Let X be a Riemann surface equipped with a projective structure (i.e., a covering by coordinate charts such that the transition functions are of the form z 7−→ (az + b)/(cz + d)). Let L be a line bundle on X such that L = TX . Let J (L) −→ X denote the jet bundle of order m for the line bundle L. For i ≥ j, there is a natural restriction homomorphism from J (L) onto J (L). We prove that for any...

Recent experiments on the effects of flight on jet engine exhaust noise have produced apparently conflicting results. Some of these results do not agree with projections based on classical jet noise theories nor with experimental results from model jet simulated flight tests. It has been shown that in some of the cases reported, the proper corrections were not made to account for the distribute...

In the repetitive approach to the theory of jet bundles there are three methods of repetition, which yield non-holonomic, semi-holonomic, and holonomic jet bundles respectively. However the classical approach to holonomic jet bundles failed to be truly repetitive, for it must resort to such a non-repetitive coordinatedependent construction as Taylor expansion. The principal objective in this pa...

Accumulation of large, high-quality satellite and in situ data led to significant improvements in the description of the mean dynamic ocean topography (MDOT) [6]. The new models of MDOT, with the resolution improved to 50-100 km, have not only revealed important details in the complex mesoscale structure of circulation systems such as the Gulf Stream, Kuroshio Extension, and Antarctic Circumpol...

We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetrie...

We give elementary proofs, using suitable jet spaces, of some old and new structural results concerning finite-dimensional differential algebraic varieties (characteristic zero). We prove analogous results for difference algebraic varieties in characteristic zero. We also mention partial results and problems in the positive characteristic case.

The notion of a prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares these prolongation spaces with algebraic jet spaces is introduced and studied.

We compute the average luminosity of X-ray flares as a function of time, for a sample of 10 long-duration gamma-ray burst afterglows. The mean luminosity, averaged over a timescale longer than the duration of the individual flares, declines as a power-law in time with index ∼ −1.5. We elaborate on the properties of the central engine that can produce such a decline. Assuming that the engine is ...

The IESG encourages those following this example to take JET’s diligence as an example, as well as its technical work. To follow their example, registration authorities may need to articulate policy, develop appropriate procedures and mechanisms for enforcement, and document the relationship between the two. JET’s LVT mechanism should be adaptable to different policies, and can be considered du...

We study the Chern-Moser operator for hypersurfaces of finite type in C2. Analysing its kernel, we derive explicit results on jet determination for the stability group, and give a description of infinitesimal CR automorphisms of such manifolds.