On critical exponents for some quasilinear parabolic equations

We study the Cauchy problem for the quasilinear parabolic equation where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with ? ? sψ′(s)/ψ(s) ? θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.     

On Central Endomorphisms of a Group with Operators

Let G be a group with a set of operators such that Z(G) is -admissible. Central -automorphisms occur in the Krull-Remak-Schmidt Theorem. We discuss the existence of a central -endomorphism of G that is not an automorphism.2000 Mathematics Subject Classification: 20E36     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Another odd thing about unparticle physics

The peculiar propagator of scale invariant unparticles has phases that produce unusual patterns of interference with Standard Model processes. We illustrate some of these effects in e⁺e⁻→μ⁺μ⁻$e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$.     

The Percolation Transition for the Zero-Temperature Stochastic Ising Model on the Hexagonal Lattice

On the planar hexagonal lattice , we analyze the Markov process whose state (t), in , updates each site v asynchronously in continuous time t0, so that _v (t) agrees with a majority of its (three) neighbors. The initial _v (0)'s are i.i.d. with P[ _v (0)=+1]=p[0,1]. We study, both rigorously and by Monte Carlo simulation, the existence and nature of the percolation transition as t and p1/2. Denoting by ⁺(t,p) the expected size of the plus cluster containing the origin, we (1) prove that ⁺(,1/2)= and (2) study numerically critical exponents associated with the divergence of ⁺(,p) as p1/2. A detailed finite-size scaling analysis suggests that the exponents and of this t= (dependent) percolation model have the same values, 4/3 and 43/18, as standard two-dimensional independent percolation. We also present numerical evidence that the rate at which (t)() as t is exponential.     

Cross section measurements of the Pd(p, γ)Ag, Sn(p, γ)Sb, and Sn(α, γ)Te reactions relevant to the astrophysical rp- and γ-processes

Total cross section measurements for the ¹⁰²Pd(p, γ)¹⁰³Ag and ¹¹⁶Sn(p, γ)¹¹⁷Sb reactions have been performed in the proton energy range 2.6 to 4.25 MeV, and for the ¹¹²Sn(α, γ)¹¹⁶Te reaction over the alpha beam energy range 7.0 to 10.5 MeV. An activation technique was used in which gamma rays from decays of the reaction products were detected off-line by two hyper-pure germanium detectors in a low background environment. Where possible, reaction rates are derived and the results compared to those of calculations generated by the NON-SMOKER and the MOST statistical model codes so as to judge their applicability for describing the cross sections needed for network calculations of nucleosynthesis in explosive astrophysical environments via the γ- and rp-processes.     

Connections and geodesics in the spacetime tangent bundle

Recent interest in maximal proper acceleration as a possible principle generalizing the theory of relativity can draw on the differential geometry of tangent bundles, pioneered by K. Yano, E. T. Davies, and S. Ishihara. The differential equations of geodesics of the spacetime tangent bundle are reduced and investigated in the special case of a Riemannian spacetime base manifold. Simple relations are described between the natural lift of ordinary spacetime geodesics and geodesics in the spacetime tangent bundle.     

Transport phenomena in fluids

July 1969, 528 pages, illustrated, $25.50