Discrete water hexamers and template-assisted molecular recognition in an elastic zincophosphate lattice

Water molecules and terephthalic acid, respectively, exist as a self-assembled monolayer of cyclic (H2O)6 clusters and (TA)infinity chiral chains between the zincophosphate sheets (in blue wires); the irremovable template H3tren3+ ions (in purple wires) are dynamic and could translate back and forth on the sheets during the conversion of the supramolecule contained in one another.     

On the X-Y convex hull of a set of X-Y polygons

We study the class of rectilinear polygons, calledX – Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the class ofX – Y polygons and present efficient algorithms for computing theX – Y convex hulls of anX – Y polygon and of a set ofX – Y polygons under various conditions. Unlike convex hulls in the Euclidean plane, theX – Y convex hull of a set ofX – Y polygons may not exist. The condition under which theX – Y convex hull exists is given and an algorithm for testing if the given set ofX – Y polygons satisfies the condition is also presented.     

Synthesis and magnetic properties of copper (II)-manganese (II) compounds with N,N′-ethylenedisalicylamidatocuprate(II)

By the reaction of sodium N,N′-ethylenedisalicylamidatocuprate ( I ) pentahydrate, Na₂[Cu(samen)]·5H₂O, with a manganese ( I ) salt and 2,2′-dipyridyl (bpy) or 1,10-phenanthroline (phen), the binuclear metal complexes [Cu(samen) Mn(L)₂] (L ? bpy, phen) have been synthesized. Based on IR, elemental analyses and electronic spectra, the complexes are proposed to consist of a four-coordinated Cu( I ) in a distorted planar environment and Mn( I ) in a distorted octahedron. The complexes have been characterized with variable-temperature magnetic susceptibility (4.2—300 K) and the susceptibility data were least-squares fit to susceptibility equation derived from the spin Hamiltonian including single-ion zero-field interaction for Mn²⁺ ion, H?—2JS₁·S₂—DS, where D is the axial zero-field splitting parameter for the Mn(II) ion. The exchange integral, J, was found to be —34.6 and —28.8 cm^?1 for [Cu(samen)Mn(bpy)₂] and [Cu(samen)Mn(phen)₂] respectively. The weak antiferromagnetic spin-exchange interaction can be interpreted by considering σ-π exchange pathway.     

Electronic structures for armchair-edge graphene nanoribbons under a small uniaxial strain

We theoretically investigate the electronic structures for armchair-edge graphene nanoribbons (AGNRs) under a small in-plane uniaxial strain along armchair (longitudinal) and zigzag (transversal) direction, respectively. We demonstrate that, by both the tight-binding calculation and first-principles study, the applying of a small asymmetrical strain results in variation of energy subband spacing, which opens a band gap for metallic AGNRs and modifies the band gaps for semiconducting AGNRs near the Fermi level. It is believed that these results are of importance in the band gap engineering and electromechanical applications of graphene-nanoribbon-based devices.     

Polarization-independent omnidirectional band gaps in heterostructures containing negative-index materials

We proposed a type of heterostructure by combining two photonic crystals (PCs) consisting of alternating negative-index materials and positive-index materials layers. It is demonstrated by transfer matrix method that the proposed structure has a polarization-independent omnidirectional band gap (OBG), which is independent of the incident angle for both TE and TM polarizations. Compared to a single PC, the frequency range of the OBG in a heterostructure can be notably enlarged. Such a structure has potential applications in improving planar microcavities, optical fibers, and Fabry-Pérot resonators, etc.     

Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold

Let M ⁿ be an n-dimensional compact C ^∞-differentiable manifold, n ≥ 2, and let S be a C ¹-differential system on M ⁿ . The system induces a one-parameter C ¹ transformation group φ _t (−∞ < t < ∞) over M ⁿ and, thus, naturally induces a one-parameter transformation group of the tangent bundle of M ⁿ . The aim of this paper, in essence, is to study certain ergodic properties of this latter transformation group. Among various results established in the paper, we mention here only the following, which might describe quite well the nature of our study. (A) Let M be the set of regular points in M ⁿ of the differential system S. With respect to a given C ^∞ Riemannian metric of M ⁿ , we consider the bundle of all (n−2) spheres Q _x ⁿ⁻², x∈M, where Q _x ⁿ⁻² for each x consists of all unit tangent vectors of M ⁿ orthogonal to the trajectory through x. Then, the differential system S gives rise naturally to a one-parameter transformation group ψ _t ^# (−∞<t<∞) of . For an l-frame α = (u ₁, u ₂,⋯, u _l ) of M ⁿ at a point x in M, 1 ≥ l ≥ n−1, each u _i being in , we shall denote the volume of the parallelotope in the tangent space of M ⁿ at x with edges u ₁, u ₂,⋯, u _l by υ(α), and let . This is a continuous real function of t. Let

Deformation of a trapped Fermi gas with unequal spin populations

The real-space densities of a polarized strongly interacting two-component Fermi gas of 6Li atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.     

Tandem radical rearrangement/Pd-catalysed translocation of bicyclo[2.2.2]lactones. An efficient access to the oxa-triquinane core structure

The skeletal rearrangement of bicyclo[2.2.2]lactones, involving a mild and chemoselective palladium-catalysed translocation key-step, provides an efficient and diastereoselective access to synthetically useful bicyclo[3.3.0]lactones.     

Modification of monomolecular self-assembled films by nitrogen-oxygen plasma

The modification of octadecanethiolate self-assembled monolayers on Au and Ag by nitrogen-oxygen downstream microwave plasma with variable oxygen content (up to 1%) has been studied by synchrotron-based high-resolution X-ray photoelectron spectroscopy. The primary processes were dehydrogenation, desorption of hydrocarbon and sulfur-containing species, and the oxidation of the alkyl matrix and headgroup-substrate interface. The exact character and the rates of the plasma-induced changes were found to be dependent on the substrate and plasma composition, with the processes in the aliphatic matrix and headgroup-substrate interface being mostly decoupled. In particular, the rates of all major plasma-induced processes were found to be directly proportional to the oxygen content in the plasma, which can be, thus, considered as a measure of the plasma reactivity. Along with the character of the observed changes, exhibiting a clear dominance of the oxidative processes, this suggests that the major effect of the oxygen-nitrogen downstream microwave plasma is provided by reactive oxygen-derived species in the downstream region, viz. long-living oxygen radicals and metastable species.