Lp mean estimates for an operator preserving inequalities between polynomials

If $P(z)$ be a polynomial of degree at most $n$ which does not vanish in $|z| < 1$, it was recently formulated by Shah and Liman \cite[\textit{Integral estimates for the family of $B$-operators, Operators and Matrices,} \textbf{5}(2011), 79 - 87]{wl} that for every $R\geq 1$, $p\geq 1$, $$\left\|B[P\circ\sigma](z)\right\|_p \leq\frac{R^{n}|\Lambda_n|+|\lambda_{0}|}{\left\|1+z\right\|_p}\left\|P(z)\right\|_p,$$ where $B$ is a $\mathcal{B}_{n}$-operator with parameters $\lambda_{0}, \lambda_{1}, \lambda_{2}$ in the sense of Rahman \cite{qir}, $\sigma(z)=Rz$ and $\Lambda_n=\lambda_{0}+\lambda_{1}\frac{n^{2}}{2} +\lambda_{2}\frac{n^{3}(n-1)}{8}$. Unfortunately the proof of this result is not correct. In this paper, we present a more general sharp $L_p$-inequalities for $\mathcal{B}_{n}$-operators which not only provide a correct proof of the above inequality as a special case but also extend them for $0 \leq p <1$ as well.Comment: 16 Page

Teaching Index Numbers to economists

Economic statistics are frequently reported in the form of index numbers. This article considers how the field of Index Numbers should be approached in the teaching of a general economic degree. While the topic finds a natural home in statistics modules, it is emphasised that the area can also be referred to in the teaching of other areas of economics. It is also emphasised that the differences between Index Numbers theory and the practice of compiling economic statistics such as inflation can help students gain a better understanding of applied economic statistics. Methods for assessing learning in the area are also considered and available material to support teaching is also summarised

Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, no figure

Could the LHC two-photon signal correspond to the heavier scalar in two-Higgs-doublet models?

LHC has reported tantalizing hints for a Higgs boson of mass 125 GeV decaying into two photons. We focus on two-Higgs-doublet Models, and study the interesting possibility that the heavier scalar (H) has been seen, with the lightest scalar (h) having thus far escaped detection. Non-observation of h at LEP severely constrains the parameter-space of two-Higgs-doublet models. We analyze cases where the decay H --> h h is kinematically allowed, and cases where it is not, in the context of type I, type II, lepton-specific, and flipped models.Comment: 9 pages, pdf figure

Heavy-light quark pseudoscalar and vector mesons at finite temperature

The temperature dependence of the mass, leptonic decay constant, and width of heavy-light quark peseudoscalar and vector mesons is obtained in the framework of thermal Hilbert moment QCD sum rules. The leptonic decay constants of both pseudoscalar and vector mesons decrease with increasing $T$, and vanish at a critical temperature $T_c$, while the mesons develop a width which increases dramatically and diverges at $T_c$, where $T_c$ is the temperature for chiral-symmetry restoration. These results indicate the disappearance of hadrons from the spectral function, which then becomes a smooth function of the energy. This is interpreted as a signal for deconfinement at $T=T_c$. In contrast, the masses show little dependence on the temperature, except very close to $T_c$, where the pseudoscalar meson mass increases slightly by 10-20 %, and the vector meson mass decreases by some 20-30

Studying the nuclear mass composition of Ultra-High Energy Cosmic Rays with the Pierre Auger Observatory

The Fluorescence Detector of the Pierre Auger Observatory measures the atmospheric depth, $X_{max}$, where the longitudinal profile of the high energy air showers reaches its maximum. This is sensitive to the nuclear mass composition of the cosmic rays. Due to its hybrid design, the Pierre Auger Observatory also provides independent experimental observables obtained from the Surface Detector for the study of the nuclear mass composition. We present $X_{max}$-distributions and an update of the average and RMS values in different energy bins and compare them to the predictions for different nuclear masses of the primary particles and hadronic interaction models. We also present the results of the composition-sensitive parameters derived from the ground level component.Comment: Proceedings of the 12th International Conference on Topics in Astroparticle and Underground Physics, TAUP 2011, Munich, German

Circularly polarized light emission in scanning tunneling microscopy of magnetic systems

Light is produced when a scanning tunneling microscope is used to probe a metal surface. Recent experiments on cobalt utilizing a tungsten tip found that the light is circularly polarized; the sense of circular polarization depends on the direction of the sample magnetization, and the degree of polarization is of order 10 %. This raises the possibility of constructing a magnetic microscope with very good spatial resolution. We present a theory of this effect for iron and cobalt and find a degree of polarization of order 0.1 %. This is in disagreement with the experiments on cobalt as well as previous theoretical work which found order of magnitude agreement with the experimental results. However, a recent experiment on iron showed 0.0 ${\pm}$2 %. We predict that the use of a silver tip would increase the degree of circular polarization for a range of photon energies.Comment: 15 pages, 4 figures, (To appear in Phys. Rev. B, February 2000