Zero sets of abelian Lie algebras of vector fields

Assume M is a 3-dimensional real manifold without boundary, A is an abelian Lie algebra of analytic vector fields on M, and X ∈ A. Theorem If K is a locally maximal compact set of zeroes of X ∈ A and the Poincaré-Hopf index of X at K is nonzero, there is a point in K at which all the elements of A vanish

Monotone flows with dense periodic orbits

The main result is Theorem 1: A flow on a connected open set X ⊂ Rd is globally periodic provided (i) periodic points are dense in X, and (ii) at all positive times the flow preserves the partial order defined by a closed convex cone that has nonempty interior and contains no straight line. The proof uses the analog for homeomorphisms due to B. Lemmens et al. [27], a classical theorem of D. Montgomery [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2)

Latest results from NA48 and NA48/1.

The first observations of the rare decays KS ! 0e+e− and KS ! 0μ+μ− have been made by the NA48/1 collaboration at the CERN SPS accelerator. From high intensity KS data collected during the 2002 run, clean signals of 7 KS ! 0e+e− events and 6 KS ! 0μ+μ− events were observed, giving branching ratio measurements of BR(KS ! 0e+e−) = 5.8+2.9 −2.4 × 10−9 and BR(KS ! 0μ+μ−) = 2.9+1.5 −1.2 × 10−9. These results constrain the indirect CP violating component of the corresponding KL decays. Other recent results from NA48 are also presented

The Galactic Kinematics of Mira Variables

The galactic kinematics of Mira variables derived from radial velocities, Hipparcos proper motions and an infrared period-luminosity relation are reviewed. Local Miras in the 145-200day period range show a large asymmetric drift and a high net outward motion in the Galaxy. Interpretations of this phenomenon are considered and (following Feast and Whitelock 2000) it is suggested that they are outlying members of the bulge-bar population and indicate that this bar extends beyond the solar circle.Comment: 7 pages, 2 figure, to be published in Mass-Losing Pulsating Stars and their Circumstellar Matter, Y. Nakada & M. Honma (eds) Kluwer ASSL serie

Quantitative analysis of macroevolutionary patterning in technological evolution: Bicycle design from 1800 to 2000

Book description: This volume offers an integrative approach to the application of evolutionary theory in studies of cultural transmission and social evolution and reveals the enormous range of ways in which Darwinian ideas can lead to productive empirical research, the touchstone of any worthwhile theoretical perspective. While many recent works on cultural evolution adopt a specific theoretical framework, such as dual inheritance theory or human behavioral ecology, Pattern and Process in Cultural Evolution emphasizes empirical analysis and includes authors who employ a range of backgrounds and methods to address aspects of culture from an evolutionary perspective. Editor Stephen Shennan has assembled archaeologists, evolutionary theorists, and ethnographers, whose essays cover a broad range of time periods, localities, cultural groups, and artifacts

Primary singularities of vector fields on surfaces

Unless another thing is stated one works in the C∞ category and manifolds have empty boundary. Let X and Y be vector fields on a manifold M. We say that Y tracks X if [Y, X] = fX for some continuous function f: M→ R. A subset K of the zero set Z(X) is an essential block for X if it is non-empty, compact, open in Z(X) and its Poincaré-Hopf index does not vanishes. One says that X is non-flat at p if its ∞-jet at p is non-trivial. A point p of Z(X) is called a primary singularity of X if any vector field defined about p and tracking X vanishes at p. This is our main result: consider an essential block K of a vector field X defined on a surface M. Assume that X is non-flat at every point of K. Then K contains a primary singularity of X. As a consequence, if M is a compact surface with non-zero characteristic and X is nowhere flat, then there exists a primary singularity of X