Weighted cohomology of arithmetic groups

M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of arithmetic groups \Gamma in a real group G, with coefficients in certain local systems, associated to arbitrary upper and lower weight profiles. The author shows, using essentially local arguments on the reductive Borel-Serre compactification, that these cohomologies agree with certain weighted L^2 cohomologies defined by J. Franke. When the rank of G is equal to that of a maximal compact subgroup, this implies that the cohomologies associated to both upper and lower middle profiles are both isomorphic to L^2 cohomology.Comment: 32 pages, published version, abstract added in migratio

Heavy Scalar, Vector and Axial-Vector Mesons in Hot and Dense Nuclear Medium

In this work we shall investigate the mass modifications of scalar mesons $\left( D_{0}, B_{0}\right)$,vector mesons $\left( D^{\ast}, B^{\ast}\right)$ and axial-vector mesons $\left(D_{1}, B_{1}\right)$ at finite density and temperature of the nuclear medium. The above mesons are modified in the nuclear medium through themodification of quark and gluon condensates. We shall find the medium modification of quark and gluon condensates within chiral SU(3) model through the medium modification of scalar-isoscalar fields $\sigma$ and $\zeta$ at finite density and temperature. These medium modified quark and gluon condensates will further be used through QCD sum rules for the evaluation of in-medium properties of above mentioned scalar, vector and axial vector mesons. We shall also discuss the effects of density and temperature of the nuclear medium on the scattering lengths of above scalar, vector and axial-vector mesons. The study of the medium modifications of above mesons may be helpful for understanding their production rates in heavy-ion collision experiments. The results of present investigations of medium modifications of scalar, vector and axial-vector mesons at finite density and temperature can be verified in the Compressed Baryonic Matter (CBM) experiment of FAIR facility at GSI, Germany.Comment: 35 pages, 11 figure

Full Current Statistics for a Disordered Open Exclusion Process

We consider the nonabelian sandpile model defined on directed trees by Ayyer, Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to the special case of a one-dimensional lattice of $n$ sites which has open boundaries and disordered hopping rates. We focus on the joint distribution of the integrated currents across each bond simultaneously, and calculate its cumulant generating function exactly. Surprisingly, the process conditioned on seeing specified currents across each bond turns out to be a renormalised version of the same process. We also remark on a duality property of the large deviation function. Lastly, all eigenvalues and both Perron eigenvectors of the tilted generator are determined.Comment: 14 pages, minor clarification

Innovative Supplier Selection: Key Success Factors

Due  to  the  emergence  of  globalization  and  shrinking  distances, companies don’t  mind  going   to new unexplored locations in search of suitable suppliers. However, the suitability of suppliers can be measured in terms of its technical competence and innovativeness. The aim of this paper is to find out the necessary parameters to check the innovativeness of suppliers. This paper looks at how the authors analyzed existing literature on supplier selection based on their innovativeness

Quantum state estimation using weak measurements

We explore the possibility of using "weak measurements" without "weak value" for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue the state, unlike for the case of projective measurements. We use this property of weak measurements and design schemes for quantum state estimation for qubits and for Gaussian states. We show, via numerical simulations, that under certain circumstances, our method can outperform the estimation by projective measurements both for qubits and for Gaussian states. It turns out that ensemble size plays an important role and the scheme based on recycling works better for small ensembles.Comment: 7 pages, 3 figures. Minor changes. Conference proceedings. Presented at DMQM2014(Bangalore Oct. 22-24, 2014). This article draws from arXiv:1402.044