Interaction of Gravitational Waves with Charged Particles

It is shown here that a cloud of charged particles could in principle absorb energy from gravitational waves (GWs) incident upon it, resulting in wave attenuation. This could in turn have implications for the interpretation of future data from early universe GWs.Comment: Appears in Gravitational Wave Astrophysics, Editor C.F. Sopuerta, Astrophysics and Space Science Proceedings, Volume 40. ISBN 978-3-319-10487-4. Springer International Publishing Switzerland, 2015, p. 29

Dense Continuity and Selections of Set-Valued Mappings

∗ The first and third author were partially supported by National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under grant MM-701/97.A theorem proved by Fort in 1951 says that an upper or lower semi-continuous set-valued mapping from a Baire space A into non-empty compact subsets of a metric space is both lower and upper semi-continuous at the points of a dense Gδ -subset of A. In this paper we show that the conclusion of Fort’s theorem holds under the weaker hypothesis of either upper or lower quasi-continuity. The existence of densely defined continuous selections for lower quasi-continuous mappings is also proved

Nearest points and delta convex functions in Banach spaces

Given a closed set $C$ in a Banach space $(X, \|\cdot\|)$, a point $x\in X$ is said to have a nearest point in $C$ if there exists $z\in C$ such that $d_C(x) =\|x-z\|$, where $d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points.Comment: To appear in Bull. Aust. Math. So

Quantifying Feedback from Narrow Line Region Outflows in Nearby Active Galaxies

Observations reveal that supermassive black holes (SMBHs) grow through the accretion of gas at the centers of galaxies as luminous active galactic nuclei (AGN), releasing radiation that drives powerful outflows of ionized and molecular gas. These winds are thought to play a critical role in galaxy evolution by regulating star formation and the growth of galaxies and their SMBHs. To test this model, we must quantify the dynamic impact of outflows by measuring their mass outflow rates and energetics. Using spatially resolved spectroscopy and imaging from the Hubble Space Telescope and Cloudy photoionization models we mapped the ionized gas kinematics and mass distributions of narrow line region (NLR) outflows in nearby active galaxies. We find that the outflows contain up to several million solar masses of ionized gas and are limited to distances of 1 - 2 kiloparsecs from the nucleus. The maximum mass outflow rates are M = 3 - 12 solar masses per year and the outflow gas mass, velocity, radial extent, and energetics are positively correlated with AGN luminosity. We use our results to test simplified techniques with less stringent data requirements and find that they significantly overestimate the gas mass. These results are crucial for modeling powerful outflows at higher redshift that may considerably influence star formation rates and the formation of galactic structure

An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical $\epsilon$-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the $\epsilon$-subdifferential enlargement

The difference vectors for convex sets and a resolution of the geometry conjecture

The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain translations of the underlying sets. In this paper, we provide a complete resolution of the geometry conjecture. Our proof relies on monotone operator theory. We revisit previously known results and provide various illustrative examples. Comments on the numerical computation of the quantities involved are also presented