Abstract. We apply the general formalism of nilpotent polynomials [Mandilara et al, Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite entanglement classification in four qubits. In addition to establishing contact with existing results, we explicitly show how the nilpotent formalism naturally suggests constructions of entanglement measures invariant under the required un...

We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, eas...

Environmental regulators have access to a large set of policy tools and instruments to create incentives for industrial facilities to abate pollution. Command and control is one approach where pollution standards for emissions or effluence are set, and fines and penalties are assessed against non-compliant facilities. Other options include pollution charges, tradable permits, voluntary particip...

We introduce nonassociative geometric objects generalizing naturally Lie groupoids and called (smooth) quasiloopoids loopoids. prove that the tangent bundles of smooth loopoids are canonically again (it is nontrivial in case loopoids). show also this not true if cotangent concerned. After providing a few natural constructions, we how Lie-like functor associates with skew algebroids almost discr...

Background: Contamination of the environment due to heavy metals is a major concern to human life and the environment. This study was conducted to investigate and quantify the copper and zinc concentrations in industrial estates soil in Arak, Iran. Methods: Four industrial estates were considered for the experimental design, including Arak 1, Arak 2, Arak 3, and Ghotbe Sanaati. For prelimin...

This paper describes an agent-based model developed to simulate the impact that different planning policies may have in enhancing the attractiveness of the industrial estates located in a network of four municipalities located in the North of Portugal. The policies were simulated using three scenarios that can be distinguished by the municipal level of coordination they are implemented and by t...

This article aims to show how the concept of “housing need” has circulated between social sciences and architectural design fields in France since second half 19th century up until today. is a particularly rich example for developing this sociohistorical overview over long span time, through three time periods: beginning housing policy which, during hygienist period legal devices statistics, de...