The Lagrange spectrum of a Veech surface has a Hall ray

We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary expansion developed by Bowen and Series to code geodesics in the corresponding Teichm\"uller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.Comment: 30 pages, 5 figures. Minor revisio

Fractional Almost Kahler - Lagrange Geometry

The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilton geometry and, in our approach, with fractional derivatives. For fundamental geometric objects induced canonically by regular Lagrange functions, we construct compatible almost symplectic forms and linear connections completely determined by a "prime" Lagrange (in particular, Finsler) generating function. We emphasize the importance of such constructions for deformation quantization of fractional Lagrange geometries and applications in modern physics.Comment: latex2e, 17 pages, v3 performed following requests of referee with additional references and explanations; accepted to "Nonlinear Dynamics

The mechanical control of bushpig, Patamochoerus porcus, in Zimbabwe

Bushpig, Potamocheorus porcus, occurring naturally in the high rainfall areas of Zimbabwe, have become a major threat to maize producers in the country. Traditional means of control including hunting have been unsuccessful in keeping the numbers to a tolerable level owing to the secretive and cunning nature of the animal. The use of poisons has been discouraged because of indiscriminate use and problems of secondary poisoning, so alternative methods of mechanical control were sought. Several methods evolved during experimentation, producing a strategy to control bushpig throughout the year

Holonomic constraints : an analytical result

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrate the equations of motions of the system. Computing analytically the Lagrange multipliers for a constrained system may be a difficult task that is depending on the complexity of systems. For complex systems, it is most of the time impossible to achieve. In computer simulations, some algorithms using iterative procedures estimate numerically Lagrange multipliers or constraint forces by correcting the unconstrained trajectory. In this work, we provide an analytical computation of the Lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length. In the appendix of the paper, one would find explicit formulas for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The