On extension of multi-parametric local semigroups of isometric operators and some applications

Universidad Central de Venezuela, Consejo de Desarrollo Científico y Humanístico. Subvención PI-03-8623-2013/2It is shown that, under certain uniqueness conditions, a strongly continuous n-parametric local semigroup of isometric operators on a Hilbert space, can be extended to a strongly continuous n-parametric group of unitary operators on a larger Hilbert space. As an application a proof of the G.I. Èskin multi-dimensional version of the M.GK ̇rei ̆n ex- tension theorem, for positive definite functions, is given.peerReviewe

On extension of multi-parametric local semigroups of isometric operators and some applications

Universidad Central de Venezuela, Consejo de Desarrollo Científico y Humanístico. Subvención PI-03-8623-2013/2It is shown that, under certain uniqueness conditions, a strongly continuous n-parametric local semigroup of isometric operators on a Hilbert space, can be extended to a strongly continuous n-parametric group of unitary operators on a larger Hilbert space. As an application a proof of the G.I. Èskin multi-dimensional version of the M.GK ̇rei ̆n ex- tension theorem, for positive definite functions, is given.peerReviewe

Distinct magnetic signatures of fractional vortex configurations in multiband superconductors

Vortices carrying fractions of a flux quantum are predicted to exist in multiband superconductors, where vortex core can split between multiple band-specific components of the superconducting condensate. Using the two-component Ginzburg-Landau model, we examine such vortex configurations in a two-band superconducting slab in parallel magnetic field. The fractional vortices appear due to the band-selective vortex penetration caused by different thresholds for vortex entry within each band-condensate, and stabilize near the edges of the sample. We show that the resulting fractional vortex configurations leave distinct fingerprints in the static measurements of the magnetization, as well as in ac dynamic measurements of the magnetic susceptibility, both of which can be readily used for the detection of these fascinating vortex states in several existing multiband superconductors.Comment: 5 pages, 4 figure

The Stellar Mass Fundamental Plane: The virial relation and a very thin plane for slow-rotators

Early-type galaxies -- slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars -- define a Fundamental Plane (FP) in the space of half-light radius $R_e$, enclosed surface brightness $I_e$ and velocity dispersion $\sigma_e$. Since $I_e$ and $\sigma_e$ are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which $I_e$ and $\sigma_e$ can be used to estimate sizes $R_e$. We show that: 1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in $R_e$ is $\sim 16\%$, of which only $\sim 9\%$ is intrinsic. Removing galaxies with $M_*<10^{11}M_\odot$ further reduces the observed scatter to $\sim 13\%$ ($\sim 4\%$ intrinsic). The observed scatter increases to the $\sim 25\%$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only $5\%$ orthogonal to the plane. 2) The structure within the FP is most easily understood as arising from the fact that $I_e$ and $\sigma_e$ are nearly independent, whereas the $R_e-I_e$ and $R_e-\sigma_e$ correlations are nearly equal and opposite. 3) If the coefficients of the FP differ from those associated with the virial theorem the plane is said to be `tilted'. If we multiply $I_e$ by the global stellar mass-to-light ratio $M_*/L$ and we account for non-homology across the population by using S\'ersic photometry, then the resulting stellar mass FP is less tilted. Accounting self-consistently for $M_*/L$ gradients will change the tilt. The tilt we currently see suggests that the efficiency of turning baryons into stars increases and/or the dark matter fraction decreases as stellar surface brightness increases.Comment: 13 pages, 9 figures, 3 tables, accepted for publication in MNRA

Eclipsing high-mass binaries I. Light curves and system parameters for CPD-518946, PISMIS24-1 and HD319702

We present first results of a comprehensive photometric O-star survey performed with a robotic twin refractor at the Universit\"atssternwarte Bochum located near Cerro Armazones in Chile. For three high-mass stars, namely Pismis24-1, CPD-518946 and HD319702, we determined the period through the Lafler-Kinman algorithm and model the light curves within the framework of the Roche geometry. For Pismis24-1, a previously known eclipsing binary, we provide first light curves and determined a photometric period of 2.36 days together with an orbital inclination of 61.8 degrees. The best-fitting model solution to the light curves suggest a detached configuration. With a primary temperature of T1 = 42520K we obtain the temperature of the secondary component as T2 = 41500K. CPD-518946 is another known eclipsing binary for which we present a revised photometric period of 1.96 days with an orbital inclination of 58.4 degrees. The system has likely a semi-detached configuration and a mass ratio q = M1/M2 = 2.8. If we adopt a primary temperature of T1 = 34550K we obtain T2 = 21500K for the secondary component. HD319702 is a newly discovered eclipsing binary member of the young open cluster NGC6334. The system shows well-defined eclipses favouring a detached configuration with a period of 2.0 days and an orbital inclination of 67.5 degrees. Combining our photometric result with the primary spectral type O8 III(f) (T1 = 34000K) we derive a temperature of T2 = 25200K for the secondary component.Comment: 7 pages, 4 figures, accepted for publication in Astronomy and Astrophysic