Phosphido pincer complexes of platinum: synthesis, structure and reactivity

A series of platinum(II) complexes supported by the tridentate bis(phosphine)phosphido ligand bis(2-diisopropylphosphinophenyl)phosphide) [iPr–PPP] have been synthesized and characterized (1–4). X-Ray structural studies of [iPr–PPP]PtCl (1) and [iPr–PPP]PtCH3 (3) complexes show meridional [iPr–PPP] ligands around approximately square-planar platinum centers. Structural data and NMR analysis highlight a strong trans influence for the phosphido phosphorous donor, comparable to that of the anionic aryl carbon of the classic PCP pincer complexes. A series of thermally stable [PPP]Pt(IV) compounds, including [PPP]Pt(CH_3)_2X [X = I (5) and SbF_6 (6)], were also synthesized. The study of the binding affinity of SO_2 and NO to complex 1 has also been addressed

Multifrequency EPR Studies of [Cu^(1.5)Cu^(1.5)]+ for Cu_2(μ-NR_2)_2 and Cu_2(μ-PR_2)_2 Diamond Cores

Multifrequency electron paramagnetic resonance (EPR) spectroscopy is used to explore the electronic structures of a series of dicopper complexes of the type {(LXL)Cu}_2^+. These complexes contain two four-coordinate copper centers of highly distorted tetrahedral geometries linked by two [LXL]^− ligands featuring bridging amido or phosphido ligands and associated thioether or phosphine chelate donors. Specific chelating [LXL]^− ligands examined in this study include bis(2-tert-butylsulfanylphenyl)amide (SNS), bis(2-di-iso-butylphosphinophenyl)amide (PNP), and bis(2-di-iso-propylphosphinophenyl)phosphide (PPP). To better map the electronic coupling to copper, nitrogen, and phosphorus in these complexes, X-, S-, and Q-band EPR spectra have been obtained for each complex. The resulting EPR parameters implied by computer simulation are unusual for typical dicopper complexes and are largely consistent with previously published X-ray absorption spectroscopy and density functional theory data, where a highly covalent {Cu_2(μ-XR_2)_2}^+ diamond core has been assigned in which removal of an electron from the neutral {Cu_2(μ-XR_2)_2} can be viewed as ligand-centered to a substantial degree. To our knowledge, this is the first family of dicopper diamond core model complexes for which the compendium of X-, S-, and Q-band EPR spectra have been collected for comparison to Cu_A

Two-tier Spatial Modeling of Base Stations in Cellular Networks

Poisson Point Process (PPP) has been widely adopted as an efficient model for the spatial distribution of base stations (BSs) in cellular networks. However, real BSs deployment are rarely completely random, due to environmental impact on actual site planning. Particularly, for multi-tier heterogeneous cellular networks, operators have to place different BSs according to local coverage and capacity requirement, and the diversity of BSs' functions may result in different spatial patterns on each networking tier. In this paper, we consider a two-tier scenario that consists of macrocell and microcell BSs in cellular networks. By analyzing these two tiers separately and applying both classical statistics and network performance as evaluation metrics, we obtain accurate spatial model of BSs deployment for each tier. Basically, we verify the inaccuracy of using PPP in BS locations modeling for either macrocells or microcells. Specifically, we find that the first tier with macrocell BSs is dispersed and can be precisely modelled by Strauss point process, while Matern cluster process captures the second tier's aggregation nature very well. These statistical models coincide with the inherent properties of macrocell and microcell BSs respectively, thus providing a new perspective in understanding the relationship between spatial structure and operational functions of BSs

No Mirror Symmetry in Landau-Ginzburg Spectra!

We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate the corresponding Hodge numbers. Surprisingly, the resulting spectra are less symmetric than the existing incomplete results. It turns out that models belonging to the large class for which an explicit construction of a mirror model as an orbifold is known show remarkable mirror symmetry. On the other hand, half of the remaining 15\% of all models have no mirror partners. This lack of mirror symmetry may point beyond the class of LG-orbifolds.Comment: 17 page

Translated tori in the characteristic varieties of complex hyperplane arrangements

We give examples of complex hyperplane arrangements for which the top characteristic variety contains positive-dimensional irreducible components that do not pass through the origin of the character torus. These examples answer several questions of Libgober and Yuzvinsky. As an application, we exhibit a pair of arrangements for which the resonance varieties of the Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic varieties are not isomorphic. The difference comes from translated components, which are not detected by the tangent cone at the origin.Comment: Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Application

Package ecespa

Documentation for the R-package "ecespa