Permanents of cyclic (0,1) matrices

AbstractAn efficient method is presented for evaluating the permanents Pnk of cyclic (0,1) matrices of dimension n and common row and column sum k. A general method is developed for finding recurrence rules for Pnk (k fixed); the recurrence rules are given in semiexplicit form for the range 4≤k≤9. A table of Pnk is included for the range 4≤k≤9, k≤n≤80. The Pnk are calculated in the formPnk=2+∑τ−1[k−12]Tτk(n)where the Ttk(n) satisfy recurrence rules given symbolically by the characteristic equations of certain (0, 1) matrices Πrk; the latter turn out to be identical with the r-th permanental compounds of certain simpler matrices Π1k. Finally, formal expressions for Pnk are given which allow one to write down the solution to the generalized Ménage Problem in terms of sums over scalar products of the iterates of a set of unit vectors

On finite limit sets for transformations on the unit interval

AbstractAn infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself. Examples of four different types are studied in some detail; tables of numerical results are included. The limit sets are characterized by certain patterns; an algorithm for their generation is described and established. The structure and order of occurrence of these patterns is universal for the class

Sr and Nd isotope data for arc-related (meta) volcanics (SW Iberia)

In the southern sector of the Ossa-Morena Zone (Iberian Variscan Chain), along its boundaries with the Beja-Acebuches Ophiolite and the South-Portuguese Zone, Upper Palaeozoic igneous mafic and intermediate rocks, both intrusive and extrusive, are widely represented. The so-called Odivelas Unit (Andrade,1983), include (meta-) basalts and (meta-) andesites, which, according with previous studies, display low-K tholeiitic to calc-alkaline signatures and, therefore, are interpreted as remnants of an active margin volcanic arc. Santos et al. (1990) subdivided those volcanics into two groups: in Alfundão-Peroguarda, the tholeiitic nature is dominant; in Odivelas-Penique, the calc-alkaline signature becomes more pronounced. Intercalation of limestone layers provided some age constraints, showing that the subduction-related volcanic activity in the studied area began in the Lower Devonian and continued, at least, through the Middle Devonian (Conde & Andrade, 1974; Machado et al., 2010). In this work, samples previously studied by Santos et al. (1990) and Silva et al. (2011) were analysed for Sm-Nd and Rb-Sr isotopes. Considering that the volcanics were systematically affected by hydrothermal metamorphism, it is expected that the Sr signatures show significant disturbance. In contrast, Nd isotope ratios probably reflect the primary features. Alfundão-Peroguarda samples show a very limited range of positive initial εNd, from +5.1 to +4.3 (assuming 400 Ma), showing no evidence for significant crustal assimilation and, therefore, allowing the attribution of negative Nb and Ta anomalies to arc-related processes On the other hand, 87Sr/86Sr varies from 0.7044 to 0.7060 (for 400Ma). These samples rocks define a horizontal trend on the initial εNd vs. initial 87Sr/86Sr plot, typical of co-genetic rocks that underwent interaction with seawater. On the other hand, Odivelas-Penique volcanics show wide spectra for both initial 87Sr/86Sr (from 0.7038 to 0.7066) and εNd (from +4.6 to -4.1). Significantly, the highest εNd values for this group are within the narrow range defined by Alfundão-Peroguarda tholeiitic basalts, suggesting a common mantle source (or very similar sources) for the most mafic magmas of both sectors. The whole set of Nd isotope ratios supports the distinction previously proposed between the two groups of volcanics. In addition, the variation from positive to negative initial εNd values in the Odivelas-Penique suite shows that its geochemical features were likely influenced by assimilation of continental crustal material

Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model

In a scalar $\phi^2\chi$ model, we exactly solve the vertex and $\phi$ propagator Dyson-Schwinger equations under the assumption of a spatially constant (Munczek-Nemirovsky) propagator for the $\chi$ field. Various truncation schemes are also considered.Comment: 7 pages,4 figures, minor changes, reference added for published versio

Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides

Ballistic spin transport through waveguides, with symmetric or asymmetric double stubs attached to them periodically, is studied systematically in the presence of a weak spin-orbit coupling that makes the electrons precess. By an appropriate choice of the waveguide length and of the stub parameters injected spin-polarized electrons can be blocked completely and the transmission shows a periodic and nearly square-type behavior, with values 1 and 0, with wide gaps when only one mode is allowed to propagate in the waveguide. A similar behavior is possible for a certain range of the stub parameters even when two-modes can propagate in the waveguide and the conductance is doubled. Such a structure is a good candidate for establishing a realistic spin transistor. A further modulation of the spin current can be achieved by inserting defects in a finite-number stub superlattice. Finite-temperature effects on the spin conductance are also considered.Comment: 19 pages, 8 figure

Solar Intranetwork Magnetic Elements: bipolar flux appearance

The current study aims to quantify characteristic features of bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack such a problem, we use the Narrow-band Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board \emph{Hinode}; these data are from quiet and an enhanced network areas. Cluster emergence of mixed polarities and IN ephemeral regions (ERs) are the most conspicuous forms of bipolar flux appearance within the network. Each of the clusters is characterized by a few well-developed ERs that are partially or fully co-aligned in magnetic axis orientation. On average, the sampled IN ERs have total maximum unsigned flux of several 10^{17} Mx, separation of 3-4 arcsec, and a lifetime of 10-15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10^{16} Mx, separations less than 1 arcsec, and lifetimes as short as 5 minutes. Most IN ERs exhibit a rotation of their magnetic axis of more than 10 degrees during flux emergence. Peculiar flux appearance, e.g., bipole shrinkage followed by growth or the reverse, is not unusual. A few examples show repeated shrinkage-growth or growth-shrinkage, like magnetic floats in the dynamic photosphere. The observed bipolar behavior seems to carry rich information on magneto-convection in the sub-photospheric layer.Comment: 26 pages, 14 figure

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure

Crystallographic structure reveals phosphorylated pilin from Neisseria : phosphoserine sites modify type IV pilus surface chemistry and fibre morphology

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72468/1/j.1365-2958.1999.01184.x.pd