Proof theory for lattice-ordered groups

Proof-theoretic methods are developed and exploited to establish properties of the variety of lattice-ordered groups. In particular, a hypersequent calculus with a cut rule is used to provide an alternative syntactic proof of the generation of the variety by the lattice-ordered group of automorphisms of the real number chain. Completeness is also established for an analytic (cut-free) hypersequent calculus using cut elimination and it is proved that the equational theory of the variety is co-NP complete.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Finite dimensional ordered vector spaces with Riesz interpolation and Effros-Shen's unimodularity conjecture

Peer reviewed

Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Synthesis and structural characterization of a new molecule-based complex constructed from dodecamolybdophosphoric acid and imidazole

A new compound, (CH5N2)(3)(PMo12O40CH4N23H2O)-C-.-H-. (1), was synthesized and structurally characterized by elemental analyses, IR spectra, UV spectra, NMR spectra and ESR spectra. This is, to our knowledge, the first example of an imidazole-polyoxometalate species. The compound was recrystallized from N,N-dimethylformamide (DMF), and then black block-like crystals of (C3H5N2)(4)((PMoMo11O40)-Mo-V-O-VI)(.)4C(3)H(7)NO(.) 2H(2)O (2), were obtained. It crystallizes in a triclinic space group P (1) over bar with n=12.423(3) Angstrom, b=12.666(3) Angstrom, c=13.341(3) Angstrom, alpha=70.56(3)degrees, beta=71.16(3)degrees, gamma=64.18(3)degrees, V= 1742.3(6) Angstrom(3), Z=1, R1 = 0.0585, wR2 = 0.1885. An X-ray crystallographic study showed that the crystal structure is constructed by electrostatic attractions and hydrogen bonds between a dodecamolybdophosphoric anion and an imidazole. The imidazole and DMF molecules occupy cavities in a polyoxometalate lattice ordered along a c-axis. The structure of (2) is similar to that of (1) from a comparison of both IR spectra and TGA Curves.

Self-assembly of star block copolymers by dynamic density functional theory

The dynamic mean-field density functional method, driven from the generalized time-dependent Ginzburg-Landau equation, was applied to the mesoscopic dynamics of the multi-arms star block copolymer melts in two-dimensional lattice model. The implicit Gaussian density functional expression of a multi-arms star block copolymer chain for the intrinsic chemical potentials was constructed for the first time. Extension of this calculation strategy to more complex systems, such as hyperbranched copolymer or dendrimer, should be straightforward. The original application of this method to 3-arms block copolymer melts in our present works led to some novel ordered microphase patterns, such as hexagonal (HEX) honeycomb lattice, core-shell HEX lattice, knitting pattern, etc. The observed core-shell HEX lattice ordered structure is qualitatively in agreement with the experiment of Thomas [Macromolecules 31, 5272 (1998)].

Synthesis and crystal structure of a novel compound: [H3PMo12O40][CO(NH2)(2)](3)center dot-5H(2)O

The title compound, [H3PMo12O40][CO(NH2)(2)](3). 5H(2)O, was synthesized and characterized by IR, C-13 NMR and X-ray diffraction. This is the first example of a urea-heteropoly acid species. Crystal data: monoclinic, C2/c, a = 17.790(4) Angstrom, b = 17.158(3) Angstrom, e = 25.512(5) Angstrom, beta = 100.65(3)degrees, V = 8514(3) Angstrom (3), Z = 6, R-1 = 0.0437, wR2 = 0. 1092. In the unit cell, the urea molecules occupy cavities in the polyoxometalate lattice ordered along b-axis. Water molecules occupy the space left by polyoxometalates, and urea. Polyoxometalate O atoms, the N atoms of urea and O atoms of water molecules are involved in hydrogen bonding. (C) 2001 Elsevier Science B.V. All rights reserved.

Synthesis and crystal structure of a novel compound constructed from tris-(2, 2 '-bipy)ruthenium(II) and decatungstate

Self-assembly of tris-[2,2 ' -bipyridine]ruthenium(II) chloride with decatunstate produced a novel cation radical salt, [Ru(bpy)(3)](2)[W10O32] . 3DMSO. This is the first product of 2,2 ' -bipyridineruthenium(II)-polyoxometalates species. Crystal data: Monoclinic, P2(1)/c, a = 12.902(3) Angstrom, b = 21.487(3) Angstrom, c = 15.854(5) Angstrom, beta = 93.46(2)degrees, V = 4387(2) Angstrom (3), Z = 2, R-1 = 0.0599, wR2 = 0.1183. X-ray crystallographic study showed that the crystal structure was constructed by electyrostatic attraction and C-H . . .O hydrogen bonds between tris-[2,2 ' -bipyridine]ruthenium(II) and decatungstate polyanion. The tris-[2,2 ' -bipyridine]ruthenium molecules occupy cavities in the polyoxometalate lattice ordered along b-axis. (C) 2001 Elsevier Science B.V. All rights reserved.

Hydrothermal Microwave: A New Route to Obtain Photoluminescent Crystalline BaTiO3 Nanoparticles

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Microwave-hydrothermal synthesis of perovskite bismuth ferrite nanoparticles

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Microwave-hydrothermal synthesis of barium strontium titanate nanoparticles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Random existence of charge ordered stripes and its influence on the magnetotransport properties of La0.6Sr0.4MnO3 perovskite substituted with diamagnetic ions at Mn sublattice

Phase-singular solid solutions of La0.6Sr0.4Mn1-yMeyO3 (0 <= y <= 0.3) [Me=Li1+, Mg2+, Al3+, Ti4+, Nb5+, Mo6+ or W6+] [LSMey] perovskite of rhombohedral symmetry (space group: R (3) over barc) have been prepared wherein the valence of the diamagnetic substituent at Mn site ranged from 1 to 6. With increasing y-content in LSMey, the metal-insulator (TM-I) transition in resistivity-temperature rho(T) curves shifted to low temperatures. The magnetization studies M(H) as well as the M(T) indicated two groups for LSMey. (1) Group A with Me=Mg, Al, Ti, or Nb which are paramagnetic insulators (PIs) at room temperature with low values of M (< 0.5 mu(B)/Mn); the magnetic transition [ferromagnetic insulator (FMI)-PI] temperature (T-C) shifts to low temperatures and nearly coincides with that of TM-I and the maximum magnetoresistance (MR) of similar to 50% prevails near T-C (approximate to TM-I). (2) Group-B samples with Me=Li, Mo, or W which are FMIs with M-s=3.3-3.58 mu(B)/Mn and marginal reduction in T-C similar to 350 K as compared to the undoped LSMO (T-C similar to 378 K). The latter samples show large temperature differences Delta T=T-c-TM-I, reaching up to similar to 288 K. The maximum MR (similar to 60%) prevails at low temperatures corresponding to the M-I transition TM-I rather than around T-C. High resolution lattice images as well as microscopy analysis revealed the prevalence of inhomogeneous phase mixtures of randomly distributed charge ordered-insulating (COI) bistripes (similar to 3-5 nm width) within FMI charge-disordered regions, yet maintaining crystallographically single phase with no secondary precipitate formation. The averaged ionic radius < r(B)>, valency, or charge/radius ratio < CRR > cannot be correlated with that of large Delta T; hence cannot be used to parametrize the discrepancy between T-C and TM-I. The M-I transition is controlled by the charge conduction within the electronically heterogeneous mixtures (COI bistripes+FMI charge disordered); large MR at TM-I suggests that the spin-ordered FM-insulating regions assist the charge transport, whereas the T-C is associated with the bulk spin ordered regions corresponding to the FMI phase of higher volume fraction of which anchors the T-C to higher temperatures. The present analysis showed that the double-exchange model alone cannot account for the wide bifurcation of the magnetic and electric transitions, contributions from the charge as well as lattice degrees of freedom to be separated from spin/orbital ordering. The heterogeneous phase mixtures (COI+FMI) cannot be treated as of granular composite behavior. (c) 2008 American Institute of Physics.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

Electrochemical generation of oxygen-containing groups in an ordered microporous zeolite-templated carbon

Zeolite templated carbon (ZTC) was electrochemically oxidized under various conditions, and its chemistry and structural evolution were compared to those produced by conventional chemical oxidation. In both oxidation methods, a general loss of the original structure regularity and high surface area was observed with increasing amount of oxidation. However, the electrochemical method showed much better controllability and enabled the generation of a large number of oxygen functional groups while retaining the original structure of the ZTC. Unlike chemical treatments, highly microporous carbons with an ordered 3-D structure, high surface area (ranging between 1900 and 3500 m2/g) and a large number of oxygen groups (O = 11,000–3300 μmol/g), have been prepared by the electrochemical method. Some insights into the electrooxidation mechanism of carbon materials are proposed from the obtained polarization curves, using ZTC as a model carbon material.

High-resolution imaging of ordered mixed-layer clays

HRTEM has been used to examine illite/smectite from the Mancos shale, rectorite from Garland County, Arkansas; illite from Silver Hill, Montana; Na-smectite from Crook County, Wyoming; corrensite from Packwood, Washington; and diagenetic chlorite from the Tuscaloosa formation. Thin specimens were prepared by ion milling, ultra-microtome sectioning and/or grain dispersal on a porous carbon substrate. Some smectite-bearing clays were also examined after intercalation with dodecylamine hydrochloride (DH). Intercalation of smectite with DH proved to be a reliable method of HRTEM imaging of expanded smectite, d(001) 16 A which could then be distinguished from unexpanded illite, d(001) 10 A. Lattice fringes of basal spacings of DH-intercalated rectorite and illite/smectite showed 26 A periodicity. These data support XRD studies which suggest that these samples are ordered, interstratified varieties of illite and smectite. The ion-thinned, unexpanded corrensite sample showed discrete crystallites containing 10 A and 14 A basal spacings corresponding with collapsed smectite and chlorite, respectively. Regions containing disordered layers of chlorite and smectite were also noted. Crystallites containing regular alternations of smectite and chlorite were not common. These HRTEM observations of corrensite did not corroborate XRD data. Particle sizes parallel to the c axis ranged widely for each sample studied, and many particles showed basal dimensions equivalent to > five layers. -J.M.H.