A Chebotarev Theorem for finite homogeneous extensions of shifts

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form :X×G/H→X×G/H where (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the -closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms. Financially supported by Universiti Kebangsaan Malaysia     

Bis(fluoroalkyl)acrylic and methacrylic phosphate monomers, their polymers and some of their properties

Ten fluoromonomers of structure (R_FO)₂P(O)OCH₂CH₂OC(O)CRCH₂ were made in 30-64% yield by treating the chloridates (R_FO)₂P(O)Cl with HOCH₂CH₂OC(O)CRCH₂ in chloroform in the presence of triethylamine [R_F=CF₃CH₂, C₂F₅CH₂, C₃F₇CH₂, C₄F₉CH₂, C₄F₉CH₂CH₂ or C₆F₁₃CH₂CH₂; R  H or Me]. The chloromonomer (CCl₃CH₂O)₂P(O)OCH₂CH₂OC(O)CHCH₂ was obtained analogously in 29% yield. Polymerisation of the acrylate monomers, but not the methacrylate monomers, could be effected using α-azoisobutyronitrile as a radical initiator. Acrylic polymers having CF₃CH₂O, CCl₃CH₂O and C₆F₁₃CH₂CH₂O side-chains were obtained as translucent rubbers. Specimens of cotton fabric were treated with solutions of the polymers, and average water and oil repellency ratings measured. Fabric coated with the polymer with the C₆F₁₃CH₂CH₂O side-chain afforded protection from penetration of the test liquids. Treated fabrics were subjected to the limiting oxygen index (LOI) test according to BS EN ISO 4589-2 (1999): this test determines the point at which a material just burns in a volumetric flow of oxygen and nitrogen. The treated fabrics were more fire-resistant (LOI 22-29%) than the untreated fabric (LOI 18%). Fabric coated with the CCl₃CH₂O-based polymer can be considered fire-retardant (LOI 29%). The fluoromonomers were tested for anti-acetylcholinesterase activity and were found to be poor enzyme inhibitors; they are predicted to possess low acute toxicity.     

Sub‐millisecond transient vertical chevron formation during the electroclinic effect in the smectic A∗ phase

X‐ray diffraction studies are carried out in order to probe the smectic layer structure in liquid crystal devices filled with FLC mixture SCE8 and AFLC mixture CS4001, at a temperature just above the SmA?–SmC? phase transtion. The data gathered are time‐resolved in synchronization with a bipolar voltage pulse applied across the device. The layers are observed to move dynamically and reversibly with voltage application and removal, giving evidence for temporary vertical chevron formation due to the electroclinic effect on a timescale consistent with this phenomenon.     

Brane Cosmology, Varying Speed of Light and Inflation in Models with One or More Extra Dimensions

We summarize the approach to brane cosmology known as mirage cosmology and use it to determine the Friedmann equation on a 3-brane embedded in different bulk spacetimes all with one or more extra dimensions. Usually, when there is more than one extra dimension the junction conditions, central to the usual brane world scenarios, are difficult to apply. This problem does not arise in mirage cosmology because the brane is treated as a test particle in the background spacetime. We discuss in detail the dynamics of a brane embedded in two specific 10D bulk spacetimes, namely Sch-AdS₅ × S₅ and a rotating black hole, and from the dynamics—which are now rather more complicated since the brane can move in all the extra dimensions—determine the new dark fluid terms in the brane Friedmann equation. Some of these, such as the cosmological constant term, are seen to be bulk dependent. We then show explicitly how this mirage cosmology approach matches with the familiar junction condition approach when there is just one extra dimension. The issue of a varying speed of light in mirage cosmology is addressed and we find a scenario in which c _eff always increases, tending asymptotically to c ₀ as the universe expands. Finally some comments are made regarding brane inflation and limitations of the mirage cosmology approach are also discussed.     

Accurate mass analysis of ethanesulfonic acid degradates of acetochlor and alachlor using high-performance liquid chromatography and time-of-flight mass spectrometry

Degradates of acetochlor and alachlor (ethanesulfonic acids, ESAs) were analyzed in both standards and in a groundwater sample using high-performance liquid chromatography-time-of-flight mass spectrometry with electrospray ionization. The negative pseudomolecular ion of the secondary amide of acetochlor ESA and alachlor ESA gave average masses of 256.0750+/-0.0049 amu and 270.0786+/-0.0064 amu respectively. Acetochlor and alachlor ESA gave similar masses of 314.1098+/-0.0061 amu and 314.1153+/-0.0048 amu; however, they could not be distinguished by accurate mass because they have the same empirical formula. On the other hand, they may be distinguished using positive-ion electrospray because of different fragmentation spectra, which did not occur using negative-ion electrospray.     

Carbonates,thiocarbonates, and the corresponding monoalkyl derivatives: III. The 13C chemical shift tensors in potassium carbonate,bicarbonate and related monomethyl derivatives

The principal values of the 13C chemical shift tensors in potassium carbonate (K2CO3), trithiocarbonate (K2CS3), bicarbonate (KHCO3), methylcarbonate (KO2COCH3), S-methyl-monothiocarbonate (KO2CSCH3), O-methyl-monothiocarbonate (KOSCOCH3), S-methyl-dithiocarbonate (KOSCSCH3), and O-methyl-dithiocarbonate (KS2COCH3), were measured in solid-state nuclear magnetic resonance experiments. Chemical shift tensor calculations on the corresponding isolated anions were used to assign the chemical shift tensor orientations in the molecular frames of all anions. The correlation between experimental and calculated principal values improves significantly when the calculations are performed on isolated anions with proton-optimized X-ray geometries rather than on isolated anions with fully optimized geometries. Further considerable improvement in the correlation is achieved by utilizing the embedded ion method, which was recently developed to include electrostatic crystal potentials in chemical shift tensor calculations on ionic compounds. Similarities and differences in the chemical shift tensor orientations and principal values of the trigonal sp2 carbon atoms in the carbonate and thiocarbonate anions are compared with those known for condensed polyaromatic hydrocarbons.     

Nonlocality and short-range wetting phenomena

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.     

5-Formyl-2-furylboronic acid as a versatile bifunctional reagent for the synthesis of pi-extended heteroarylfuran systems

5-Formyl-2-furylboronic acid reacts cleanly with a range of heteroaryl bromides under Suzuki-Miyaura cross-coupling conditions to produce 2-formyl-5-heteroarylfuran derivatives. Subsequent Wittig olefination reactions afford pi-conjugated alkene-pyridyl-furan derivatives.     

Imaging macrophages in trehalose with SIMS

Phagocytosis is a major component of the animal immune system where apoptotic cellular material, metabolites, and waste are safely processed. Further, efficient phagocytosis by macrophages is key to maintaining healthy vascular systems and preventing atherosclerosis. Single-cell images of macrophage phagocytosis of red blood cells, RBCs, and polystyrene microspheres have been chemically mapped with TOF-SIMS. We demonstrate here cholesterol and phosphocholine localizations as relative to time and activity.