Fibre-fed spectrographs now have throughputs equivalent to slit spectrographs. However, the sky subtraction accuracy that can be reached has often been pinpointed as one of the major issues associated with the use of fibres. Using technical time obse
rvations with FLAMES-GIRAFFE, two observing techniques, namely dual staring and cross beam-switching, were tested and the resulting sky subtraction accuracy reached in both cases was quantified. Results indicate that an accuracy of 0.6% on sky subtraction can be reached, provided that the cross beam-switching mode is used. This is very encouraging with regard to the detection of very faint sources with future fibre-fed spectrographs, such as VLT/MOONS or E-ELT/MOSAIC.
We present optical nuclear spectra for nine 3CR radio sources obtained with the Telescopio Nazionale Galileo, that complete our spectroscopic observations of the sample up to redshifts $<$ 0.3. We measure emission line luminosities and ratios, and de
rive a spectroscopic classification for these sources.
A Chebyshev knot ${cal C}(a,b,c,phi)$ is a knot which has a parametrization of the form $ x(t)=T_a(t); y(t)=T_b(t) ; z(t)= T_c(t + phi), $ where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev polynomial of degree $n$ and $phi in R.$ We show that any
two-bridge knot is a Chebyshev knot with $a=3$ and also with $a=4$. For every $a,b,c$ integers ($a=3, 4$ and $a$, $b$ coprime), we describe an algorithm that gives all Chebyshev knots $cC(a,b,c,phi)$. We deduce a list of minimal Chebyshev representations of two-bridge knots with small crossing number.
We show that every two-bridge knot $K$ of crossing number $N$ admits a polynomial parametrization $x=T_3(t), y = T_b(t), z =C(t)$ where $T_k(t)$ are the Chebyshev polynomials and $b+deg C = 3N$. If $C (t)= T_c(t)$ is a Chebyshev polynomial, we call s
uch a knot a harmonic knot. We give the classification of harmonic knots for $a le 3.$ Most results are derived from continued fractions and their matrix representations.
We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when $ n otequiv 0 Mod 4$ and $(n,j) eq (3,3),$ the Fibonacci knot $ cF_j^{(n)} $ is not a Lissajous knot.
For every odd integer $N$ we give an explicit construction of a polynomial curve $cC(t) = (x(t), y (t))$, where $deg x = 3$, $deg y = N + 1 + 2pent N4$ that has exactly $N$ crossing points $cC(t_i)= cC(s_i)$ whose parameters satisfy $s_1 < ... < s_{N
} < t_1 < ... < t_{N}$. Our proof makes use of the theory of Stieltjes series and Pade approximants. This allows us an explicit polynomial parametrization of the torus knot $K_{2,N}$.
A SST survey in the NOAO Deep-Wide Field in Bootes provides a complete, 8-micron-selected sample of galaxies to a limiting (Vega) magnitude of 13.5. In the 6.88 deg$^2$ field sampled, 79% of the 4867 galaxies have spectroscopic redshifts, allowing an
accurate determination of the local (z<0.3) galaxy luminosity function. Stellar and dust emission can be separated on the basis of observed galaxy colors. Dust emission (mostly PAH) accounts for 80% of the 8 micron luminosity, stellar photospheres account for 19%, and AGN emission accounts for roughly 1 %. A sub-sample of the 8 micron-selected galaxies have blue, early-type colors, but even most of these have significant PAH emission. The luminosity functions for the total 8 micron luminosity and for the dust emission alone are both well fit by Schechter functions. For the 8 micron luminosity function, the characteristic luminosity is u L_{ u}^*(8.0 micron) = 1.8 times 10^{10}$ Lsun while for the dust emission alone it is 1.6 x 10^{10}$ Lsun ull. The average 8 micron luminosity density at z<0.3 is 3.1 x 10^7 Lsun Mpc^{-3}, and the average luminosity density from dust alone is 2.5 x 10^7 Lsun Mpc^{-3}. This luminos ity arises predominantly from galaxies with 8 micron luminosities ($ u L_{ u}$) between $2times 10^9$ and $2 x 10^{10}$ Lsun, i.e., normal galaxies, not LIRGs or ULIRGs.
