Briot–Bouquet differential superordinations and sandwich theorems

AbstractBriot–Bouquet differential subordinations play a prominent role in the theory of differential subordinations. In this article we consider the dual problem of Briot–Bouquet differential superordinations. Let β and γ be complex numbers, and let Ω be any set in the complex plane C. The function p analytic in the unit disk U is said to be a solution of the Briot–Bouquet differential superordination ifΩ⊂{p(z)+zp′(z)βp(z)+γ|z∈U}. The authors determine properties of functions p satisfying this differential superordination and also some generalized versions of it.In addition, for sets Ω1 and Ω2 in the complex plane the authors determine properties of functions p satisfying a Briot–Bouquet sandwich of the formΩ1⊂{p(z)+zp′(z)βp(z)+γ|z∈U}⊂Ω2. Generalizations of this result are also considered

Extragalactic Millimeter-wave Point-source Catalog, Number Counts and Statistics from 771 deg^2 of the SPT-SZ Survey

We present a point-source catalog from 771 deg^2 of the South Pole Telescope Sunyaev-Zel'dovich survey at 95, 150, and 220 GHz. We detect 1545 sources above 4.5σ significance in at least one band. Based on their relative brightness between survey bands, we classify the sources into two populations, one dominated by synchrotron emission from active galactic nuclei, and one dominated by thermal emission from dust-enshrouded star-forming galaxies. We find 1238 synchrotron and 307 dusty sources. We cross-match all sources against external catalogs and find 189 unidentified synchrotron sources and 189 unidentified dusty sources. The dusty sources without counterparts are good candidates for high-redshift, strongly lensed submillimeter galaxies. We derive number counts for each population from 1 Jy down to roughly 11, 4, and 11 mJy at 95, 150, and 220 GHz. We compare these counts with galaxy population models and find that none of the models we consider for either population provide a good fit to the measured counts in all three bands. The disparities imply that these measurements will be an important input to the next generation of millimeter-wave extragalactic source population models

Random walks and search in time-varying networks

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time varying networks created from the activity potential of the nodes, and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval and diffusion processes in time-varying network

Liquid crystal properties resulting from synergetic effects between non-mesogenic organic molecules and a one nanometre sized octahedral transition metal cluster.

International audienceThis work presents the synthesis and studies of a red-NIR luminescent liquid crystal compound based on an octahedral metallic cluster core orthogonally bounded to six non-mesogenic organic ligands. It evidences synergetic effects between the organic and inorganic parts of the hybrid, resulting in the generation of liquid crystal properties on cooling from the isotropic melt

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea