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.

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

Peer reviewed

Consideraciones sobre cuerpos ordenados y cuerpos reales maximales

El presente trabajo se puede considerar como prolongación del trabajo (I) del autor, se amplía un resultado de este último que era válido sólo en el caso metrizable, y aquí se estudia el caso general; se hace un estudio de los cuerpos reales maximales y completos, y, finalmente se da un apéndice sobre cuerpos reales contenidos en un cuerpo algebraicamente cerrado y de característica 0

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.

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.

A study of five cervicocephalic relocation tests in three different subject groups

Objective: To compare head relocation accuracy in traumatic ( whiplash), insidious onset neck pain patients and asymptomatic subjects when targeting a natural head posture (NHP) and complex predetermined positions. Design: A case-control study. Setting: University-based musculoskeletal research clinic. Participants: Sixty-three volunteers divided into three groups of similar gender and age: Group 1 (n=21) an asymptomatic group; group 2 (n=20) insidious onset neck pain; group 3 (n=22) a history of whiplash injury. Intervention: Five randomly ordered tests designed to detect relocation accuracy of the head. Outcome measures: A 3-Space Fastrak system measured the mean absolute relocation error of three trials of each relocation test. Results: A significant difference was found between groups in one of the tests targeting the NHP (p=0.001). Post-hoc pairwise comparisons revealed a significant difference (pless than or equal to0.05) between the asymptomatic group and each symptomatic group. The difference between the symptomatic groups just failed to reach significance (p=0.07). None of the other four tests revealed significant differences. Conclusion: The test of targeting the NHP indicates that relocation inaccuracy exists in patients with neck pain with a trend to suggest that the deficit may be greater in whiplash patients. Tests employing unfamiliar postures or more complex movement were not successful in differentiating subject groups.

Normally ordered semigroups

Glasgow Mathematical Journal, nº 50 (2008), p. 325-333

Chemistry and structure by design: ordered CuNi(CN)4 sheets with copper(II) in a square-planar environment

Layered copper–nickel cyanide, CuNi(CN)4, a 2-D negative thermal expansion material, is one of a series of copper(II)-containing cyanides derived from Ni(CN)2. In CuNi(CN)4, unlike in Ni(CN)2, the cyanide groups are ordered generating square-planar Ni(CN)4 and Cu(NC)4 units. The adoption of square-planar geometry by Cu(II) in an extended solid is very unusual.

On the existence of ordered phases of encapsulated diamondoids into carbon nanotubes

We have investigated some diamondoids encapsulation into single walled carbon nanotubes (with diameters ranging from1.0 up to 2.2 nm) using fully atomistic molecular dynamics simulations. Diamondoids are the smallest hydrogen-terminated nanosized diamond-like molecules. Diamondois have been investigated for a large class of applications, ranging from oil industry to pharmaceuticals. Molecular ordered phases were observed for the encapsulation of adamantane, diamantane, and dihydroxy diamantanes. Chiral ordered phases, such as; double, triple, 4- and 5-stranded helices were also observed for those diamondoids. Our results also indicate that the modification of diamondoids through chemical functionalization with hydroxyl groups can lead to an enhancement of the molecular packing inside the carbon nanotubes in comparison to non-functionalized molecules. For larger diamondoids (such as, adamantane tetramers), we have not observed long-range ordering, but only a tendency of incomplete helical structural formation. © 2012 Materials Research Society.

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.

Control of ordered structure and morphology of large-pore periodic mesoporous organosilicas by inorganic salt

Highly ordered rodlike periodic mesoporous organosilicas (PMO) were successfully synthesized using 1.2-bis(trimethoxysilyl)ethane as an precursor and triblock copolymer P123 as a template at low acid concentration and in the presence of inorganic salts (KCl). The role of acid and salt as well as the effects of synthesis temperature and reactant mole ratio in the control of morphology and the formation of ordered mesostructure was systematically examined. It was found that the addition of inorganic salt can dramatically expand the range of the synthesis parameters to produce highly ordered PMO structure and improve the quality of PMO materials. The morphology of PMOs was significantly dependent on the induction time for precipitation. The uniform PMO rods can only be synthesized in a narrow range of acid and salt concentrations. The results also show that the optimized salt concentration (I M) and low acidity (0.167 M) were beneficial to the formation of not only highly ordered mesostructure but also rodlike morphology. Increasing acidity resulted in fast hydrolysis reaction and short rod or plate-like particles. Highly ordered rod can also be prepared at low temperature (35 degrees C) with high salt amount (1.5 M) or high temperature (45 degrees C) with low salt amount (0.5 M). Optimum reactant molar composition at 40 degrees C is 0.035P123:8KCl:1.34HCI:444H(2)O:1.0bis(trimethoxysilyl)ethane. Lower or higher SiO2/PI23 ratio led to the formation of uniform meso-macropores or pore-blocking effect. (c) 2005 Elsevier Inc. All rights reserved.

Groups with Decomposable Set of Quasinormal Subgroups

A subgroup H of a group G is said to be quasinormal if HX = XH for all subgroups X of G. In this article groups are characterized for which the partially ordered set of quasinormal subgroups is decomposable.

The Applicability Of Ordered Mesoporous Sba-15 And Its Hydrophobic Glutaraldehyde-bridge Derivative To Improve Ibuprofen-loading In Releasing System.

The mesoporous SBA-15 silica with uniform hexagonal pore, narrow pore size distribution and tuneable pore diameter was organofunctionalized with glutaraldehyde-bridged silylating agent. The precursor and its derivative silicas were ibuprofen-loaded for controlled delivery in simulated biological fluids. The synthesized silicas were characterized by elemental analysis, infrared spectroscopy, (13)C and (29)Si solid state NMR spectroscopy, nitrogen adsorption, X-ray diffractometry, thermogravimetry and scanning electron microscopy. Surface functionalization with amine containing bridged hydrophobic structure resulted in significantly decreased surface area from 802.4 to 63.0 m(2) g(-1) and pore diameter 8.0-6.0 nm, which ultimately increased the drug-loading capacity from 18.0% up to 28.3% and a very slow release rate of ibuprofen over the period of 72.5h. The in vitro drug release demonstrated that SBA-15 presented the fastest release from 25% to 27% and SBA-15GA gave near 10% of drug release in all fluids during 72.5 h. The Korsmeyer-Peppas model better fits the release data with the Fickian diffusion mechanism and zero order kinetics for synthesized mesoporous silicas. Both pore sizes and hydrophobicity influenced the rate of the release process, indicating that the chemically modified silica can be suggested to design formulation of slow and constant release over a defined period, to avoid repeated administration.

Design, Synthesis And Biological Evaluation Of Hybrid Bioisoster Derivatives Of N-acylhydrazone And Furoxan Groups With Potential And Selective Anti-trypanosoma Cruzi Activity.

Hybrid bioisoster derivatives from N-acylhydrazones and furoxan groups were designed with the objective of obtaining at least a dual mechanism of action: cruzain inhibition and nitric oxide (NO) releasing activity. Fifteen designed compounds were synthesized varying the substitution in N-acylhydrazone and in furoxan group as well. They had its anti-Trypanosoma cruzi activity in amastigotes forms, NO releasing potential and inhibitory cruzain activity evaluated. The two most active compounds (6, 14) both in the parasite amastigotes and in the enzyme contain the nitro group in para position of the aromatic ring. The permeability screening in Caco-2 cell and cytotoxicity assay in human cells were performed for those most active compounds and both showed to be less cytotoxic than the reference drug, benznidazole. Compound 6 was the most promising, since besides activity it showed good permeability and selectivity index, higher than the reference drug. Thereby the compound 6 was considered as a possible candidate for additional studies.

Comparative Cytogenetics Of Physalaemus albifrons And Physalaemus Cuvieri Species Groups (anura, leptodactylidae).

Recently, Physalaemus albifrons (Spix, 1824) was relocated from the Physalaemus cuvieri group to the same group as Physalaemus biligonigerus (Cope, 1861), Physalaemus marmoratus (Reinhardt & Lütken, 1862) and Physalaemus santafecinus Barrio, 1965. To contribute to the analysis of this proposition, we studied the karyotypes of Physalaemus albifrons, Physalaemus santafecinus and three species of the Physalaemus cuvieri group. The karyotype of Physalaemus santafecinus was found to be very similar to those of Physalaemus biligonigerus and Physalaemus marmoratus, which were previously described. A remarkable characteristic that these three species share is a conspicuous C-band that extends from the pericentromeric region almost to the telomere in the short arm of chromosome 3. This characteristic is not present in the Physalaemus albifrons karyotype and could be a synapomorphy of Physalaemus biligonigerus, Physalaemus marmoratus and Physalaemus santafecinus. The karyotype of Physalaemus santafecinus is also similar to those of Physalaemus marmoratus and Physalaemus biligonigerus owing to the presence of several terminal C-bands and the distal localization of the NOR in a small metacentric chromosome. In contrast, the Physalaemus albifrons karyotype has no terminal C-bands and its NOR is located interstitially in the long arm of submetacentric chromosome 8. The NOR-bearing chromosome of Physalaemus albifrons very closely resembles those found in Physalaemus albonotatus (Steindachner, 1864), Physalaemus cuqui Lobo, 1993 and some populations of Physalaemus cuvieri Fitzinger, 1826. Additionally, the Physalaemus albifrons karyotype has an interstitial C-band in chromosome 5 that has been exclusively observed in species of the Physalaemus cuvieri group. Therefore, we were not able to identify any chromosomal feature that supports the reallocation of Physalaemus albifrons.