128 research outputs found

    Rational quintics in the real plane

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    Tropical eigenwave and intermediate Jacobians

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    Tropical manifolds are polyhedral complexes enhanced with certain kind of affine structure. This structure manifests itself through a particular cohomology class which we call the eigenwave of a tropical manifold. Other wave classes of similar type are responsible for deformations of the tropical structure. If a tropical manifold is approximable by a 1-parametric family of complex manifolds then the eigenwave records the monodromy of the family around the tropical limit. With the help of tropical homology and the eigenwave we define tropical intermediate Jacobians which can be viewed as tropical analogs of classical intermediate Jacobians.Comment: 38 pages, 8 figure

    Two dimensional periodic box-ball system and its fundamental cycle

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    We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of the discrete KP equation. We construct an algorithm to calculate the fundamental cycle, which is an important conserved quantity of the 2-dim. Box-Ball system with periodic boundary condition, by using the tropical curve theory.Comment: 16 pages, 5 figure

    Six degree of freedom FORTRAN program, ASTP docking dynamics, users guide

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    The digital program ASTP Docking Dynamics as outlined is intended to aid the engineer using the program to determine the docking system loads and attendant vehicular motion resulting from docking two vehicles that have an androgynous, six-hydraulic-attenuator, guide ring, docking interface similar to that designed for the Apollo/Soyuz Test Project (ASTP). This program is set up to analyze two different vehicle combinations: the Apollo CSM docking to Soyuz and the shuttle orbiter docking to another orbiter. The subroutine modifies the vehicle control systems to describe one or the other vehicle combinations; the rest of the vehicle characteristics are changed by input data. To date, the program has been used to predict and correlate ASTP docking loads and performance with docking test program results from dynamic testing. The program modified for use on IBM 360 computers. Parts of the original docking system equations in the areas of hydraulic damping and capture latches are modified to better describe the detail design of the ASTP docking system

    Tropical descendant Gromov-Witten invariants

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    We define tropical Psi-classes on the moduli space of rational tropical curves in R^2 and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to prove that tropical numbers of curves satisfying certain Psi- and evaluation conditions are equal to the corresponding classical numbers. We present an algorithm that generalizes Mikhalkin's lattice path algorithm and counts rational plane tropical curves satisfying certain Psi- and evaluation conditions.Comment: 33 pages, 14 Postscript figures; minor changes to fit the published versio