of the Dissertation On the moduli space of quintic surfaces

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...

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...

This paper deals with the geometry of the space (GIT quotient) M8 of 8 points in P, and the Gale-quotient N ′ 8 of the GIT quotient of 8 points in P. The space M8 comes with a natural embedding in P, or more precisely, the projectivization of the S8-representation V4,4. There is a single S8-skew cubic C in P. The fact that M8 lies on the skew cubic C is a consequence of Thomae’s formula for hyp...

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...

Abstract Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult find better desired trajectory. In this paper, multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) proposed. Trajectory function planned with new composite...

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 respectively produce sequences of vertices fk and bk. The Js refinement proposed here produces vertices vk=(1–s)fk+sbk. Iterative applications of Js yield a family of curves parameterized by s. It includes the four-point curve (J0), the un...