On the distribution of multiplicatively dependent vectors

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\R^n$ and \C^n. We also study this property in a more detailed manner by considering the covering radius of such vectors.Comment: 19 page

Using the Annotated Bibliography as a Resource for Indicative Summarization

We report on a language resource consisting of 2000 annotated bibliography entries, which is being analyzed as part of our research on indicative document summarization. We show how annotated bibliographies cover certain aspects of summarization that have not been well-covered by other summary corpora, and motivate why they constitute an important form to study for information retrieval. We detail our methodology for collecting the corpus, and overview our document feature markup that we introduced to facilitate summary analysis. We present the characteristics of the corpus, methods of collection, and show its use in finding the distribution of types of information included in indicative summaries and their relative ordering within the summaries.Comment: 8 pages, 3 figure

Efficient and Perfect domination on circular-arc graphs

Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$. An \emph{efficient dominating set} is a perfect dominating set $V'$ where $V'$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them

Laboratory mid-IR spectra of equilibrated and igneous meteorites. Searching for observables of planetesimal debris

Meteorites contain minerals from Solar System asteroids with different properties (like size, presence of water, core formation). We provide new mid-IR transmission spectra of powdered meteorites to obtain templates of how mid-IR spectra of asteroidal debris would look like. This is essential for interpreting mid-IR spectra of past and future space observatories, like the James Webb Space Telescope. We show that the transmission spectra of wet and dry chondrites, carbonaceous and ordinary chondrites and achondrite and chondrite meteorites are distinctly different in a way one can distinguish in astronomical mid-IR spectra. The two observables that spectroscopically separate the different meteorites groups (and thus the different types of parent bodies) are the pyroxene-olivine feature strength ratio and the peak shift of the olivine spectral features due to an increase in the iron concentration of the olivine

Spectroscopic diagnostic for the mineralogy of large dust grains

We examine the thermal infrared spectra of large dust grains of different chemical composition and mineralogy. Strong resonances in the optical properties result in detectable spectral structure even when the grain is much larger than the wavelength at which it radiates. We apply this to the thermal infrared spectra of compact amorphous and crystalline silicates. The weak resonances of amorphous silicates at 9.7 and 18 micron virtually disappear for grains larger than about 10 micron. In contrast, the strong resonances of crystalline silicates produce emission dips in the infrared spectra of large grains; these emission dips are shifted in wavelength compared to the emission peaks commonly seen in small crystalline silicate grains. We discuss the effect of a fluffy or compact grain structure on the infrared emission spectra of large grains, and apply our theory to the dust shell surrounding Vega.Comment: Submitted to A&A Letter

Iron(III) chelating resins-IV. Crosslinked copolymer beads of 1-(B-acrylamidoethyl)-3-hydroxy-2-methyl-4(1H)-pyridinone (AHMP) with 2-hydroxyethyl methacrylate (HEMA)

Iron(III) chelating beads have been synthesized by copolymerization of 1-(ß-acrylamidoethyl)-3-hydroxy-2-methyl-4(IH)-pyridinone (AHMP) with 2-hydroxyethyl methacrylate (HEMA), and ethyleneglycol dimethacrylate (EGDMA) as the crosslinking agent. The synthesis of the AHMP-HEMA beads was performed by suspension polymerization of AHMP, HEMA and EGDMA in benzyl alchol¿20% aqueous NaCl solution using 2,2¿-azobisisobutyronitrile (AIBN) as the initiator and polyvinylalcohol (40¿88) as a suspending agent.\ud \ud The crosslinked copolymer beads were characterized by IR, and the AHMP content was determined by elemental analysis. The AHMP-HEMA beads were not too hydrophilic, and the copolymers absorbed at equilibrium only 40¿50% water. It was found that the copolymer beads were very stable at 25°, but some degradation was observed at 121°.\ud \ud The AHMP-HEMA copolymers were able to chelate iron(III) and the chelation was dependent on the conditions such as pH and temperature. However, the capacities towards iron(III) chelation were always found to be much lower than the calculated values. The influence of the polymeric matrix on the iron(III) chelating ability was studied with iron(III) chelating resins containing various polymeric matrices. It was found that the iron(III) chelating efficiencies of the resins were strongly affected by their hydrophilicities. The low chelating efficiency of the AHMP-HEMA beads (0¿40%) is probably due to their poor swelling in water

Feedback local optimality principle applied to rocket vertical landing VTVL

Vertical landing is becoming popular in the last fifteen years, a technology known under the acronym VTVL, Vertical Takeoff and Vertical Landing [1,2]. The interest in such landing technology is dictated by possible cost reductions [3,4], that impose spaceship’s recycling. The rockets are not generally de- signed to perform landing operations, rather their design is aimed at takeoff operations, guaranteeing a very high forward acceleration to gain the velocity needed to escape the gravitational force. In this paper a new control method based on Feedback Local Optimality Principle, named FLOP is applied to the rocket landing problem. The FLOP belongs to a special class of optimal controllers, developed by the mechatronic and vehicle dynamics lab of Sapienza, named Variational Feedback Controllers - VFC, that are part of an ongoing research and are recently applied in different field: nonlinear system [5], marine and terrestrial autonomous vehicles [6,7,8], multi agents interactions and vibration control [9, 10]. The paper is devoted to show the robustness of the nonlinear controlled system, comparing the performances with the LQR, one of the most acknowledged methods in optimal control