On the future infimum of positive self-similar Markov processes

We establish integral tests and laws of the iterated logarithm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at 0 and infinity. Our proofs are based on the Lamperti representation and time reversal arguments due to Chaumont and Pardo [9]. These results extend laws of the iterated logarithm for the future infimum of Bessel processes due to Khoshnevisan et al. [11]

The making of South Korea's COVID-19 test success. IES Policy Brief Issue 2020/04 - April 2020

At least 120 countries have asked South Korea for COVID-19 test kits and other materials to fight against the ongoing coronavirus pandemic. South Korean biotech firms are shipping the kits everywhere from Europe and the United States to the Middle East and Southeast Asia. The secret to South Korea’s test development and manufacturing success lies in Daejeon. This city is home to Daedeok Innopolis, South Korea’s main R&D cluster, including for biotech. Developed since the 1990s, South Korea’s biotech industry is a textbook case of the country’s industrial policy. It is based on two pillars: public-private cooperation and continuity across administrations. This is what Daedeok Innopolis and South Korea’s COVID-19 test success embody

Splitting hairs with transcendental entire functions

For polynomials of degree at least two, local connectivity of their Julia set is an important property, since it leads to a complete description of their topological dynamics in terms of a simpler model. There is no such connection between the topology of the Julia set of a transcendental entire function $f$ and its dynamics. Nonetheless, it has been shown that one can still describe the dynamics of $f$ in terms of a simpler model, assuming that its \textit{postsingular set} is bounded and $f$ satisfies certain additional hyperbolicity assumptions. Our goal in this paper is, for the first time, to give analogous results in cases when the postsingular set is unbounded. More specifically, we show that if $f$ is of finite order, has \textit{bounded criticality} on its Julia set, and its singular set consists of finitely many critical values that escape to infinity and satisfy a certain separation condition, then its Julia set $J(f)$ is a collection of \textit{dynamic rays} or \emph{hairs}, that \emph{split} at (preimages of) critical points, together with their corresponding landing points. In fact, our result holds for a much larger class of functions; in particular, the assumption of finite order is relaxed to the existence of a map in their parameter space whose Julia set is a \textit{Cantor bouquet}. The existence and landing of rays is a consequence of a more general result; we provide a \textit{topological model} for the action of $f$ on $J(f)$. Finally, we present new results concerning \textit{disjoint type} functions in the case that the Julia set is a Cantor bouquet.Comment: 69 pages, 8 figure

Multiple Petty Offenses With Serious Penalties: A Case for the Right to Trial by Jury

This Note outlines the history and development of the petty offense exception and the Supreme Court\u27s jury trial entitlement jurisprudence. In particular, it discusses the fundamental principle of gauging criminal seriousness by the length of a penalty as authorized by statute. This Note sets out the Circuit split and explains why the courts are divided on the aggregation issue. It argues that courts must aggregate maximum penalties for multiple petty offenses charged together to accurately reflect legislative determinations of criminal seriousness. It also criticizes the use of pre-trial sentencing stipulations to circumvent trial by jury when it would otherwise be required

Global environmental change and sustainable development

The UC3M group of “Global environmental change and sustainable development: social trends and emerging policies” offers its experience on the following fields: • Sustainable Development. • Environmental Education. • Agenda 21. • Sustainable Cities and Sustainable Land Planning. • Environmental Impact Evaluation. • Sustainable Transport and Mobility. • Social Management and Saving Policies (energy, waste, water, noise). Within this framework, the work of this research group aims to: 1) The analysis and diagnosis of how Global Environmental Change and Sustainable Development can affect each specific organization. 2) The proposal of solutions. 3) The management of their implementation. 4) Instruction and training. These objectives are tackled from their basic study to their applied development through reports and consultancy services

Bifurcation From Infinity For Reaction–Diffusion Equations Under Nonlinear Boundary Conditions

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle