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

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

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

Metallo-Anti-aromatic Al4Na4 and Al4Na3- compounds: A theoretical investigation

We propose a theoretical investigation in this paper to understand the bonding and structural properties of neutral Al4Na4 and anion Al4Na3- clusters. We show that the Al4 species in Al4Na4 and Al4Na3- clusters is a rectangular planar structure with alternate pi-bonds and hence satisfying the basic criteria for anti-aromaticity. We prove that the Al4Na4 and Al4Na3- clusters are metallo-anti-aromatic compounds

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

Structure, electronic properties and magnetic transition in manganese clusters

We systematically investigate the structural, electronic and magnetic properties of Mn$_n$ clusters ($n =$ 2$-$20) within the {\it ab-initio} pseudopotential plane wave method using generalized gradient approximation for the exchange-correlation energy. A new kind of icosahedral structural growth has been predicted in the intermediate size range. Calculated magnetic moments show an excellent agreement with the Stern-Gerlach experiment. A transition from ferromagnetic to ferrimagnetic Mn$-$Mn coupling takes place at $n=$ 5 and the ferrimagnetic states continue to be the ground states for the entire size range. Possible presence of multiple isomers in the experimental beam has been argued. No signature of non-metal to metal transition is observed in this size range and the coordination dependence of $d-$electron localization is discussed.Comment: 11 Pages and 9 Figures. Physical Review B (in press