); however in the presence of modestly larger ligands like p-xylene and o-xylene, the Val111 rotamer flips to the gauche(−) conformation (χ 1 =−60°).…”

A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

“…For domain , some works treat the square case [4][5][6][7][8][9][10] and some are based on discrete Galerkin method [5], Monte Carlo methods [6], or piecewise approximating polynomials [7], Nytröm methods based on cubature rules obtained as the tensor product of two-variate Gaussian 2 Mathematical Problems in Engineering rules [8,10], and meshless method with complex factors [11]. Rational approximation has extensive application in engineering, technology and calculation [12][13][14][15][16][17][18]. As efficient rational approximating techniques, a generalized inverse function-valued Padé approximants had been used in solving integral equation [13,14], and a function-valued Padé-type approximation method was used to solve one and twodimensional Fredholm integral equation of the second kind [15][16][17][18].…”

“…If the generator polynomial V ( ) is determined, we can compute the 2DFPTA of type ( , ) according to (10) and (12). In the section, we will apply Sylvester's identity [20] to propose a three-term recurrence formula for computingṼ ( ) and establish a complete recursive algorithm for calculating 2DFPTA.…”