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

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

Double radiative pion capture on hydrogen and deuterium and the nucleon's pion cloud

We report measurements of double radiative capture in pionic hydrogen and pionic deuterium. The measurements were performed with the RMC spectrometer at the TRIUMF cyclotron by recording photon pairs from pion stops in liquid hydrogen and deuterium targets. We obtained absolute branching ratios of $(3.02 \pm 0.27 (stat.) \pm 0.31 (syst.)) \times 10^{-5}$ for hydrogen and $(1.42 \pm ^{0.09}_{0.12} (stat.) \pm 0.11 (syst.)) \times 10^{-5}$ for deuterium, and relative branching ratios of double radiative capture to single radiative capture of $(7.68 \pm 0.69(stat.) \pm 0.79(syst.)) \times 10^{-5}$ for hydrogen and $(5.44 \pm^{0.34}_{0.46}(stat.) \pm 0.42(syst.)) \times 10^{-5}$ for deuterium. For hydrogen, the measured branching ratio and photon energy-angle distributions are in fair agreement with a reaction mechanism involving the annihilation of the incident $\pi^-$ on the $\pi^+$ cloud of the target proton. For deuterium, the measured branching ratio and energy-angle distributions are qualitatively consistent with simple arguments for the expected role of the spectator neutron. A comparison between our hydrogen and deuterium data and earlier beryllium and carbon data reveals substantial changes in the relative branching ratios and the energy-angle distributions and is in agreement with the expected evolution of the reaction dynamics from an annihilation process in S-state capture to a bremsstrahlung process in P-state capture. Lastly, we comment on the relevance of the double radiative process to the investigation of the charged pion polarizability and the in-medium pion field.Comment: 44 pages, 7 tables, 13 figures, submitted to Phys. Rev.

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