Nonlinear degenerate curvature flows for weakly convex hypersurfaces

We study the evolution of closed, weakly convex hypersurfaces in in direction of their normal vector, where the speed equals a quotient of successive elementary symmetric polynomials of the principal curvatures. We show that there exists a solution for these weakly convex surfaces at least for some short time if the elementary symmetric polynomial in the denominator of the quotient is positive. The results for this nonlinear, degenerate flow are obtained by a cylindrically symmetric barrier construction.Received: 10 November 2003, Accepted: 5 April 2004, Published online: 16 July 2004     

Flow invariance for nonlinear accretive evolutions under range conditions

Let A be a nonlinear accretive operator in a real Banach space X and f : J × X  X be continuous or of Carathéodory type, where We investigate the existence of mild solutions of the evolution system

Forward K1+ (892) production in K+p → π+Ks0p at 12.7 GeV/c

We have measured 618 K⁺p → π⁺K_S⁰p events at 12.7 GeV/c incident lab momentum, mass range 790 ? m_π⁺Ks⁰ ? 990 MeV and t range 0.01 ? ?t ? 0.60 (GeV/c)². The π⁺K_S⁰ mass spectrum is dominated by the K¹⁺ (892) resonance and a Breit-Wigner fit yields a mass m = 893.5 ± 1.1 MeV and a width Γ = 33.2 ± 4.1 MeV which is much narrower than measured hitherto. The t distribution of K¹⁺ (892) events shows a dip in the forward direction and an exponential fall off thereafter, consistent with dominance of helicity flip amplitudes. The spin density matrix is almost saturated by ρ₁₁ and ρ_1?1 which are very close to their maximum allowed value of $\text{1}\text{2}$ throughout the measured t range except in the very forward direction where ρ₀₀ and Re ρ₁₀ deviate from zero. Natural parity exchanges, therefore, dominate with unnatural parity exchanges being restricted to a small region in the forward direction. A Regge pole analysis of the differential cross sections of the present measurement in conjunction with previously measured total cross sections supports the f-coupled-pomeron hypothesis.     

Die Differentialgeometrie des Galileischen Relativitätsprinzips

Ohne Zusammenfassung     

Energy-transport by radiative diffusion

A new derivation of the general-relativistic Fourier equation is given for radiation transport by using the principle of conservation of momentum plus some rather simple assumptions. The Fourier equation at which I arrive is not the usual one but has an additional term. For this reason it leads to a hyperbolic equation for heat conduction, thus avoiding the paradox of infinite velocity of heat propagation, which is a consequence of the usual Fourier equation, as the latter one leads to a parabolic equation for heat conduction. The new Fourier equation is compared with the one that was given by Kranys by using ad hoc assumptions.