A continuous model for quasinilpotent operators.

A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space HH . More precisely, given a quasinilpotent operator T on HH , there exists a compact quasinilpotent operator K in HH such that T is similar to a part of K⊕K⊕⋯⊕K⊕⋯K⊕K⊕⋯⊕K⊕⋯ acting on the direct sum of countably many copies of HH . We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0C0 -semigroups of quasinilpotent operators.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

Caught in the act: gas and stellar velocity dispersions in a fast Quenching compact star-forming galaxy at z ~ 1.7

We present Keck I MOSFIRE spectroscopy in the Y and H bands of GDN-8231, a massive, compact, star-forming galaxy at a redshift of z ~ 1.7. Its spectrum reveals both Hα and [Nii] emission lines and strong Balmer absorption lines. The Hα and Spitzer MIPS 24 μm fluxes are both weak, thus indicating a low star-formation rate of SFR≲5-10 M_⨀ yr−1. This, added to a relatively young age of ~700 Myr measured from the absorption lines, provides the first direct evidence for a distant galaxy being caught in the act of rapidly shutting down its star formation. Such quenching allows GDN-8231 to become a compact, quiescent galaxy, similar to three other galaxies in our sample, by z ~ 1.5. Moreover, the color profile of GDN-8231 shows a bluer center, consistent with the predictions of recent simulations for an early phase of inside-out quenching. Its line-of-sight velocity dispersion for the gas, σ_LOG^gas = 127 ± 32 km s^−1, is nearly 40% smaller than that of its stars, σ_LOG^* = 215 ± 35 km s^−1. High-resolution hydro-simulations of galaxies explain such apparently colder gas kinematics of up to a factor of ~1.5 with rotating disks being viewed at different inclinations and/or centrally concentrated star-forming regions. A clear prediction is that their compact, quiescent descendants preserve some remnant rotation from their star-forming progenitors.

CANDELS: The progenitors of compact quiescent galaxies at z ~ 2

We combine high-resolution Hubble Space Telescope/WFC3 images with multi-wavelength photometry to track the evolution of structure and activity of massive (M_*> 10^10 M_☉) galaxies at redshifts z = 1.4-3 in two fields of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. We detect compact, star-forming galaxies (cSFGs) whose number densities, masses, sizes, and star formation rates (SFRs) qualify them as likely progenitors of compact, quiescent, massive galaxies (cQGs) at z = 1.5-3. At z≲2, cSFGs present SFR = 100-200 M_☉ yr^–1, yet their specific star formation rates (sSFR ~ 10^–9 yr^–1) are typically half that of other massive SFGs at the same epoch, and host X-ray luminous active galactic nuclei (AGNs) 30 times (~30%) more frequently. These properties suggest that cSFGs are formed by gas-rich processes (mergers or disk-instabilities) that induce a compact starburst and feed an AGN, which, in turn, quench the star formation on dynamical timescales (few 10^8 yr). The cSFGs are continuously being formed at z = 2-3 and fade to cQGs down to z ~ 1.5. After this epoch, cSFGs are rare, thereby truncating the formation of new cQGs. Meanwhile, down to z = 1, existing cQGs continue to enlarge to match local QGs in size, while less-gas-rich mergers and other secular mechanisms shepherd (larger) SFGs as later arrivals to the red sequence. In summary, we propose two evolutionary tracks of QG formation: an early (z≲2), formation path of rapidly quenched cSFGs fading into cQGs that later enlarge within the quiescent phase, and a late-arrival (z≳2) path in which larger SFGs form extended QGs without passing through a compact state.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Solderjet bumping technique used to manufacture a compact and robust green solid-state laser

Solder-joining using metallic solder alloys is an alternative to adhesive bonding. Laser-based soldering processes are especially well suited for the joining of optical components made of fragile and brittle materials such as glasses, ceramics and optical crystals due to a localized and minimized input of thermal energy. The Solderjet Bumping technique is used to assemble a miniaturized laser resonator in order to obtain higher robustness, wider thermal conductivity performance, higher vacuum and radiation compatibility, and better heat and long term stability compared with identical glued devices. The resulting assembled compact and robust green diode-pumped solid-state laser is part of the future Raman Laser Spectrometer designed for the Exomars European Space Agency (ESA) space mission 2018.

Sub-kiloparsec alma imaging of compact star-forming galaxies at z ~ 2.5: revealing the formation of dense galactic cores in the progenitors of compact quiescent galaxies

We present spatially resolved Atacama Large Millimeter/submillimeter Array (ALMA) 870 μm dust continuum maps of six massive, compact, dusty star-forming galaxies at z ~ 2.5. These galaxies are selected for their small rest-frame optical sizes (r_e,F160W ~ 1.6 kpc) and high stellar mass densities that suggest that they are direct progenitors of compact quiescent galaxies at z ~ 2. The deep observations yield high far-infrared (FIR) luminosities of L_IR = 10^12.3-12.8 L_⨀ and star formation rates (SFRs) of SFR = 200–700 M_⊙ yr^−1, consistent with those of typical star-forming "main sequence" galaxies. The high spatial resolution (FWHM ~ 0 12–0 18) ALMA and Hubble Space Telescope photometry are combined to construct deconvolved, mean radial profiles of their stellar mass and (UV+IR) SFR. We find that the dusty, nuclear IR–SFR overwhelmingly dominates the bolometric SFR up to r ~ 5 kpc, by a factor of over 100× from the unobscured UV–SFR. Furthermore, the effective radius of the mean SFR profile (r_e,SFR ~ 1 kpc) is ~30% smaller than that of the stellar mass profile. The implied structural evolution, if such nuclear starburst last for the estimated gas depletion time of Δt = ±100 Myr, is a 4×increase of the stellar mass density within the central 1 kpc and a 1.6× decrease of the half-mass–radius. This structural evolution fully supports dissipation-driven, formation scenarios in which strong nuclear starbursts transform larger, star-forming progenitors into compact quiescent galaxies.