A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...

A new family, Pylojacquesidae. is proposed for Pylojacquesia colemani. new genus and species. Although (he new family, with its monoiypic genus, exhibits characicrs of both supcrfamilles of the Section Paguridea, it is tentatively assigned to the Paguroideu until additional material becomes available that would permit a more detailed study. The new family Pylojacquesidae is diagnosed, and its t...

Spline methods provide an important tool to solve singularly perturbed boundary value problems. The present paper gives a comprehensive review of computational methods based on splines used in the solution of various classes of singularly perturbed problems such as self adjoint, linear, non-linear, semi-linear, quasi-linear, singular, single parameter and multi parameter. The spline based numer...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

To observe the complicate physical world by a WSN, the sensors in the WSN senses and samples the data from the physical world. Currently, most of the existing work use equi-frequency sampling methods (EFS) or EFS based sampling methods for data acquisition in sensor networks. However, the accuracies of EFS and EFS based sampling methods cannot be guaranteed in practice since the physical world ...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...