In this paper, we enumerate all number fields of degree 10 of discriminant smaller than 1011 in absolute value containing a quintic field having one real place. For each one of the 21509 (resp. 18167) found fields of signature (0, 5) (resp. (2, 4)) the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discrimin...

A three-generation SU(5) GUT (three 10 and a single 5–5 pair) is constructed by compactification of the E8 heterotic string. The base manifold is the Z5 × Z5-quotient of the quintic, and the vector bundle is the quotient of a positive monad. The group action on the monad and its bundle-valued cohomology is discussed in detail, including topological restrictions on the existence of equivariant s...

In this paper we investigate the properties of series of vacua in the string theory landscape. In particular, we study minima to the flux potential in type IIB compactifications on the mirror quintic. Using geometric transitions, we embed its onedimensional complex structure moduli space in that of another Calabi–Yau with h = 86 and h = 2. We then show how to construct infinite series of contin...

In this paper we present methods for approximating a helix segment by quintic Bézier curves or quintic rational Bézier curves based on the geometric Hermite interpolation technique in space. The fitting curve interpolates the curvatures as well as the Frenet frames of the original helix at both ends. We achieve a high accuracy of the approximation by giving a proper parametrization of the curve...

Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation ~CGLE! are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable pulselike solutions of the quintic CGLE exis...

Introduction Part I: Hodge-theoretic analysis I.A. Notations and general background Review of material from [GGK] I.B. Integral symplectic linear algebra background I.C. Analysis of the LMHS in the three cases Part II. Boundary component structure II.A. Review of material from [KU] II.B. Boundary component structure for degenerations of Hodge structure of mirror quintic type Part III: Geometric...

A method for family of G Pythagorean hodograph (PH) quintic spiral transition from straight line to circle is discussed in this paper. This method is then extended to a pair of spirals between two straight lines or two circles. We derive a family of quintic transition spiral curves joining them. Due to flexibility and wide range of shape control parameters, our method can be easily applied for ...

Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...

We consider the dynamics of dark matter solitons moving through nonuniform cigar-shaped Bose-Einstein condensates described by the mean field GrossPitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is d...