Interaction of NH3_3 gas on α\alpha-MoO3_3 nanostructures −- a DFT investigation

The structural stability, electronic properties and NH$_3$ adsorption properties of pristine, Ti, Zr and F substituted $\alpha$-MoO$_3$ nanostructures are successfully studied using density functional theory with B3LYP/LanL2DZ basis set. The structural stability of $\alpha$-MoO$_3$ nanostructures is discussed in terms of formation energy. The electronic properties of pristine, Ti, Zr and F incorporated $\alpha$-MoO$_3$ nanostructures are discussed in terms of HOMO-LUMO gap, ionization potential and electron affinity. $\alpha$-MoO$_3$ nanostructures can be fine-tuned with suitable substitution impurity to improve the adsorption characteristics of ammonia, which can be used to detect NH$_3$ in a mixed environment. The present work gives an insight into tailoring $\alpha$-MoO$_3$ nanostructures for NH$_3$ detection.Comment: 16 pages, 20 figures, 2 table

Lattice expansion and non-collinear to collinear ferrimagnetic order in MnCr2_2O4_4 nanoparticle

We report magnetic behaviour of MnCr$_2$O$_4$, which belongs to a special class of spinel, known as chromite. Bulk MnCr$_2$O$_4$ shows a sequence of magnetic states, which follows paramagnetic (PM) to collinear ferrimagnetic (FM) state below T$_C$ $\sim$ 45 K and collinear FM state to non-collinear FM state below T$_S$ $\sim$ 18 K. The non-collinear spin structure has been modified on decreasing the particle size, and magnetic transition at T$_S$ decreases in nanoparticle samples. However, ferrimagnetic order is still dominating in nanoparticles, except the observation of superparamagnetic like blocking and decrease of spontaneous magnetization for nanoparticle. This may, according to the core-shell model of ferrimagnetic nanoparticle, be the surface disorder effect of nanoparticle. The system also show the increase of T$_C$ in nanoparticle samples, which is not consistent with the core-shell model. The analysis of the M(T) data, applying spin wave theory, has shown an unusual Bloch exponent value 3.35 for bulk MnCr$_2$O$_4$, which decreases and approaches to 1.5, a typical value for any standard ferromagnet, with decreasing the particle size. MnCr$_2$O$_4$ has shown a few more unusual behaviour. For example, lattice expansion in nanoparticle samples. The present work demonstrates the correlation between a systematic increase of lattice parameter and the gradual decrease of B site non-collinear spin structure in the light of magnetism of MnCr$_2$O$_4$ nanoparticles

Sensing behavior of acetone vapors on TiO2_2 nanostructures --- application of density functional theory

The electronic properties of TiO$_2$ nanostructure are explored using density functional theory. The adsorption properties of acetone on TiO$_2$ nanostructure are studied in terms of adsorption energy, average energy gap variation and Mulliken charge transfer. The density of states spectrum and the band structure clearly reveals the adsorption of acetone on TiO$_2$ nanostructures. The variation in the energy gap and changes in the density of charge are observed upon adsorption of acetone on n-type TiO$_2$ base material. The results of DOS spectrum reveal that the transfer of electrons takes place between acetone vapor and TiO$_2$ base material. The findings show that the adsorption property of acetone is more favorable on TiO$_2$ nanostructure. Suitable adsorption sites of acetone on TiO$_2$ nanostructure are identified at atomistic level. From the results, it is confirmed that TiO$_2$ nanostructure can be efficiently utilized as a sensing element for the detection of acetone vapor in a mixed environment.Comment: 13 pages, 14 figures, 3 table

Super Fibonacci Graceful Labeling of Some Special Class of Graphs

A Fibonacci graceful labeling and a super Fibonacci graceful labeling on graphs were introduced by Kathiresan and Amutha in 2006

Robust and MaxMin Optimization under Matroid and Knapsack Uncertainty Sets

Consider the following problem: given a set system (U,I) and an edge-weighted graph G = (U, E) on the same universe U, find the set A in I such that the Steiner tree cost with terminals A is as large as possible: "which set in I is the most difficult to connect up?" This is an example of a max-min problem: find the set A in I such that the value of some minimization (covering) problem is as large as possible. In this paper, we show that for certain covering problems which admit good deterministic online algorithms, we can give good algorithms for max-min optimization when the set system I is given by a p-system or q-knapsacks or both. This result is similar to results for constrained maximization of submodular functions. Although many natural covering problems are not even approximately submodular, we show that one can use properties of the online algorithm as a surrogate for submodularity. Moreover, we give stronger connections between max-min optimization and two-stage robust optimization, and hence give improved algorithms for robust versions of various covering problems, for cases where the uncertainty sets are given by p-systems and q-knapsacks.Comment: 17 pages. Preliminary version combining this paper and http://arxiv.org/abs/0912.1045 appeared in ICALP 201

Minimum Makespan Multi-vehicle Dial-a-Ride

Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion time (makespan) of the vehicles. We study the "preemptive" version of the problem, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation for its special case when there is no capacity constraint. We also show that the approximation ratios improve by a log-factor when the underlying metric is induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200

Dial a Ride from k-forest

The k-forest problem is a common generalization of both the k-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices $V$, with $m$ demand pairs $\subseteq V \times V$ and a ``target'' $k\le m$, the goal is to find a minimum cost subgraph that connects at least $k$ demand pairs. In this paper, we give an $O(\min\{\sqrt{n},\sqrt{k}\})$-approximation algorithm for $k$-forest, improving on the previous best ratio of $O(n^{2/3}\log n)$ by Segev & Segev. We then apply our algorithm for k-forest to obtain approximation algorithms for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the following: given an $n$ point metric space with $m$ objects each with its own source and destination, and a vehicle capable of carrying at most $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We prove that an $\alpha$-approximation algorithm for the $k$-forest problem implies an $O(\alpha\cdot\log^2n)$-approximation algorithm for Dial-a-Ride. Using our results for $k$-forest, we get an $O(\min\{\sqrt{n},\sqrt{k}\}\cdot\log^2 n)$- approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an $O(\sqrt{k}\log n)$-approximation by Charikar & Raghavachari; our results give a different proof of a similar approximation guarantee--in fact, when the vehicle capacity $k$ is large, we give a slight improvement on their results.Comment: Preliminary version in Proc. European Symposium on Algorithms, 200