For scattering on the modular surface and on the hyperbolic cylinder, we show that the solutions of the wave equations can be expanded in terms of resonances, despite the presence of trapping. Expansions of this type are expected to hold in greater generality but have been understood only in non-trapping situations. 1. Introduction In this note we give two examples for which we can obtain, on c...

Abstract In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels description. Transport is formulated within kinetic polarized phonons, unpolarized hydrodynamics phonons. These description are linked by Poisson reductions, where no linearizations made. Consequently, obtain new phonon that contains convective terms dependent vorticity the flux, which ...

This work introduces a new thermoelastic model of an isotropic and homogeneous annular cylinder. The cylinder’s bounding inner surface is shocked thermally, the outer has no temperature increment volumetric strain. governing equations in context hyperbolic two-temperature generalized thermoelasticity with fractional-order strain theory have been derived. numerical solutions conductive temperatu...

The end of a hyperbolic surface is studied in terms of the behavior at innnity of geodesics on the surface. For a class of surfaces called untwisted utes it is possible to give a fairly precise description of the ending geometry. From the point of view of a Fuchsian group representing such a surface this provides new information about the existence of Dirichlet and Garnett points. 0. Introducti...

A simple model for the localization of category $\mathbf{CLoc}_2$ oriented and time-oriented globally hyperbolic conformal Lorentzian $2$-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description $2$-dimensional algebraic quantum field theories (AQFTs) satisfying time-slice axiom in terms only two algebras, one Minkowski spacetime flat cylinder, together with a s...

the effective factors of forward speed, cylinder rotation, and clearance between a combine’s cylinder and concave on wheat kernel breakage and seed germination were studied in karaj area using a 955 model john dear combine. this study was conducted on three levels of adjustment for each of the variables, 1.2, 1.8 and 2.5 km/hr for forward speed, 800, 900, 1000 rpm for cylinder rotation as well ...

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.