We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

in this paper mathematical extensions and generalizations of the pearl-reed model for'growth with saturation are discussed. the derived differential equation are of bernoulli and riccati type that owing to their special forms could be explicitely integrated resulting in closed form solutions. the asymptotic bahaviour of the system in each case is briefly examined and the results are compar...

A kinetic equation which combines the quasiparticle drift of Landau’s equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider’s equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary coll...

the present experiment was conducted to determine metabolizable energy of pomegranate peel and pulp by adult cockerels. the pomegranate peel and pulp samples were gathered from three industries. this study had two experiments. each experiment was done in a completely randomized design with 4 treatments and 4 replicate (1 cockerel each). the cockerels fed conventional addition method (cam). the ...