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.

Phases of many flavors QCD: Lattice results

This note is based on our recent results on QCD with varying number of flavors of fundamental fermions. Topics include unusual, strong dynamics in the preconformal, confining phase, the physics of the conformal window and the role of ab-initio lattice simulations in establishing our current knowledge of the phases of many flavor QCD.

High-temperature induced dehydration, phase transition and exsolution in amicite: A single-crystal X-ray study

Temperature dependent single-crystal X-ray data were collected on amicite K4Na4(Al8Si8O32)·11H2O from Kola Peninsula (Russia) in steps of 25 °C from room temperature to 175 °C and of 50 °C up to 425 °C. At room temperature amicite has space group I2 with a = 10.2112(1), b = 10.4154(1), c = 9.8802(1) Å, β = 88.458(1)°, V = 1050.416(18) Å3. Its crystal structure is based on a Si–Al ordered tetrahedral framework of the GIS type with two systems of eight-membered channels running along the a and c axes. Extraframework K and Na cations are ordered at two fully occupied sites. Above 75 °C amicite was found to partly dehydrate into two separate but coherently intergrown phases, both of space group I2/a, one K-rich ∼K8(Al8Si8O32) ·4H2O (at 75 °C: a = 10.038(2), b = 9.6805(19), c = 9.843(2) Å, β = 89.93(3)°, V = 956.5(3) Å3) and the other Na-rich ∼Na8(Al8Si8O32)·2H2O (at 75 °C: a = 9.759(2), b = 8.9078(18), c = 9.5270(19) Å, β = 89.98(3)°, V = 828.2(3) Å3). Upon further heating above 75 °C the Na- and K-phases lost remaining H2O with only minor influence on the framework structure and became anhydrous at 175 °C and 375 °C, respectively. The two anhydrous phases persisted up to 425 °C. Backscattered electron images of a heated crystal displayed lamellar intergrowth of the K- and Na-rich phases. Exposed to ambient humid conditions K- and Na-rich phases rehydrated and conjoined to the original one phase I2 structure.

Developing a Web-Based Course in Phases

Introduction: Distance education has grown in popularity and usage. At the same time, enrollments at postsecondary institutions continue to increase. This places significant growth pressures on institutions of higher learning. Institutions providing nursing education have historically faced limited faculty resources. This has made it difficult to meet demand for distance education; and an “all-at-once” approach to course development does little to ease this problem. In this approach, resources are expended up front before a course is offered. [See PDF for complete abstract].

REE and Hf distribution among mineral phases in the CV-CK clan : a way to explain present-day Hf isotopic variations in chondrites

Chondrites are among the most primitive objects in the Solar System and constitute the main building blocks of telluric planets. Among the radiochronometers currently used for dating geological events, Sm–Nd and Lu–Hf are both composed of refractory, lithophile element. They are thought to behave similarly as the parent elements (Sm and Lu) are generally less incompatible than the daughter elements (Nd and Hf) during geological processes. As such, their respective average isotopic compositions for the solar system should be well defined by the average of chondrites, called Chondritic Uniform Reservoir (CHUR). However, while the Sm–Nd isotopic system shows an actual spread of less than 4% in the average chondritic record, the Lu–Hf system shows a larger variation range of 28% [Bouvier A., Vervoort J. D. and Patchett P. J. (2008) The Lu–Hf and Sm–Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth Planet. Sci. Lett.273, 48–57]. To better understand the contrast between Sm–Nd and Lu–Hf systems, the REE and Hf distribution among mineral phases during metamorphism of Karoonda (CK) and Vigarano-type (CV) carbonaceous chondrites has been examined. Mineral modes were determined from elemental mapping on a set of five CK chondrites (from types 3–6) and one CV3 chondrite. Trace-element patterns are obtained for the first time in all the chondrite-forming minerals of a given class (CK chondrites) as well as one CV3 sample. This study reveals that REE are distributed among both phosphates and silicates. Only 30–50% of Sm and Nd are stored in phosphates (at least in chondrites types 3–5); as such, they are not mobilized during early stages of metamorphism. The remaining fraction of Sm and Nd is distributed among the same mineral phases; these elements are therefore not decoupled during metamorphism. Of the whole-rock total of Lu, the fraction held in phosphate decreases significantly as the degree of metamorphism increases (30% for types 3 and 4, less than 5% in type 6). In contrast to Lu, Hf is mainly hosted by silicates with little contribution from phosphates throughout the CK metamorphic sequence. A significant part of Sm and Nd are stored in phosphates in types 3–5, and these elements behave similarly during CK chondrite metamorphism. That explains the robustness of the Sm/Nd ratios in chondrites through metamorphism, and the slight discrepancies observed in the present-day isotopic Nd values in chondrites. On the contrary, Lu and Hf are borne by several different minerals and consequently they are redistributed during metamorphism–induced recrystallization. The Lu/Hf ratios are therefore significantly disturbed during chondrites metamorphism, leading to the high discrepancies observed in present-day Hf isotopic values in chondrites.

Hyalotekite, (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2)(Si,B)(2)O28F, a Tectosilicate Related to Scapolite: New Structure Refinement, Phase Transitions and a Short-Range Ordered 3B Superstructure

Hyalotekite, a framework silicate of composition (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2) (Si,B)(2)O28F, is found in relatively high-temperature(greater than or equal to 500 degrees C) Mn skarns at Langban, Sweden, and peralkaline pegmatites at Dara-i-Pioz, Tajikistan. A new paragenesis at Dara-i-Pioz is pegmatite consisting of the Ba borosilicates leucosphenite and tienshanite, as well as caesium kupletskite, aegirine, pyrochlore, microcline and quartz. Hyalotekite has been partially replaced by barylite and danburite. This hyalotekite contains 1.29-1.78 wt.% Y2O3, equivalent to 0.172-0.238 Y pfu or 8-11% Y on the Ca site; its Pb/(Pb+Ba) ratio ranges 0.36-0.44. Electron microprobe F contents of Langban and Dara-i-Pioz hyalotekite range 1.04-1.45 wt.%, consistent with full occupancy of the F site. A new refinement of the structure factor data used in the original structural determination of a Langban hyalotekite resulted in a structural formula, (Pb1.96Ba1.86K0.18)Ca-2(B1.76Be0.24)(Si1.56B0.44)Si8O28F, consistent with chemical data and all cations with positive-definite thermal parameters, although with a slight excess of positive charge (+57.14 as opposed to the ideal +57.00). An unusual feature of the hyalotekite framework is that 4 of 28 oxygens are non-bridging; by merging these 4 oxygens into two, the framework topology of scapolite is obtained. The triclinic symmetry of hyalotekite observed at room temperature is obtained from a hypothetical tetragonal parent structure via a sequence of displacive phase transitions. Some of these transitions are associated with cation ordering, either Pb-Ba ordering in the large cation sites, or B-Be and Si-B ordering on tetrahedral sites. Others are largely displacive but affect the coordination of the large cations (Pb, Ba, K, Ca). High-resolution electron microscopy suggests that the undulatory extinction characteristic of hyalotekite is due to a fine mosaic microstructure. This suggests that at least one of these transitions occurs in nature during cooling, and that it is first order with a large volume change. A diffuse superstructure observed by electron diffraction implies the existence of a further stage of short-range cation ordering which probably involves both (Pb,K)-Ba and (BeSi,BB)-BSi.

Autophagy in Trypanosoma brucei: amino acid requirement and regulation during different growth phases.

Autophagy in the protozoan parasite, Trypanosoma brucei, may be involved in differentiation between different life cycle forms and during growth in culture. We have generated multiple parasite cell lines stably expressing green fluorescent protein- or hemagglutinin-tagged forms of the autophagy marker proteins, TbAtg8.1 and TbAtg8.2, in T. brucei procyclic forms to establish a trypanosome system for quick and reliable determination of autophagy under different culture conditions using flow cytometry. We found that starvation-induced autophagy in T. brucei can be inhibited by addition of a single amino acid, histidine, to the incubation buffer. In addition, we show that autophagy is induced when parasites enter stationary growth phase in culture and that their capacity to undergo starvation-induced autophagy decreases with increasing cell density.

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.

A Compact Tetrathiafulvalene-Benzothiadiazole Dyad and Its Highly Symmetrical Charge-Transfer Salt: Ordered Donor π-Stacks Closely Bound to Their Acceptors

A compact and planar donor–acceptor molecule 1 comprising tetrathiafulvalene (TTF) and benzothiadiazole (BTD) units has been synthesised and experimentally characterised by structural, optical, and electrochemical methods. Solution-processed and thermally evaporated thin films of 1 have also been explored as active materials in organic field-effect transistors (OFETs). For these devices, hole field-effect mobilities of μFE=(1.3±0.5)×10−3 and (2.7±0.4)×10−3 cm2 V s−1 were determined for the solution-processed and thermally evaporated thin films, respectively. An intense intramolecular charge-transfer (ICT) transition at around 495 nm dominates the optical absorption spectrum of the neutral dyad, which also shows a weak emission from its ICT state. The iodine-induced oxidation of 1 leads to a partially oxidised crystalline charge-transfer (CT) salt {(1)2I3}, and eventually also to a fully oxidised compound {1I3}⋅1/2I2. Single crystals of the former CT compound, exhibiting a highly symmetrical crystal structure, reveal a fairly good room temperature electrical conductivity of the order of 2 S cm−1. The one-dimensional spin system bears compactly bonded BTD acceptors (spatial localisation of the LUMO) along its ridge.

Small quantity but large effect — How minor phases control strain localization in upper mantle shear zones

Low viscosity domains such as localized shear zones exert an important control on the geodynamics of the uppermost mantle. Grain size reduction and subsequent strain localization related to a switch from dislocation to diffusion creep is one mechanism to form low viscosity domains. To sustain strain localization, the grain size of mantle minerals needs to be kept small over geological timescales. One way to keep olivine grain sizes small is by pinning of mobile grain boundaries during grain growth by other minerals (second phases). Detailed microstructural studies based on natural samples from three shear zones formed at different geodynamic settings, allowed the derivation of the olivine grain-size dependence on the second-phase content. The polymineralic olivine grain-size evolution with increasing strain is similar in the three shear zones. If the second phases are to pin the mobile olivine grain boundary the phases need to be well mixed before grain growth. We suggest that melt-rock and metamorphic reactions are crucial for the initial phase mixing in mantle rocks. With ongoing deformation and increasing strain, grain boundary sliding combined with mass transfer processes and nucleation of grains promotes phase mixing resulting in fine-grained polymineralic mixtures that deform by diffusion creep. Strain localization due to the presence of volumetrically minor minerals in polymineralic mantle rocks is only important at high strain deformation (ultramylonites) at low temperatures (<~800°C). At smaller strain and stress conditions and/or higher temperatures other parameters like overall energy available to deform a given rock volume, the inheritance of mechanical anisotropies or the presence of water or melts needs to be considered to explain strain localization in the upper mantle.