Resolution of Veronese Embedding of plane curves

Let $C$ be a smooth (irreducible) curve of degree $d$ in $\mathbb{P}^{2}$. Let $\mathbb{P}^{2} \hookrightarrow \mathbb{P}^{5}$ be the Veronese embedding and let $\mathcal{I}_{C}$ denote the homogeneous ideal of $C$ on $\mathbb{P}^{5}$. In this note we explicitly write down the minimal free resolution of $\mathcal{I}_{C}$ for $d\geq

Magic Melters' Have Geometrical Origin

Recent experimental reports bring out extreme size sensitivity in the heat capacities of Gallium and Aluminum clusters. In the present work we report results of our extensive {\it ab initio} molecular dynamical simulations on Ga$_{30}$ and Ga$_{31}$, the pair which has shown rather dramatic size sensitivity. We trace the origin of this size sensitive heat capacities to the relative order in their respective ground state geometries. Such an effect of nature of the ground state on the characteristics of heat capacities is also seen in case of small Gallium and Sodium clusters indicating that the observed size sensitivity is a generic feature of small clusters.Comment: 4 pages, 6 figure

A Trust-based Recruitment Framework for Multi-hop Social Participatory Sensing

The idea of social participatory sensing provides a substrate to benefit from friendship relations in recruiting a critical mass of participants willing to attend in a sensing campaign. However, the selection of suitable participants who are trustable and provide high quality contributions is challenging. In this paper, we propose a recruitment framework for social participatory sensing. Our framework leverages multi-hop friendship relations to identify and select suitable and trustworthy participants among friends or friends of friends, and finds the most trustable paths to them. The framework also includes a suggestion component which provides a cluster of suggested friends along with the path to them, which can be further used for recruitment or friendship establishment. Simulation results demonstrate the efficacy of our proposed recruitment framework in terms of selecting a large number of well-suited participants and providing contributions with high overall trust, in comparison with one-hop recruitment architecture.Comment: accepted in DCOSS 201

Finite temperature behavior of impurity doped Lithium cluster {\em viz} Li6_6Sn

We have carried out extensive isokinetic {\it ab initio} molecular dynamic simulations to investigate the finite temperature properties of the impurity doped cluster Li$_6$Sn along with the host cluster Li$_7$. The data obtained from about 20 temperatures and total simulation time of at least 3 ns is used to extract thermodynamical quantities like canonical specific heat. We observe a substantial charge transfer from all Li atoms to Sn which inturn weakens the Li-Li bonds in Li$_6$Sn compared to the bonds in Li$_7$. This weakening of bonds changes the finite temperature behavior of Li$_6$Sn significantly. Firstly, Li$_6$Sn becomes liquid-like around 250 K, a much lower temperature than that of Li$_7$ ($\approx$~425 K). Secondly, an additional quasirotational motion of lithium atoms appears at lower temperatures giving rise to a shoulder around 50 K in the specific heat curve of Li$_6$Sn. The peak in the specific heat of Li$_7$ is very broad and the specific heat does not show any premelting features.Comment: 16 pages, 10 figures Submitted to J. Chem. Phy

Recharging of Flying Base Stations using Airborne RF Energy Sources

This paper presents a new method for recharging flying base stations, carried by Unmanned Aerial Vehicles (UAVs), using wireless power transfer from dedicated, airborne, Radio Frequency (RF) energy sources. In particular, we study a system in which UAVs receive wireless power without being disrupted from their regular trajectory. The optimal placement of the energy sources are studied so as to maximize received power from the energy sources by the receiver UAVs flying with a linear trajectory over a square area. We find that for our studied scenario of two UAVs, if an even number of energy sources are used, placing them in the optimal locations maximizes the total received power, while achieving fairness among the UAVs. However, in the case of using an odd number of energy sources, we can either maximize the total received power, or achieve fairness, but not both at the same time. Numerical results show that placing the energy sources at the suggested optimal locations results in significant power gain compared to nonoptimal placements.Comment: 6 pages, 5 figures, conference pape

Magnetic impurities in graphane with dehydrogenated channels

We have investigated the electronic and magnetic response of a single Fe atom and a pair of interacting Fe atoms placed in patterned dehydrogenated channels in graphane within the framework of density functional theory. We have considered two channels: "armchair" and "zigzag" channels. Fully relaxed calculations have been carried out for three different channel widths. Our calculations reveal that the response to the magnetic impurities is very different for these two channels. We have also shown that one can stabilize magnetic impurities (Fe in the present case) along the channels of bare carbon atoms, giving rise to a magnetic insulator or a spin gapless semiconductor. Our calculations with spin-orbit coupling shows a large in-plane magnetic anisotropy energy for the case of the armchair channel. The magnetic exchange coupling between two Fe atoms placed in the semiconducting channel with an armchair edge is very weakly ferromagnetic whereas a fairly strong ferromagnetic coupling is observed for reasonable separations between Fe atoms in the zigzag-edged metallic channel with the coupling mediated by the bare carbon atoms. The possibility of realizing an ultrathin device with interesting magnetic properties is discussed

Metallic clusters on a model surface: quantum versus geometric effects

We determine the structure and melting behavior of supported metallic clusters using an ab initio density-functional-based treatment of intracluster interactions and an approximate treatment of the surface as an idealized smooth plane yielding an effective Lennard-Jones interaction with the ions of the cluster. We apply this model to determine the structure of sodium clusters containing from 4 to 22 atoms, treating the cluster-surface interaction strength as a variable parameter. For a strong cluster-surface interaction, the clusters form two-dimensional (2D) monolayer structures; comparisons with calculations of structure and dissociation energy performed with a classical Gupta interatomic potential show clearly the role of quantum shell effects in the metallic binding in this case, and evidence is presented that these shell effects correspond to those for a confined 2D electron gas. The thermodynamics and melting behavior of a supported Na_20 cluster is considered in detail using the model for several cluster-surface interaction strengths. We find quantitative differences in the melting temperatures and caloric curve from density-functional and Gupta treatments of the valence electrons. A clear dimensional effect on the melting behavior is also demonstrated, with 2D structures showing melting temperatures above those of the bulk or (at very strong cluster-surface interactions) no clear meltinglike transition