Fractal Strings and Multifractal Zeta Functions

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to certain multifractal measures. However, we primarily show that they associate a new zeta function, the topological zeta function, to a fractal string in order to take into account the topology of its fractal boundary. This expands upon the geometric information garnered by the traditional geometric zeta function of a fractal string in the theory of complex dimensions. In particular, one can distinguish between a fractal string whose boundary is the classical Cantor set, and one whose boundary has a single limit point but has the same sequence of lengths as the complement of the Cantor set. Later work will address related, but somewhat different, approaches to multifractals themselves, via zeta functions, partly motivated by the present paper.Comment: 32 pages, 9 figures. This revised version contains new sections and figures illustrating the main results of this paper and recent results from others. Sections 0, 2, and 6 have been significantly rewritte

Avaliação da severidade da murcha de fusário em tomateiro em diferentes níveis de água no solo por meio do teor de clorollila das folhas.

O objetivo deste experimento foi avaliar a severidade da murcha de fusário em 4 diferentes niveis de água no solo por meio do teor de clorofila das folhas.Resumo 820-1

Avaliação da severidade da murcha de fusário em tomateiro em diferentes níveis de água no solo por meio da temperatura na superficie foliar.

O objetivo do trabalho foi avaliar o efeito do manejo de água de irrigação por meio de diferentes níveis de água no solo sobre o desenvolvimento temporal da murcha de fusário em tomateiro.Resumo 849-1

The Long Term Stability of Oscillations During Thermonuclear X-ray Bursts: Constraining the Binary X-ray Mass Function

We report on the long term stability of the millisecond oscillations observed with the Rossi X-ray Timing Explorer (RXTE) during thermonuclear X-ray bursts from the low mass X-ray binaries (LMXB) 4U 1728-34 and 4U 1636-53. We show that bursts from 4U 1728-34 spanning more than 1.5 years have observed asymptotic oscillation periods which are within 0.2 microsec. of each other, well within the magnitude which could be produced by the orbital motion of the neutron star in a typical LMXB. This stability implies a timescale to change the oscillation period of > 23,000 years, suggesting a highly stable process such as stellar rotation as the oscillation mechanism. We show that period offsets in three distinct bursts from 4U 1636-53 can be plausibly interpreted as due to orbital motion of the neutron star in this 3.8 hour binary system. We discuss the constraints on the mass function which can in principle be derived using this technique.Comment: 11 pages, 4 figures. AASTeX, to be published in the Astrophysical Journal Letter

Survey of charge symmetry breaking operators for dd -> alpha pi0

The charge-symmetry-breaking amplitudes for the recently observed d d -> alpha pi0 reaction are investigated. Chiral perturbation theory is used to classify and identify the leading-order terms. Specific forms of the related one- and two-body tree level diagrams are derived. As a first step toward a full calculation, a few tree-level two-body diagrams are evaluated at each considered order, using a simplified set of d and alpha wave functions and a plane-wave approximation for the initial dd state. The leading-order pion-exchange term is shown to be suppressed in this model because of poor overlap of the initial and final states. The higher-order one-body and short-range (heavy-meson-exchange) amplitudes provide better matching between the initial and final states and therefore contribute significantly and coherently to the cross section. The consequences this might have for a full calculation, with realistic wave functions and a more complete set of amplitudes, are discussed.Comment: REVTeX 4, 35 pages, 8 eps figures, submitted to PR