Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Quantitative studies of the optical and UV spectra of Galactic early B supergiants - I. Fundamental parameters

Aims. We undertake an optical and ultraviolet spectroscopic analysis of a sample of 20 Galactic B0-B5 supergiants of luminosity classes Ia, Ib, Iab, and II. Fundamental stellar parameters are obtained from optical diagnostics and a critical comparison of the model predictions to observed UV spectral features is made.

Creating and probing multipartite macroscopic entanglement with light

We propose an immediately realizable scheme showing signatures of multipartite entanglement generated by radiation pressure in a cavity system with a movable mirror. We show how the entanglement involving the inaccessible massive object is unraveled by means of field-field quantum correlations and persists within a wide range of working conditions. Our proposal provides an operative way to infer the quantum behavior of a system that is only partially accessible.