Prototiles and Tilings from Voronoi and Delone cells of the Root Lattice A_n

We exploit the fact that two-dimensional facets of the Voronoi and Delone cells of the root lattice A_n in n-dimensional space are the identical rhombuses and equilateral triangles respectively.The prototiles obtained from orthogonal projections of the Voronoi and Delaunay (Delone) cells of the root lattice of the Coxeter-Weyl group W(a)_n are classified. Orthogonal projections lead to various rhombuses and several triangles respectively some of which have been extensively discussed in the literature in different contexts. For example, rhombuses of the Voronoi cell of the root lattice A_4 projects onto only two prototiles: thick and thin rhombuses of the Penrose tilings. Similarly the Delone cells tiling the same root lattice projects onto two isosceles Robinson triangles which also lead to Penrose tilings with kites and darts. We point out that the Coxeter element of order h=n+1 and the dihedral subgroup of order 2n plays a crucial role for h-fold symmetric aperiodic tilings of the Coxeter plane. After setting the general scheme we give examples leading to tilings with 4-fold, 5-fold, 6-fold,7-fold, 8-fold and 12-fold symmetries with rhombic and triangular tilings of the plane which are useful in modelling the quasicrystallography with 5-fold, 8-fold and 12-fold symmetries. The face centered cubic (f.c.c.) lattice described by the root lattice A_(3)whose Wigner-Seitz cell is the rhombic dodecahedron projects, as expected, onto a square lattice with an h=4 fold symmetry.Comment: 22 pages, 17 figure

Measurement of the production of charged pions by protons on a tantalum target

A measurement of the double-differential cross-section for the production of charged pions in proton--tantalum collisions emitted at large angles from the incoming beam direction is presented. The data were taken in 2002 with the HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 \GeVc to 12 \GeVc hitting a tantalum target with a thickness of 5% of a nuclear interaction length. The angular and momentum range covered by the experiment (100 \MeVc \le p < 800 \MeVc and 0.35 \rad \le \theta <2.15 \rad) is of particular importance for the design of a neutrino factory. The produced particles were detected using a small-radius cylindrical time projection chamber (TPC) placed in a solenoidal magnet. Track recognition, momentum determination and particle identification were all performed based on the measurements made with the TPC. An elaborate system of detectors in the beam line ensured the identification of the incident particles. Results are shown for the double-differential cross-sections ${{\mathrm{d}^2 \sigma}} / {{\mathrm{d}p\mathrm{d}\theta}}$ at four incident proton beam momenta (3 \GeVc, 5 \GeVc, 8 \GeVc and 12 \GeVc). In addition, the pion yields within the acceptance of typical neutrino factory designs are shown as a function of beam momentum. The measurement of these yields within a single experiment eliminates most systematic errors in the comparison between rates at different beam momenta and between positive and negative pion production.Comment: 49 pages, 31 figures. Version accepted for publication on Eur. Phys. J.

Planetary nebulae abundances and stellar evolution II

Context: In recent years mid- and far infrared spectra of planetary nebulae have been analysed and lead to more accurate abundances. It may be expected that these better abundances lead to a better understanding of the evolution of these objects. Aims: The observed abundances in planetary nebulae are compared to those predicted by the models of Karakas (2003) in order to predict the progenitor masses of the various PNe used. The morphology of the PNe is included in the comparison. Since the central stars play an important role in the evolution, it is expected that this comparison will yield additional information about them. Methods: First the nitrogen/oxygen ratio is discussed with relation to the helium/hydrogen ratio. The progenitor mass for each PNe can be found by a comparison with the models of Karakas. Then the present luminosity of the central stars is determined in two ways: first by computing the central star effective temperature and radius, and second by computing the nebular luminosity from the hydrogen and helium lines. This luminosity is also a function of the initial mass so that these two values of initial mass can be compared. Results: Six of the seven bipolar nebulae can be identified as descendants of high mass stars (4Msun - 6Msun) while the seventh is ambiguous. Most of the elliptical PNe have central stars which descend from low initial mass stars, although there are a few caveats which are discussed. There is no observational evidence for a higher mass for central stars which have a high carbon/oxygen ratio. The evidence provided by the abundance comparison with the models of Karakas is consistent with the HR diagram to which it is compared. In the course of this discussion it is shown how `optically thin' nebulae can be separated from those which are 'optically thick'.Comment: 12 pages, 4 tables, 4 figures. Accepted for publication in A&

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio

Creation of Spin-1/2 Particles in the Hyperboloid de Sitter Space-Time

In this work we solve Dirac equation by using the method of seperation of variables. Then we analyzed the particle creation process. To compute the density number of particles created Bogoliubov transformation technique is used.Comment: 5 pages, no figures, presented at the 1st Int. Hellenic&Turkish Phys. Con

Effect of Some Nutrient Applications on Plant Properties in Organic Strawberry Production

This study was conducted with the “Camarosa” strawberry cultivar at the Egirdir Horticultural Research Institute between 2004 and 2006. In these experiments, the impact of some nutrition applications upon plant development in conventional and organic production has been analyzed. The planting has been performed with frigo plants in the third week of July and black plastic mulch was used for mulch system and dripping method was used for watering system in the experiment. When evaluating the data of two years statistically according to plant width, plant stem number, leaf number and root length, the difference in both applications and years has given importance

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Foliar-applied glyphosate substantially reduced uptake and transport of iron and manganese in sunflower (helianthus annuus L.) plants

Evidence clearly shows that cationic micronutrients in spray solutions reduce the herbicidal effectiveness of glyphosate for weed control due to the formation of metal-glyphosate complexes. The formation of these glyphosate-metal complexes in plant tissue may also impair micronutrient nutrition of nontarget plants when exposed to glyphosate drift or glyphosate residues in soil. In the present study, the effects of simulated glyphosate drift on plant growth and uptake, translocation, and accumulation (tissue concentration) of iron (Fe), manganese (Mn), zinc (Zn), and copper (Cu) were investigated in sunflower ( Helianthus annuusL.) plants grown in nutrient solution under controlled environmental conditions. Glyphosate was sprayed on plant shoots at different rates between 1.25 and 6.0% of the recommended dosage (i.e., 0.39 and 1.89 mM glyphosate isopropylamine salt). Glyphosate applications significantly decreased root and shoot dry matter production and chlorophyll concentrations of young leaves and shoot tips. The basal parts of the youngest leaves and shoot tips were severely chlorotic. These effects became apparent within 48 h after the glyphosate spray. Glyphosate also caused substantial decreases in leaf concentration of Fe and Mn while the concentration of Zn and Cu was less affected. In short-term uptake experiments with radiolabeled Fe (59Fe), Mn (54Mn), and Zn (65Zn), root uptake of 59Fe and 54Mn was significantly reduced in 12 and 24 h after application of 6% of the recommended dosage of glyphosate, respectively. Glyphosate resulted in almost complete inhibition of root-to-shoot translocation of 59Fe within 12 h and 54Mn within 24 h after application. These results suggest that glyphosate residues or drift may result in severe impairments in Fe and Mn nutrition of nontarget plants, possibly due to the formation of poorly soluble glyphosate-metal complexes in plant tissues and/or rhizosphere interactions

Effect of soil applied zinc sulphate on wheat (Triticum aestivum L.) grown on a calcareous soil in Pakistan

A field experiment was conducted to investigate the effect of soil application of zinc fertilizer on yield and yield components of wheat (Triticum aestivum L. cv. Inqlab 91) grown on calcareous soil in Pakistan. The levels of zinc sulphate were 0 (control), 5, 10, 15, 20, 25 and 30 kg ha-2 and the zinc sulphate was combine-drilled at the time of sowing. Zinc sulphate increased the Leaf Area Index, the total number of fertile tillers m -2, number of spikelets spike-2, spike length, grain spike-2, thousand grain weight, grain yield, straw yield and biological yield and decreased harvest index. Most of the response trends were curvilinear although the decrease in harvest index was linear. All applications of zinc sulphate gave economic increases in margins over costs but the application of 5 kg ha-2 gave the highest marginal rate of return. It is recommended that under such calcareous soil conditions growers can expect good returns from the application of 5 kg zinc sulphate ha-2 at the time of sowing but if the grain price were to increase or the price of zinc sulphate were reduced economic responses could be expected from higher levels of zinc sulphate. © 2008 Akadémiai Kiadó

A Search For Supernova Remnants in The Nearby Spiral Galaxy M74 (NGC 628)

We have identified nine new SNR candidates in M74 with [S II]/H$\alpha$ $\geq$ 0.4 as the basic criterion. We obtain [S II]/H$\alpha$ ratio in the range from 0.40 to 0.91 and H$\alpha$ intensities from 2.8 $\times$ $10^{-15}$ erg cm$^{-2}$ s$^{-1}$ to 1.7 $\times$ $10^{-14}$ erg cm$^{-2}$ s$^{-1}$. We also present spectral follow-up observations of the SNR candidates and can confirm only three of them (SNR2, SNR3, and SNR5). The lack of confirmation for the rest might be due to the contamination by the nearby H II emission regions as well as due to the inaccurate positioning of the long slit on these objects. In addition, we search the $Chandra$ Observatory archival data for the X-ray counterparts to the optically identified candidates. We find positional coincidence with only three SNR candidates, SNR1, SNR2, and SNR8. The spectrum of SNR2 yields a shock temperature of 10.8 keV with an ionization timescale of 1.6 $\times$ 10$^{10}$ s cm$^{-3}$ indicating a relatively young remnant in an early Sedov phase which is not supported by our optical wavelength analysis. Given the high luminosity of 10$^{39}$ erg s$^{-1}$ and the characteristics of the X-ray spectrum, we favor an Ultra Luminous X-ray Source interpretation for this source associated with an SNR. We calculate an X-ray flux upper limit of 9.0 $\times$ $10^{-15}$ erg cm$^{-2}$ s$^{-1}$ for the rest of the SNRs including spectroscopically identified SNR3 and SNR5.Comment: 10 pages, 8 figures, accepted to be published in A&