In this paper, the boundary value problems for nonlinear third order differential equations are treated. A generic approach based on nonpolynomial quintic spline is developed to solve such boundary value problem. We show that the approximate solutions of such problems obtained by the numerical algorithm developed using nonpolynomial quintic spline functions are better than those produced by oth...

For each 1 ≤ n ≤ 6 we present formulas for the number of n−nodal curves in an n−dimensional linear system on a smooth, projective surface. This yields in particular the numbers of rational curves in the system of hyperplane sections of a generic K3−surface imbedded in IP n by a complete system of curves of genus n as well as the number 17,601,000 of rational (singular) plane quintic curves in a...

We analyse timing jitter of ultrashort soliton systems taking into account the major higher order effects, namely, intrapulse Raman scattering and third order dispersion and using adiabatic perturbation theory. We obtain an expression for the soliton arrival time variance that depends on the quintic power of propagation distance. This timing jitter could be partly overcome by use of bandwidth-l...

We discuss the implementation of a C quintic superspline method for interpolating scattered data in IR based on a modification of Alfeld’s generalization of the Clough-Tocher scheme described by Lai and LeMéhauté [4]. The method has been implemented in MATLAB, and we test for the accuracy of reproduction on a basis of quintic polynomials. We present numerical evidences that when the partition i...

According to Hermite there exists only a finite number of number fields having a given degree, and a given value of the discriminant, nevertheless this number is not known generally. The determination of a maximum number of number fields of degree 10 having a given discriminant that contain a subfield of degree 5 having a fixed class number, narrow class number and Galois group is the purpose o...

The complex quintic Swift-Hohenberg equation (CSHE) is a model for describing pulse generation in mode-locked lasers with fast saturable absorbers and a complicated spectral response. Using numerical simulations, we study the single- and two-soliton solutions of the (1+1)-dimensional complex quintic Swift-Hohenberg equations. We have found that several types of stationary and moving composite s...

We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an a...

This paper theoretically describes how to compose a single Pythagorean hodograph (PH) quintic Bézier spiral segment, between two circles with one circle inside the other. A spiral is free of local curvature extrema, making spiral design an interesting mathematical problem with importance for both physical and aesthetic applications. The curvature of a spiral varies monotonically with arc-length...

A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian #ux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme is strictly mass conservative and positive de"nite while maintaining high peak retention. The new algorithm is compared ...