Showing papers on "Quintic function published in 1991"

Picard-Fuchs equations and mirror maps for hypersurfaces

Abstract: We describe a strategy for computing Yukawa couplings and the mirror map, based on the Picard-Fuchs equation. (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes in the case of quintic hypersurfaces.) We then explain a technique of Griffiths which can be used to compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the computation for four specific examples (including quintic hypersurfaces, previously done by Candelas et al.). This yields predictions for the number of rational curves of various degrees on certain hypersurfaces in weighted projective spaces. Some of these predictions have been confirmed by classical techniques in algebraic geometry.

Picard-Fuchs equations and mirror maps for hypersurfaces

Abstract: We describe a strategy for computing Yukawa couplings and the mirror map, based on the Picard-Fuchs equation (Our strategy is a variant of the method used by Candelas, de la Ossa, Green, and Parkes in the case of quintic hypersurfaces) We then explain a technique of Griffiths which can be used to compute the Picard-Fuchs equations of hypersurfaces Finally, we carry out the computation for four specific examples (including quintic hypersurfaces, previously done by Candelas et al) This yields predictions for the number of rational curves of various degrees on certain hypersurfaces in weighted projective spaces Some of these predictions have been confirmed by classical techniques in algebraic geometry

Natural shape functions of a compressed Vlasov element

Abstract: To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly.

A family of cyclic quartic fields arising from modular curves

Abstract: We study a family of cyclic quartic fields arising from the covering of modular curves X1(16) -XO(16). An integral basis and a fundamental system of units are found. It is shown that a root of the quartic polynomial we construct is a translate of a cyclotomic period by an integer of the quadratic subfield of the quartic field. Recently, 0. Lecacheux [9, 10] and H. Darmon [4] showed how to use coverings of modular curves to obtain cyclic extensions of Q. In particular, they were able to give a geometric construction of a family of cyclic quintic fields discovered by E. Lehmer [11]. The covering X1 (N) --* X0(N) (for N > 2) has degree q$(N)/2 and group (Z/NZ) X /{I 1 }. For the quintic case, they took N = 25, which gave a cyclic covering of degree 10, then took the subcovering of degree 5. An important ingredient in the construction was the fact that XO(25) has genus 0. This also occurs for N = 1, ..., 10, 12, 13, 16, 18. These all give trivial or quadratic coverings except for N = 7, 9, 13, 16, 18. The values N = 7, 9, 18 yield cubic extensions and can be shown to yield the family of polynomials X3 aX2 (a + 3)X 1, namely the "simplest cubic fields" [17]. (However, it should be remarked that every cyclic cubic extension of Q comes from a polynomial of this form if a is allowed to be rational. Similarly, we are guaranteed that the quadratic extensions obtained from the coverings mentioned above correspond to polynomials of the form X2 aX 1 with a rational.) The case N = 13 is treated by Lecacheux [9]. It might be suspected that the sextic fields she obtains are the same as the "simplest sextics" constructed by M.-N. Gras [6]. However, these latter fields were found by taking the fixed field of an element of order 6 in PGL2(Q) = Aut(Q(X)). Therefore, they come from a covering of curves of genus 0. But X1 (13) has genus 2. Alternatively, these sextic fields must be different because the discriminants of the quadratic, and cubic, subfields are different. In the present paper, we study the case N = 16. As above, it might be hoped that this case would give a geometric construction of the quartic fields studied Received March 14, 1990; revised October 22, 1990. 1980 Mathematics Subject Classification ( 1985 Revision). Primary 1 I R 16. Research supported in part by N.S.F. ? 1991 American Mathematical Society 0025-5718/91 $1.00 + $.25 per page

A table of totally real quintic number fields

Abstract: We give a table of the 1077 totally real number fields of degree five having a discriminant less than 2 000 000. There are two nonisomorphic fields of discriminant 1 810 969 and two nonisomorphic fields of discriminant 1 891 377. All the other number fields in the table are characterized by their discriminant. Among these fields, three are cyclic and four have a Galois closure whose Galois group is the dihedral group D5 . The Galois closure for all the other fields in the table has a Galois group isomorphic to S5 .

An algorithm for calculating the roots of a general quintic equation from its coefficients

Abstract: Classical mathematics is used to derive an algorithm for expressing the roots of a general quintic equation in terms of its coefficients. This algorithm requires the solution of two quadratic equations and one cubic equation as well as the evaluation of two infinite series, namely, one Jacobi nome and one theta series. This algorithm has been implemented on a microcomputer.

On normal quintic Enriques surfaces.

Abstract: In this paper we describe normal quintic surfaces in P which are birationally isomorphic to Enriques surfaces. especially we characterize the sublinear systems which give rise to one of two Stagnaro's normal quintic surfaces in P3.

Modified hermite quintic curves and applications

Abstract: The work described in the paper represents point files with curvature-tangency information by means of a modified Hermite quintic parametric curve. It is seen that the quintic curve can be developed using only some of the points and tangents in the interval, and passed through the remaining points in the manner described. The curve can then be tested for goodness of fit, and replaced with a ‘shorter’ sector if necessary.

An optimal quintic polynomial trajectory planning for robot

Abstract: This new trajectory is prented to avoid the disadvantages of the conventional po1ynomial trajecto-rics.A set of equations in banded structure that the optimal solution must satisfy,according to the per-formance spccifications givcn＊are derived from the program libuary in PROLOG that the author devel-oped.Thus all the coofficients of quintic polynomial can be calculated out easily and fast.As some specialcases of quintic trajectory,several other trajectories consisting of various piecewise polynomials with dif-ferent or same degrees are also presented.Some comparative examples given demonstrate theireffectiveness.