Plurisubharmonic polynomials and bumping

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain \Omega\subset C^n in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with bdy(\Omega), at the site of the bumping, are explicitly realised. Generally, when \Omega\subset C^n, n\geq 3, the known methods lead to bumpings with high orders of contact -- which are not explicitly known either -- at the site of the bumping. Precise orders are known for h-extendible/semiregular domains. This paper is motivated by certain families of non-semiregular domains in C^3. These families are identified by the behaviour of the least-weight plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity.Comment: 24 pages; corrected typos, fixed errors in Lemma 3.3; accepted for publication in Math.

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

An Integral Kernel for Weakly Pseudoconvex Domains

A new explicit construction of Cauchy-Fantappi\'e kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form of the boundary. Some estimates are obtained for the corresponding integral operator, which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

Does Garbage Have Standing?: Democracy, Flow Control and a Principled Constitutional Approach to Municipal Solid Waste Management

This article advocates that citizens, through state and municipal government, should constitutionally be allowed to choose whether to manage their local waste. For federal courts to dictate otherwise allows the garbage industry to trump local democratic decision making, and therefore profit at the expense of the American public

Mining semantic relations between research areas

For a number of years now we have seen the emergence of repositories of research data specified using OWL/RDF as representation languages, and conceptualized according to a variety of ontologies. This class of solutions promises both to facilitate the integration of research data with other relevant sources of information and also to support more intelligent forms of querying and exploration. However, an issue which has only been partially addressed is that of generating and characterizing semantically the relations that exist between research areas. This problem has been traditionally addressed by manually creating taxonomies, such as the ACM classification of research topics. However, this manual approach is inadequate for a number of reasons: these taxonomies are very coarse-grained and they do not cater for the finegrained research topics, which define the level at which typically researchers (and even more so, PhD students) operate. Moreover, they evolve slowly, and therefore they tend not to cover the most recent research trends. In addition, as we move towards a semantic characterization of these relations, there is arguably a need for a more sophisticated characterization than a homogeneous taxonomy, to reflect the different ways in which research areas can be related. In this paper we propose Klink, a new approach to i) automatically generating relations between research areas and ii) populating a bibliographic ontology, which combines both machine learning methods and external knowledge, which is drawn from a number of resources, including Google Scholar and Wikipedia. We have tested a number of alternative algorithms and our evaluation shows that a method relying on both external knowledge and the ability to detect temporal relations between research areas performs best with respect to a manually constructed standard

Cervical artery dissection: An atypical presentation with Ehlers-Danlos-like collagen pathology?

The authors took skin biopsies of the macroscopically normal skin of seven consecutive patients with spontaneous cervical artery dissection (SCAD). Histologically, alterations of the collagen and elastic fiber networks were found in six patients. In five, the histologic, immunohistochemical, and ultrastructural changes were similar to those usually found in Ehlers-Danlos syndrome (EDS). This suggests that SCAD is frequently associated with the dermal alterations seen in EDS

Resonant tunneling through a C60 molecular junction in liquid environment

We present electronic transport measurements through thiolated C$_{60}$ molecules in liquid environment. The molecules were placed within a mechanically controllable break junction using a single anchoring group per molecule. When varying the electrode separation of the C$_{60}$-modified junctions, we observed a peak in the conductance traces. The shape of the curves is strongly influenced by the environment of the junction as shown by measurements in two distinct solvents. In the framework of a simple resonant tunneling model, we can extract the electronic tunneling rates governing the transport properties of the junctions.Comment: 13 pages, 4 figures. To appear in Nanotechnolog