Extending and Exploring the 2 cm Survey Sample

We present new results from the VLBA 2 cm Survey, an imaging survey of active galactic nuclei (AGN) at sub-milliarcsecond resolution. We extend the structural variability monitoring program of more than 130 extragalactic parsec-scale radio jets from over 170 AGN to a total of eight years. The sample is explored further in time for all sources, and intensively for individual objects. We report new detailed results on the compact sources III Zw 2, AO 0235+16, and NRAO 512.Comment: Proceedings of the 7th European VLBI Network Symposium (October 12-15 2004, Toledo, Spain), eds. Bachiller, R., Colomer, F., Desmurs, J. F., & de Vicente, P., 2 tables, 3 figures, needs evn2004.cl

Average household incomes for UK pensioners are reducing each year due to harmful government reforms and the Bank of England’s monetary policies

Ros Altmann argues for supporting pensioners who have been negatively impacted by monetary and fiscal policy since 2008. She highlights the distributional inequities of the Bank of England’s policies in dealing with the economy and calls for more consideration for pensioners who are seeing their savings dwindle

VIPS: simple, efficient, and scalable cache coherence

Directory-based cache coherence is the de-facto standard for scalable shared-memory multi/many-cores and significant effort is invested in reducing its overhead. However, directory area and complexity optimizations are often antithetical to each other. This talk presents VIPS, a family of cache coherence protocols based on self-invalidation and self-downgrade. VIPS protocols remove the complexity and cost associated with directories in their entirety, thus increasing multiprocessors scalability, and at the same time, provide better performance and energy efficiency than traditional directory-based protocols

The VLBA 2cm Survey: Kinematics of pc-Scale Structures in Active Galactic Nuclei

The kinematics of jets in active galactic nuclei (QSOs, BL Lacs, Radio Galaxies and Empty Field objects) on parsec scales is being studied with Very Long Baseline Array observations at 15 GHz of a sample of more than 170 radio sources. More than 1000 images have been taken since 1994. Here we present an overview of the results of our study, including the proper motions of components in the jets, and their relationship with other source properties.Comment: To be published in the volume "Highlights of Spanish Astrophysics (III), Proceedings of the 5th Scientific Meeting of the Spanish Astronomical Society" of the Astrophysics and Space Science Library (Kluwer), J. Gallego, J. Zamorano, N. Cardiel (eds.), 4 pages, 2 figures, needs kapproc.st

Nonlocal elliptic equations in bounded domains: a survey

In this paper we survey some results on the Dirichlet problem $$\left\{ \begin{array}{rcll} L u &=&f&\textrm{in }\Omega \\ u&=&g&\textrm{in }\mathbb R^n\backslash\Omega \end{array}\right.$$ for nonlocal operators of the form $$Lu(x)=\textrm{PV}\int_{\mathbb R^n}\bigl\{u(x)-u(x+y)\bigr\}K(y)dy.$$ We start from the very basics, proving existence of solutions, maximum principles, and constructing some useful barriers. Then, we focus on the regularity properties of solutions, both in the interior and on the boundary of the domain. In order to include some natural operators $L$ in the regularity theory, we do not assume any regularity on the kernels. This leads to some interesting features that are purely nonlocal, in the sense that have no analogue for local equations. We hope that this survey will be useful for both novel and more experienced researchers in the field

Bad Wadge-like reducibilities on the Baire space

We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on X (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of X, and we show that the resulting hierarchies of degrees are much more complicated than the classical Wadge hierarchy; in particular, they always contain large infinite antichains, and in most cases also infinite descending chains.Comment: 31 pages, 3 figures. Revised version, accepted for publication on Fundamenta Mathematica

Boundary regularity, Pohozaev identities, and nonexistence results

In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $\Omega$, $u\equiv0$ in $\mathbb R^n\backslash\Omega$. We first discuss in detail the boundary regularity of solutions, stating the main known results of Grubb and of the author and Serra. We also give a simplified proof of one of such results, focusing on the main ideas and on the blow-up techniques that we developed in \cite{RS-K,RS-stable}. After this, we present the Pohozaev identities established in \cite{RS-Poh,RSV,Grubb-Poh} and give a sketch of their proofs, which use strongly the fine boundary regularity results discussed previously. Finally, we show how these Pohozaev identities can be used to deduce nonexistence of solutions or unique continuation properties. The operators $L$ under consideration are integro-differential operator of order $2s$, $s\in(0,1)$, the model case being the fractional Laplacian $L=(-\Delta)^s$.Comment: Survey article. To appear as a chapter in "Recent Developments in the Nonlocal Theory" by De Gruyte