A three-dimensional copper(II) coordination polymer featuring the 2,3-dioxyquinoxalinate(-2) ligand: Preparation,structural characterization and magnetic study

The synthesis, single-crystal X-ray structure and magnetic properties of [Cu₃L₂Cl₂(DMF)₄]_n (1), where L^2? is the 2,3-dioxyquinoxalinate(-2) ligand, are reported. The complex was prepared by the reaction of CuCl₂ and 1,4-dihydro-2,3-quinoxalinedione (H₂L′) under basic conditions using either solvothermal or normal laboratory techniques. Compound 1 is a 3D coordination polymer with an (8².10)-a, lig (LiGe) topology, containing the ligand in a novel 3.1111 (Harris notation) coordination mode. Variable-temperature and variable-field magnetic studies reveal that the ligand L^2? propagates weak antiferromagnetic exchange interactions through its “quinoxaline” part. IR data are discussed in terms of the structural features of 1 and the coordination mode of L^2?.     

Large transitive models in local ZFC

This paper is a sequel to Tzouvaras (Arch Math Log 49(5):571–601, 2010), where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and ${\Pi_1^1}$ -indescribable models, were considered. By analogy we refer to such models as “large models”, and the properties in question as “large model properties”. Continuing here in the same spirit we consider further large model properties, that resemble stronger large cardinals, namely, “elementarily embeddable”, “extendible” and “strongly extendible”, “critical” and “strongly critical”, “self-critical” and “strongly self-critical”, the definitions of which involve elementary embeddings. Each large model property ? gives rise to a localization axiom Loc ^? (ZFC) saying that every set belongs to a transitive model of ZFC satisfying ?. The theories LZFC ^?  = LZFC + Loc ^? (ZFC) are local analogues of the theories ZFC+“there is a proper class of large cardinals ψ”, where ψ is a large cardinal property. If sext(x) is the property of strong extendibility, it is shown that LZFC ^sext proves Powerset and Σ₁-Collection. In order to refute V = L over LZFC, we combine the existence of strongly critical models with an axiom of different flavor, the Tall Model Axiom (TMA). V = L can also be refuted by TMA plus the axiom GC saying that “there is a greatest cardinal”, although it is not known if TMA + GC is consistent over LZFC. Finally Vopěnka’s Principle (V P) and its impact on LZFC are examined. It is shown that LZFC ^sext  + V P proves Powerset and Replacement, i.e., ZFC is fully recovered. The same is true for some weaker variants of LZFC ^sext . Moreover the theories LZFC ^sext +V P and ZFC+V P are shown to be identical.     

A postscript on aggregate Farrell efficiencies

In this note we derive alternative weighting schemes that complement those of Färe and Zelenyuk (2003) for consistent aggregation of Farrell efficiencies when the technology exhibits (global) constant returns to scale.     

On aggregate composite indicators

In this paper it is shown that the unweighted arithmetic average is the theoretically consistent scheme to aggregate composite indicators, derived from the benefit-of-the-doubt model, across decision-making units.     

Economic model predictive inventory routing and control

Central European Journal of Operations Research - The paper proposes an economic model predictive control (EMPC) strategy for the inventory routing problem under demand uncertainty. The strategy is...     

An empirical study of PLAD regression using the bootstrap

Partial LAD regression uses the L ₁ norm associated with least absolute deviations (LAD) regression while retaining the same algorithmic structure of univariate partial least squares (PLS) regression. We use the bootstrap in order to assess the partial LAD regression model performance and to make comparisons to PLS regression. We use a variety of examples coming from NIR experiments as well as two sets of experimental data.