Discussion on Lechicki and Spakowski's counterexample

It is well-known that intersection of continuous correspondences can lost the continuity property. Lechicki and Spakowski's theorem says that intersection of H-lsc functions remains H-lsc if the intersection is a bounded subset of a normed space and its interior is nonempty. Lechicki and Spakowski pointed to the importance of the boundedness assumption in the case of infinite dimensional range giving a counterexample. Even though the counterexample works properly and is one of the most cited patterns of discontinuity, it has no detailed discussion in the literature of economics and optimization theory. What is more, some misleading interpretation of this very important counterexample can be observed. Our technical note clarifies the exact role of Lechicki and Spakowski's counterexample, computing each of the important properties of the correspondences rigorously

Green Jobs Update

[Excerpt] It was no accident that the first Middle Class Task Force was on green jobs. Our focus on clean energy and energy efficiency jobs for the middle class occurs at the intersection of two of the Obama Administration’s most important policy initiatives: creating good jobs and protecting the environment

Safety problems in urban cycling mobility. A quantitative risk analysis at urban intersections

The attention to the most vulnerable road users has grown rapidly in recent decades. The experience gained reveals an important number of cyclist fatalities due to road crashes; most of which occur at intersections. In this study, dispersion of trajectories in urban intersections has been considered to identify the whole conflict area and the largest conflict areas between cars and bicycles, and the speeds have been used to calculate exposure time of cyclists and reaction time available to drivers to avoid collision. These data allow the summary approach to the problem, while a risk probability model has been developed to adopt an elementary approach analysis. A quantitative damage model has been proposed to classify each conflict point, and a probabilistic approach has been defined to consider the traffic volume and the elementary unit of exposure. The combination of damage and probability, permitted to assess the risk of crash, at the examined intersection. Three types of urban four-arm intersection, with and without bike paths, were considered. For each scheme, the authors assessed the risk of collision between the cyclist and the vehicle. The obtained results allowed the identification of the most hazardous maneuvers and highlighted that geometry and kinematics of traffic movements cannot be overlooked, when designing an urban road intersection. The strategy proposed by the authors could have a significant impact on the risk management of urban intersections. The obtained results and the proposed hazard estimation methodology could be used to design safer intersections

Holomorphic functions of slow growth on nested covering spaces of compact manifolds

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let phi be the smoothed distance from a fixed point in Y in a metric pulled up from M. Let O_phi(X) be the Hilbert space of holomorphic functions f on X such that f^2 e^(-phi) is integrable on X, and define O_phi(Y) similarly. Our main result is that (under more general hypotheses than described here) the restriction O_phi(Y) to O_phi(X) is an isomorphism for d large enough. This yields new examples of Riemann surfaces and domains of holomorphy in C^n with corona. We consider the important special case when Y is the unit ball B in C^n, and show that for d large enough, every bounded holomorphic function on X extends to a unique function in the intersection of all the nontrivial weighted Bergman spaces on B. Finally, assuming that the covering group is arithmetic, we establish three dichotomies concerning the extension of bounded holomorphic and harmonic functions from X to B

Research support-oriented MATLAB learning: tackling difficult concepts and promoting personalised learning

This study investigated the acquisition of MATLAB programming skills by postgraduate students, and whether this learning was improved by research support-oriented teaching. Questionnaire surveys were given to academic staff asking about what they considered the most important knowledge and skills in programming to be. Questionnaire surveys were also given to students asking about what programming concepts they found the most difficult and confusing to understand. The intersection between what knowledge and skills in programming the researchers deemed the most important, and what areas in programming students had most difficulty with, was carefully addressed in subsequent teaching in a module teaching the essentials of programming to postgraduate students. Student learning performance, as measured by examination marks on the module, before and after the intersection concepts were emphasised was compared. The student learning performance improvement, together with interviews to students about their perceptions about programming, suggests that teaching oriented to research support is effective at increasing student understanding of programming in MATLAB

Near Hagedorn Dynamics of NS Fivebranes, or A New Universality Class of Coiled Strings

We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to vary the temperature of the near extremal solution by taking into account $g_s$ corrections. The Hagedorn temperature is shown to be a limiting temperature for the theory. We then compare the thermodynamics to that of a toy model made of free strings and find basic discrepancies. This suggests a need for a new class of string interactions. We suggest that this new universality class is characterized by a strong attractive self-intersection interaction, which causes strings to be coiled. This model might also explain why ``Little String Theories'' exist in at most 5+1 dimensions.Comment: 37 pages, important signs in section 6.4 corrected, references adde