As usual, denote by KW [a, b] the Sobolev class consisting of every function whose (r − 1)st derivative is absolutely continuous on the interval [a, b] and its rth derivative is bounded by K a.e. in [a, b]. For a function f ∈ KW [a, b], its values and derivatives up to r−1 order at a set of nodes x are known. These values are said to be given Hermite information. This work reports results on be...

C-B spline can not represent semi-circle and semi-elliptical arcs precisely. This paper will discuss the nature of C-B spline’s and C-Bézier curve’s endpoints. Then, on the basis of the analysis of their characteristics and by means of adding control points to make C-B spline dominate the first and last vertices of the polygon and get tangency with the first and end sides. Thus it has given out...

This article is dedicated to the characterisation of relative hyperbolicity Haglund and Wise’s special groups. More precisely, we introduce a new combinatorial formalism study (virtually) groups, prove that, given cocompact group G finite collection subgroups \({\cal H}\), then hyperbolic H}\) if only (i) each subgroup convex-cocompact, (ii) an almost malnormal collection, (iii) every non-virtu...

B-spline functions play important roles in both mathematics and engineering. To describe a numerical method for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis functions are introduced, then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving ...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

The aim of the current study is to develop a numerical tool that is capable of achieving an optimum shape and design of hyperbolic cooling towers based on coupling a non-linear finite element model developed in-house and a genetic algorithm optimization technique. The objective function is set to be the minimum weight of the tower. The geometric modeling of the tower is represented by means of ...

This paper is devoted to the shape control of B-spline curves achieved by the modification of one of its knot values. At first those curves are described along which the points of a B-spline curve move under the modification of a knot value. Then we show that the one-parameter family of k order B-spline curves obtained by modifying a knot value has an envelope which is also a B-spline curve of ...