Polyhedral polarity defined by a general bilinear inequality

LetX andY be finite dimensional vector spaces over the real numbers. Let be a binary relation betweenX andY given by a bilinear inequality. The-polar of a subsetP ofX is the set of all elements ofY which are related by to all elements ofP. The-polar of a subset ofY is defined similarly. The-polar of the-polar ofP is called the-closure ofP andP is called-closed ifP equals its-closure. We describe the-polar of any finitely generated setP as the solution set of a finite system of linear inequalities and describe the-closure ofP as a finitely generated set. The-closed polyhedra are characterized in terms of defining systems of linear inequalities and also in terms of the relationship of the polyhedronP with its recessional cone and with certain subsets ofX andY determined by the relation. Six classes of bilinear inequalities are distinguished in the characterization of-closed polyhedra.     

Elucidating the Beneficial Effect of Vinylene Carbonate on the Electrochemistry of Antimony Electrodes in Lithium Batteries

Vinylene carbonate (VC) is an effective electrolyte additive for improving electrode performance in lithium‐ion batteries. We confirm its beneficial effects in a nanosized Sb–cellulose fiber composite electrode and examine its mechanism of action by X‐ray photoelectron spectroscopy, the most suitable technique for characterizing active particle surfaces (especially electrode/electrolyte interfaces). Vinylene carbonate clearly increases electrolyte stability (particularly that of LiPF₆) by avoiding the formation of a thick layer of LiF that conceals Sb and prevents its reaction with Li. Decreasing the layer thickness therefore increases the reversibility of the electrochemical reaction and improves capacity retention on cycling. The presence of VC afforded high‐quality Sb 4d and Li 1s photoemissions, fitting of which clearly exposed a previously unreported low‐energy component. We believe that this component is an Li_xSb alloy, which for the first time is identified spectroscopically.     

Mach-Zehnder all-fiber interferometer using two in-series fattened fiber gratings

We present an all-fiber Mach-Zehnder interferometer consisting of two consecutive fattened sections of dispersion-shifted fiber that act as in-series long period fiber gratings. The proposed Mach-Zehnder interferometer shows a broad fringe pattern ranging from 1000 to 1500 nm and is stable against changes in temperature and strain. By tapering a section of 5mm in length to 50% diameter between the fattened sections we observe an increased sensitivity to temperature changes. The measured temperature and strain sensitivities were in the range of 9–17 pm/°C and 1.44–2.9 pm/μɛ, respectively.     

Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach

The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. We deal with minimizers of the Rayleigh quotient ‖u‖² _H ¹ _(Ω) ²/‖u‖² _L ² _(∂Ω) for functions that vanish in a subset A⊂ Ω, which we call the hole. We look for holes that minimize the best Sobolev trace constant among subsets of Ω with prescribed volume. First, we find a formula for the first variation of the first eigenvalue with respect to the hole. As a consequence of this formula, we prove that when Ω is a ball the symmetric hole (a centered ball) is critical when we consider deformations that preserves volume but is not optimal. Finally, we prove that by the Finite Element Method we can approximate the optimal configuration and, by means of the shape derivative, we design an algorithm to compute the discrete optimal holes. Mathematics Subject Classification (2000) 35P15, 49K20, 49M25, 49Q10     

Sexual differentiation of the zebra finch song system: potential roles for sex chromosome genes

Background  

Recent evidence suggests that some sex differences in brain and behavior might result from direct genetic effects, and not solely the result of the organizational effects of steroid hormones. The present study examined the potential role for sex-biased gene expression during development of sexually dimorphic singing behavior and associated song nuclei in juvenile zebra finches.     

Structural analysis of chiral complexes of palladium(0) with 15-membered triolefinic macrocyclic ligands

The complete structural analysis of the palladium complexes of the triolefinic macrocycles (E,E,E)-1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-trienes, which featured from three identical to three different aryl groups, was achieved by performing X-ray diffraction studies, NMR spectroscopy, and other calculations. The stereochemical complexity is determined by the different isomers formed through complexation of the metal to one or other face of each of the three olefins involved. The palladacyclopropane formulation of the palladium-olefin interaction offers a clear picture of the stereogenicity of the olefin carbon atoms that are complexed to the metal. The energetically favorable isomers were identified in the solid-state and in solution by performing X-ray diffraction and NMR spectroscopic analysis, respectively.     

Synthesis and structure of the molecular complex between N-(N′, N′-dimethylaminopropyl)phenothiazine hydrochloride and 7,7,8,8-tetracyano-p-quinodimethane (DAPP-TCNQ)

Synthesis, spectroscopic, and X-ray structural analysis of the molecular complex between the N-(N, N-dimethylaminopropyl)phenothiazine hydrochloride, monohydrate, (DAPP) and 7,7,8,8-tetracyano-p-quinodimethane (TCNQ), has been carried out. Crystals of C₂₉H₂₇N₆OSCl are monoclinic, P2₁/c,a=12.190(2),b=7.695(2),c=28.928(3)Å, =91.68(1)°. The molecular complex consists of DAPP as donor binding to TCNQ as acceptor by the thiazine central ring and one of the aromatic rings stacking in parallel planes along thec-axis with an interplanar separation of 3.24Å and 3.16Å, respectively. The electronic and epr spectra of the complex are discussed.     

Reducing power of simple polyphenols by electron-transfer reactions using a new stable radical of the PTM series, tris(2,3,5,6-tetrachloro-4-nitrophenyl)methyl radical

The synthesis and characterization of a new radical and its use for testing the antioxidant activity of polyphenols by electron transfer are reported. This new and stable species of magnetic nature, tris(2,3,5,6-tetrachloro-4-nitrophenyl)methyl (TNPTM) radical, has been characterized by electron paramagnetic resonance and its molecular structure determined by X-ray analysis. This new radical of the PTM (perchlorotriphenylmethyl) series, unlike 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical, is stable in conditions of hydrogen abstraction reactions. TNPTM radical is able to discriminate between the antioxidant activities of catechol and pyrogallol in hydroxylated solvent mixtures such as chloroform/methanol (2:1). These features determine the antioxidant/pro-oxidant character and the biological activities of natural and synthetic flavonoids.     

Ligand-free copper-catalyzed regioselective C-2 arylation of imidazo[2,1-b]thiazoles

An effective, regioselective C-2 arylation of imidazo[2,1-b]thiazoles catalyzed by Cu(I) has been developed. This arylation proceeded smoothly without promotion of the ligands, and various functional (22 samples) groups were well tolerated. Preliminary mechanistic studies of this arylation are also reported.