Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...

We consider cubic polynomials f(z) = z + az + b defined over C(λ), with a marked point of period N and multiplier λ. In the case N = 1, there are infinitely many such objects, and in the case N ≥ 3, only finitely many. The case N = 2 has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field S

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

A graph is 1-regular if its automorphism group acts regularly on the set of its arcs. Miller [J. Comb. Theory, B, 10 (1971), 163–182] constructed an infinite family of cubic 1-regular graphs of order 2p, where p ≥ 13 is a prime congruent to 1 modulo 3. Marušič and Xu [J. Graph Theory, 25 (1997), 133– 138] found a relation between cubic 1-regular graphs and tetravalent half-transitive graphs wit...

Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the to...

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

The Cayley cubic surface is given by the equation 4 i=1 X −1 i = 0. We show that the number of non-trivial primitive integer points of size at most B is of exact order B(log B) 6 , as predicted by Manin's conjecture.

For a smooth plane cubic B, we count curves C of degree d such that the normalizations of C\B are isomorphic to A, for d ≤ 7 (for d = 7 under some assumption). We also count plane rational quartic curves intersecting B at only one