Definability of Frobenius orbits and a result on rational distance sets

We prove that the first order theory of (possibly transcendental) meromorphic functions of positive characteristic \(p>2\) is undecidable. We also establish a negative solution to an analogue of Hilbert’s tenth problem for such fields of meromorphic functions, for Diophantine equations including vanishing conditions. These undecidability results are proved by showing that the binary relation \(\exists s\ge 0, f=g^{p^s}\) is positive existentially definable in such fields. We also prove that the abc conjecture implies a solution to the Erdös–Ulam problem on rational distance sets. These two seemingly distant topics are addressed by a study of power values of bivariate polynomials of the form F(X)G(Y).     

Bile UPLC-MS fingerprinting and bile acid fluxes during human liver transplantation

Bile flow restoration is a crucial step in the recovery process post transplantation of the liver. Here, metabolic trajectories based on changes in bile secretion - a known marker of functionality - have been utilised as an approach for discovering bile fluxes during transplantation. A total of ten liver transplants were monitored and from these 68 bile samples from both donors and recipients were collected and analysed using ultra-performance LC-MS in combination with multivariate statistical analysis. Based on the principal component scores constructed from the total bile fingerprint, differentiation of the bile acid concentrations before and after transplantation was detected. A trend was also observed, by constructing metabolic trajectories, whereby the post-transplant profiles approached the position of pre-transplant profiles within 30-60?min of the restoration of bile secretion function. The ten major conjugated bile acid salts were measured and a significant increase in concentrations of taurocholic acid and taurochenodeoxycholic acid were seen after transplantation. In addition, the ratios of secondary bile acids detected in gall bladder and hepatic bile were measured before and after transplantation. This study suggests that bile acid ratios in the donor liver at the pre-transplant and post-transplant stage may be important and that profiling of secreted bile after transplantation may aid clinical assessment and progress post-transplantation.     

Insulator-based dielectrophoresis of microorganisms: theoretical and experimental results

Dielectrophoresis (DEP) is the motion of particles due to polarization effects in nonuniform electric fields. DEP has great potential for handling cells and is a non-destructive phenomenon. It has been utilized for different cell analysis, from viability assessments to concentration enrichment and separation. Insulator-based DEP (iDEP) provides an attractive alternative to conventional electrode-based systems; in iDEP, insulating structures are used to generate nonuniform electric fields, resulting in simpler and more robust devices. Despite the rapid development of iDEP microdevices for applications with cells, the fundamentals behind the dielectrophoretic behavior of cells has not been fully elucidated. Understanding the theory behind iDEP is necessary to continue the progress in this field. This work presents the manipulation and separation of bacterial and yeast cells with iDEP. A computational model in COMSOL Multiphysics was employed to predict the effect of direct current-iDEP on cells suspended in a microchannel containing an array of insulating structures. The model allowed predicting particle behavior, pathlines and the regions where dielectrophoretic immobilization should occur. Experimental work was performed at the same operating conditions employed with the model and results were compared, obtaining good agreement. This is the first report on the mathematical modeling of the dielectrophoretic response of yeast and bacterial cells in a DC-iDEP microdevice.     

Split injection: A simple introduction of subnanoliter sample volumes for chip electrophoresis

The ability to accurately inject small volumes of sample into microfluidic channels is of great importance in electrophoretic separations. While electrokinetic injection of nanoliter scale volumes is commonly utilized in microchip capillary electrophoresis (MCE), mobility and matrix bias makes quantitation difficult. Herein, we describe a new injection method based on the simple patterning of the crossing of channels that does not require sophisticated instrumentation. The sample volume injected into the separation channel is dependent on the ratio of the widths of the crossing channels. This injection method is capable of introducing, into a separation channel, multiple plugs of sample on a large scale. This injection technique is tested for zone electrophoresis in native and surface modified poly(dimethylsiloxane) (PDMS) chips.     

Photoprotection in the brown alga Macrocystis pyrifera: evolutionary implications

The dissipation of energy as heat is essential for photosynthetic organisms to protect themselves against excess light. We compared Photosystem II florescence changes (non-photochemical quenching, NPQ) in the brown alga Macrocystis pyrifera with that of Ficus sp., a higher plant to examine if the mechanism of heat dissipation (energy-dependent quenching, qE) differs between these evolutionary distant groups of phototrophs. We discovered that M. pyrifera had a slower rise of NPQ upon illumination than the Ficus sp. Further, the NPQ relaxation phase that takes place in the first minutes after light to dark transition is absent in this brown alga. We found that the NPQ induction rate in this alga was 1.5 times faster in preilluminated samples than in dark-adapted samples; this was associated with an increase in the rate of accumulation of the carotenoid zeaxanthin. Therefore, we conclude that NPQ in M. pyrifera is associated only with the formation of zeaxanthin. These results indicate that M. pyrifera lacks the fast component of qE that is related to allosteric changes in the light harvesting complexes of Ficus sp., a representative of higher plants. Although the xanthophyll cycle of this brown alga is similar to that of Ficus sp., yet, the transthylakoid proton gradient (ΔpH) does not influence NPQ beyond the activation of the violaxanthin de-epoxidase enzyme. These findings suggest that NPQ control mechanisms are not universal and we suggest that it may have diverged early in the evolution of different groups of eukaryotic phototrophs.     

Mechanistic studies of ethylene hydrophenylation catalyzed by bipyridyl Pt(II) complexes

Cationic platinum(II) complexes [((t)bpy)Pt(Ph)(L)](+) [(t)bpy =4,4'-di-tert-butyl-2,2'-bipyridyl; L = THF, NC(5)F(5), or NCMe] catalyze the hydrophenylation of ethylene to generate ethylbenzene and isomers of diethylbenzene. Using ethylene as the limiting reagent, an 89% yield of alkyl arene products is achieved after 4 h at 120 °C. Catalyst efficiency for ethylene hydrophenylation is diminished only slightly under aerobic conditions. Mechanistic studies support a reaction pathway that involves ethylene coordination to Pt(II), insertion of ethylene into the Pt-phenyl bond, and subsequent metal-mediated benzene C-H activation. Studies of stoichiometric benzene (C(6)H(6) or C(6)D(6)) C-H/C-D activation by [((t)bpy)Pt(Ph-d(n))(THF)](+) (n = 0 or 5) indicate a k(H)/k(D) = 1.4(1), while comparative rates of ethylene hydrophenylation using C(6)H(6) and C(6)D(6) reveal k(H)/k(D) = 1.8(4) for the overall catalytic reaction. DFT calculations suggest that the transition state for benzene C-H activation is the highest energy species along the catalytic cycle. In CD(2)Cl(2), [((t)bpy)Pt(Ph)(THF)][BAr'(4)] [Ar' = 3,5-bis(trifluoromethyl)phenyl] reacts with ethylene to generate [((t)bpy)Pt(CH(2)CH(2)Ph)(η(2)-C(2)H(4))][BAr'(4)] with k(obs) = 1.05(4) × 10(-3) s(-1) (23 °C, [C(2)H(4)] = 0.10(1) M). In the catalytic hydrophenylation of ethylene, substantial amounts of diethylbenzenes are produced, and experimental studies suggest that the selectivity for the monoalkylated arene is diminished due to a second aromatic C-H activation competing with ethylbenzene dissociation.     

Synthesis and characterization of (smif)2M(n) (n = 0, M = V, Cr, Mn, Fe, Co, Ni, Ru; n = +1, M = Cr, Mn, Co, Rh, Ir; smif =1,3-di-(2-pyridyl)-2-azaallyl)

A series of Werner complexes featuring the tridentate ligand smif, that is, 1,3-di-(2-pyridyl)-2-azaallyl, have been prepared. Syntheses of (smif)(2)M (1-M; M = Cr, Fe) were accomplished via treatment of M(NSiMe(3))(2)(THF)(n) (M = Cr, n = 2; Fe, n = 1) with 2 equiv of (smif)H (1,3-di-(2-pyridyl)-2-azapropene); ortho-methylated ((o)Mesmif)(2)Fe (2-Fe) and ((o)Me(2)smif)(2)Fe (3-Fe) were similarly prepared. Metatheses of MX(2) variants with 2 equiv of Li(smif) or Na(smif) generated 1-M (M = Cr, Mn, Fe, Co, Ni, Zn, Ru). Metathesis of VCl(3)(THF)(3) with 2 Li(smif) with a reducing equiv of Na/Hg present afforded 1-V, while 2 Na(smif) and IrCl(3)(THF)(3) in the presence of NaBPh(4) gave [(smif)(2)Ir]BPh(4) (1(+)-Ir). Electrochemical experiments led to the oxidation of 1-M (M = Cr, Mn, Co) by AgOTf to produce [(smif)(2)M]OTf (1(+)-M), and treatment of Rh(2)(O(2)CCF(3))(4) with 4 equiv Na(smif) and 2 AgOTf gave 1(+)-Rh. Characterizations by NMR, EPR, and UV-vis spectroscopies, SQUID magnetometry, X-ray crystallography, and DFT calculations are presented. Intraligand (IL) transitions derived from promotion of electrons from the unique CNC(nb) (nonbonding) orbitals of the smif backbone to ligand π*-type orbitals are intense (ε ≈ 10,000-60,000 M(-1)cm(-1)), dominate the UV-visible spectra, and give crystals a metallic-looking appearance. High energy K-edge spectroscopy was used to show that the smif in 1-Cr is redox noninnocent, and its electron configuration is best described as (smif(-))(smif(2-))Cr(III); an unusual S = 1 EPR spectrum (X-band) was obtained for 1-Cr.     

Physical properties of small water clusters in low and moderate electric fields

Likely candidates for the lowest minima of water clusters (H(2)O)(N) for N ≤ 20 interacting with a uniform electric field strength in the range E ≤ 0.6 V/? have been identified using basin-hopping global optimization. Two water-water model potentials were considered, namely TIP4P and the polarizable Dang-Chang potential. The two models produce some consistent results but also exhibit significant differences. The cluster internal energy and dipole moment indicate two varieties of topological transition in the structure of the global minimum as the field strength is increased. The first takes place at low field strengths (0.1 V/? 10) usually forming helical structures.     

Correlating the scattered intensities of P3HT and PCBM to the current densities of polymer solar cells

Grazing-incidence X-ray diffraction and rocking scans have quantified the structure of poly(3-hexylthiophene) and [6,6]-phenyl-C(61)-butyric acid methyl ester in the active layers of organic solar cells. Our study reveals that the device J(SC) correlates with the local structural development of pure PCBM and, to second order, the extent of out-of-plane P3HT π-stacking.     

A facile method to tune zeolite L crystals with low aspect ratio

We demonstrate an alternative route to tune the morphology of zeolite L crystals using C(2)H(5)OH as the co-solvent in the synthesis gel. A low aspect ratio (0.2 to 0.4) of zeolite L crystals was obtained at lower synthesis temperature (150 °C) and shorter synthesis duration (3 days).