A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form aresomewhat complex - usually invoking the use of new spaces, and what not. These demonstrationsare usually too difficult for an average Mathematics student to understand how he or she can obtainthe Jordan Canonical Form for any square matrix. The method here proposed not only demonstratesthe existence of such forms but, additionally, shows how to find them in a step by step manner. I donot claim that the following demonstration is in any way “elegant” (by the standards of elegance infashion nowadays among mathematicians) but merely simple (undergraduate students taking a fistcourse in Matrix Algebra would understand how it works).

The X-ray emission of z>2.5 active galactic nuclei can be obscured by their host galaxies

We present a multi-wavelength study of seven AGN at spectroscopic redshift >2.5 in the 7 Ms Chandra Deep Field South, selected to have good FIR/sub-mm detections. Our aim is to investigate the possibility that the obscuration observed in the X-rays can be produced by the interstellar medium (ISM) of the host galaxy. Based on the 7 Ms Chandra spectra, we measured obscuring column densities N$_{H, X}$ in excess of 7x10$^{22}$ cm$^{-2}$ and intrinsic X-ray luminosities L$_{X}$>10$^{44}$ erg s$^{-1}$ for our targets, as well as equivalent widths for the Fe K$\alpha$ emission line EW>0.5-1 keV. We built the UV-to-FIR spectral energy distributions by using broad-band photometry from CANDELS and Herschel catalogs. By means of an SED decomposition technique, we derived stellar masses (M$_{*}$~10$^{11}$ Msun), IR luminosities (L$_{IR}$>10$^{12}$ Lsun), star formation rates (SFR~190-1680 Msun yr$^{-1}$) and AGN bolometric luminosities (L$_{bol}$~10$^{46}$ erg s$^{-1}$) for our sample. We used an empirically-calibrated relation between gas masses and FIR/sub-mm luminosities and derived M$_{gas}$~0.8-5.4x10$^{10}$ Msun. High-resolution (0.3-0.7'') ALMA data (when available, CANDELS data otherwise) were used to estimate the galaxy size and hence the volume enclosing most of the ISM under simple geometrical assumptions. These measurements were then combined to derive the column density associated with the ISM of the host, on the order of N$_{H, ISM}$~10$^{23-24}$ cm$^{-2}$. The comparison between the ISM column densities and those measured from the X-ray spectral analysis shows that they are similar. This suggests that, at least at high redshift, significant absorption on kpc scales by the dense ISM in the host likely adds to or substitutes that produced by circumnuclear gas on pc scales (i.e., the torus of unified models). The lack of unobscured AGN among our ISM-rich targets supports this scenario.Comment: 15 pages, 3 figures. Accepted for publication in A&

Evolution in the iron abundance of the ICM

We present a Chandra analysis of the X-ray spectra of 56 clusters of galaxies at $z>0.3$, which cover a temperature range of $3> kT > 15$ keV. Our analysis is aimed at measuring the iron abundance in the ICM out to the highest redshift probed to date. We find that the emission-weighted iron abundance measured within $(0.15-0.3) R_{vir}$ in clusters below 5 keV is, on average, a factor of $\sim2$ higher than in hotter clusters, following $Z(T)\simeq 0.88 T^{-0.47} Z_\odot$, which confirms the trend seen in local samples. We made use of combined spectral analysis performed over five redshift bins at $0.3> z > 1.3$ to estimate the average emission weighted iron abundance. We find a constant average iron abundance $Z_{Fe}\simeq 0.25 Z_\odot$ as a function of redshift, but only for clusters at $z>0.5$. The emission-weighted iron abundance is significantly higher ($Z_{Fe}\simeq0.4 Z_\odot$) in the redshift range $z\simeq0.3-0.5$, approaching the value measured locally in the inner $0.15 R_{vir}$ radii for a mix of cool-core and non cool-core clusters in the redshift range $0.1<z<0.3$. The decrease in $Z_{Fe}$ with $z$ can be parametrized by a power law of the form $\sim(1+z)^{-1.25}$. The observed evolution implies that the average iron content of the ICM at the present epoch is a factor of $\sim2$ larger than at $z\simeq 1.2$. We confirm that the ICM is already significantly enriched ($Z_{Fe}\simeq0.25 Z_\odot$) at a look-back time of 9 Gyr. Our data provide significant constraints on the time scales and physical processes that drive the chemical enrichment of the ICM.Comment: 4 pages, 4 figures, to appear in the Proceedings of "The Extreme Universe in the Suzaku Era", Dicember 2006, Kyoto (Japan

Study of thermal neutron capture gamma rays using a lithium-drifted germanium spectrometer / [by] Victor John Orphan [and] Norman C. Rasmussen

"January 1967.""AFCRL-67-0104."Also issued as an Sc. D. thesis by the first author and advised by the second author, MIT, Dept. of Nuclear Engineering, 1967Includes bibliographical references (pages 199-203)Scientific report, interim; January 1967A gamma-ray spectrometer, using a 30 cc coaxial Ge(Li) detector, which can be operated as a pair spectrometer at high energies and in the Compton suppression mode at low energies provides an effective means of obtaining thermal neutron capture gamma spectra over nearly the entire capture gamma energy range. The energy resolution (fwhm) of the spectrometer is approximately 0.5% at 1 MeV and 0.1% at 7 MeV. Capture gamma-ray energies can be determined to an accuracy of about 1 keV. The relatively high efficiency of this spectrometer allows the use of an external neutron beam geometry, which simplifies sample changing. Using a 4096 channel pulse height analyzer, the capture gamma spectrum of an element may be obtained in about one day. Low cross section (order of 0.1 b) elements with many weak intensity gammas may be studied. Over 100 gamma rays have been identified in the spectrum of one such element, Zr. The spectra of Be, Sc, Fe, Ge, and Zr are presented.United States Air Force contract no. AF19 (628)5551Project no. 5620; Task no. 56200

Dynamic nuclear polarization from current-induced electron spin polarization

Current-induced electron spin polarization is shown to produce nuclear hyperpolarization through dynamic nuclear polarization. Saturated fields of several millitesla are generated upon the application of electric field over a timescale of a hundred seconds in InGaAs epilayers and measured using optical Larmor magnetometry. The dependence on temperature, external magnetic field, and applied voltage is investigated. We find an asymmetry in which the saturation nuclear field depends on the relative alignment of the electrically generated spin polarization and the external magnetic field, which we attribute to an interplay between various electron spin dynamical processes.Comment: 5 pages, 4 figure

Sociedades e Mudanças Sociais

Neste Texto Tentamos Mostrar como o Processo de Desenvolvimento não Pode ser Entendido como um Mero Processo de Mudança Econômica, Valendo-Nos das Contribuições dos Sociólogos Evolucionistas, para Tal.

The Temperature Evolution of the Spectral Peak in High Temperature Superconductors

Recent photoemission data in the high temperature cuprate superconductor Bi2212 have been interpreted in terms of a sharp spectral peak with a temperature independent lifetime, whose weight strongly decreases upon heating. By a detailed analysis of the data, we are able to extract the temperature dependence of the electron self-energy, and demonstrate that this intepretation is misleading. Rather, the spectral peak loses its integrity above Tc due to a large reduction in the electron lifetime.Comment: 5 pages, revtex, 4 encapsulated postscript figure

Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas

Extending our previous work \cite{filinov-etal.jpa03ik} we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: i) the diagonal Kelbg potential, ii) the off-diagonal Kelbg potential iii) the {\em improved} diagonal Kelbg potential, iv) an effective potential obtained with the Feynman-Kleinert variational principle v) the ``exact'' quantum pair potential derived from the two-particle density matrix. For the {\em improved} diagonal Kelbg potential a simple temperature dependent fit is derived which accurately reproduces the ``exact'' pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo (PIMC) and molecular dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about $60 000$ K. Finally, we point out an interesting relation between the quantum potentials and effective potentials used in density functional theory.Comment: 18 pages, 11 figure

Tracing the evolution in the iron content of the ICM

We present a Chandra analysis of the X-ray spectra of 56 clusters of galaxies at z>0.3, which cover a temperature range of 3>kT>15 keV. Our analysis is aimed at measuring the iron abundance in the ICM out to the highest redshift probed to date. We find that the emission-weighted iron abundance measured within (0.15-0.3)R_vir in clusters below 5 keV is, on average, a factor of ~2 higher than in hotter clusters, following Z(T)~0.88T^-(0.47)Z_o, which confirms the trend seen in local samples. We made use of combined spectral analysis performed over five redshift bins at 0.3>z>1.3 to estimate the average emission weighted iron abundance. We find a constant average iron abundance Z_Fe~0.25Z_o as a function of redshift, but only for clusters at z>0.5. The emission-weighted iron abundance is significantly higher (Z_Fe~0.4Z_o) in the redshift range z~0.3-0.5, approaching the value measured locally in the inner 0.15R_vir radii for a mix of cool-core and non cool-core clusters in the redshift range 0.1<z<0.3. The decrease in Z_Fe with redshift can be parametrized by a power law of the form ~(1+z)^(-1.25). The observed evolution implies that the average iron content of the ICM at the present epoch is a factor of ~2 larger than at z=1.2. We confirm that the ICM is already significantly enriched (Z_Fe~0.25Z_o) at a look-back time of 9 Gyr. Our data provide significant constraints on the time scales and physical processes that drive the chemical enrichment of the ICM.Comment: 6 pages, 6 figures, to appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany