Sheaves and duality

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a generalization of this fact and prove a converse of the generalization. To be precise, we exhibit a one-to-one correspondence (up to isomorphism) between soft sheaf representations of universal algebras over stably compact spaces and frame homomorphisms from the dual frames of such spaces into subframes of pairwise commuting congruences of the congruence lattices of the universal algebras. For distributive-lattice-ordered algebras this allows us to dualize such sheaf representations.     

A new cyclopeptide alkaloid from the bark of waltheria douradinha

Waltherine-C (5), a novel 14-membered cyclopeptide alkaloid has been isolated, together with four known cyclopeptide alkaloids, waltherine-A (1) and -B (2), scutianine-B (3) and adouetine-Y' (4), from the bark of Waltheria douradinha (Sterculiaceae) from Rio Grande do Sul, Brazil. The structure and NMR assignments of this new alkaloid were determined by 1D and 2D NMR techniques. The stereochemistry of the ring amino acid residue and the N,N-dimethyl amino acid side-chain has been assigned by gas chromatography employing modified cyclodextrins as chiral stationary phases.     

Investigation of failure mechanisms in polymer composites by simultaneous measurement of ultra-small-angle scattering and acoustic emission during the deformation. I. Method

Failure mechanisms in polymer composites were investigated with the method of ultra-small-angle X-ray scattering using synchrotron radiation and acoustic emission analysis simultaneously. The composites were prepared from polystyrene filled with glass beads with different coatings. The two-dimensional scattering patterns were analyzed by means of a cylinder model, while the curves of the acoustic emission signals per stress or amplitude interval were calculated and fitted by a Weibull distribution function.     

Facile preparation of macroscopic soft colloidal crystals with fiber symmetry

A facile, efficient way to fabricate macroscopic soft colloidal crystals with fiber symmetry by drying a latex dispersion in a tube is presented. A transparent, stable colloidal crystal was obtained from a 25 wt % latex dispersion by complete water evaporation for 4 days. The centimeter-long sample was investigated by means of synchrotron small-angle X-ray diffraction (SAXD). Analysis of a large number of distinct Bragg peaks reveals that uniaxially oriented colloidal crystals with face-centered cubic lattice structure were formed. The measurement of evaporation rates under different conditions indicates that the water evaporates primarily through the optically clear regions (i.e., via the solid material) even when the region is more than 2 mm thick.     

Negative refraction observed in a metallic ferromagnet in the gigahertz frequency range

It is generally believed that nature does not provide materials with negative refraction. Here we demonstrate experimentally that such materials do exist at least at GHz frequencies: ferromagnetic metals reveal a negative refraction index close to the frequency of the ferromagnetic resonance. The experimental realization utilizes a colossal magnetoresistance manganite La(2/3)Ca(1/3)MnO(3) as an example. In this material the negative refractive index can be achieved even at room temperature using external magnetic fields.     

Structure and Characterization of the Condensation Products of Dextran and Organostannane Halides

The modification of dextran, a water-soluble polysaccharide, through condensation with organostannane halides was accomplished utilizing the interfacial technique. Structural analysis agreed with condensation of the dextran-hydroxyls forming tin ether linkages with the dextran. Thermal degradation occurs through several stability plateaus and in air occurs through an oxidative pathway(s). Some of the products inhibit bacteria commonly responsible for mildew and rot.     

Pattern formation of colloidal suspensions by dip‐coating: An in situ grazing incidence X‐ray scattering study

Dip‐coating of a colloidal suspension is investigated in situ with microbeam grazing incidence small‐angle X‐ray scattering. We focus on the real‐time monitoring of a vertical dip‐coating process yielding insights into structural changes during pattern formation of the thin film. With the selected configuration a fixed spot on the sample surface is probed and the structural information at the time the contact line passes this spot is obtained, hence revealing the structure at the vicinity of the flowing meniscus owing to the microfocused beam. After dip‐coating the morphology is analyzed with atomic force microscopy, yielding real space information about the arrangement of individual nanoparticles at the film surface.

     

A non-commutative Priestley duality

We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras.     

A-site ordering versus electronic inhomogeneity in colossally magnetoresistive manganite films

Epitaxial La(3/4)Ca(1/4)MnO3/MgO(100) (LCMO) thin film shows an unusual rhombohedral (R-3c) structure with a new perovskite superstructure at room temperature due to the CE-type ordering of La and Ca with modulation vector q=1/4[011]. A-site ordered film was found to be electronically homogeneous down to the 1 nm scale as revealed by scanning tunnelling microscopy/spectroscopy. In contrast, orthorhombic and A-site disordered LCMO demonstrate a mesoscopic phase separation far below the Curie temperature (TC). Unique La/Ca ordering compensates the cation mismatch stress within one supercell, a(S) approximately 1.55 nm, and enhances the electronic homogeneity. The phase separation does not seem to be a unique mechanism for the colossal magnetoresistance (CMR) as very large CMR approximately 500% was also observed in A-site ordered films.     

Measurement and 3D simulation of self-organized filaments in a barrier discharge

We report on pattern formation phenomena in the filamentary dielectric barrier discharge between plane glass electrodes. It is for the first time that a three-dimensional (3D) self-organized glow pattern was both observed in an actual experiment and directly calculated in a full 3D discharge simulation in a quantitative manner. Specifically, we investigate the genesis of periodic patterns during the first breakdowns. Despite our simple drift-diffusion discharge model, the correspondence of experimental and numerical findings is surprisingly good.