Bulky Polyfluorinated Terphenyldiphenylboranes: Water Tolerant Lewis Acids

Protocols for the synthesis of the bulky polyfluorinated triarylboranes 2,6-(C₆F₅)₂C₆F₃B(C₆F₅)₂ ( 1 ), 2,6-(C₆F₅)₂C₆F₃B[3,5-(CF₃)₂C₆H₃] ( 2 ), 2,4,6-(C₆F₅)₃C₆H₂B(C₆F₅)₂ ( 3 ), 2,4,6-(C₆F₅)₃C₆H₂B[3,5-(CF₃)₂C₆H₃] ( 4 ) were developed. All boranes are water tolerant and according to the Gutmann-Beckett method, 1 – 3 display Lewis acidities larger than that of the prominent B(C₆F₅)₃.     

One-Dimensional Parametric Determining form for the Two-Dimensional Navier–Stokes Equations

The evolution of a determining form for the 2D Navier–Stokes equations (NSE) which is an ODE on a space of trajectories is completely described. It is proved that at every stage of its evolution, the solution is a convex combination of the initial trajectory and a chosen, fixed steady state, with a dynamical convexity parameter \(\theta \), which will be called the characteristic determining parameter. That is, we show a separation of variables formula for the solution of the determining form. Moreover, for a given initial trajectory, the dynamics of the infinite-dimensional determining form are equivalent to those of the characteristic determining parameter \(\theta \) which is governed by a one-dimensional ODE. This one-dimensional ODE is used to show that if the solution to the determining form converges to the fixed state it does so no faster than \({\mathcal {O}}(\tau ^{-1/2})\), otherwise it converges to a projection of some other trajectory in the global attractor of the NSE, but no faster than \({\mathcal {O}}(\tau ^{-1})\), as \(\tau \rightarrow \infty \), where \(\tau \) is the evolutionary variable in determining form. The one-dimensional ODE is also exploited in computations which suggest that the one-sided convergence rate estimates are in fact achieved. The ODE is then modified to accelerate the convergence to an exponential rate. It is shown that the zeros of the scalar function that governs the dynamics of \(\theta \), which are called characteristic determining values, identify in a unique fashion the trajectories in the global attractor of the 2D NSE     

Wiring of glucose oxidase with graphene nanoribbons: an electrochemical third generation glucose biosensor

A reagentless third generation electrochemical glucose biosensor was fabricated based on wiring the template enzyme glucose oxidase (GOx) with graphene nanoribbons (GN) in order to create direct electron transfer between the co-factor (flavin adenine dinucleotide, FAD) and the electrode. The strategy involved: (i) isolation of the apo-enzyme by separating it from its co-enzyme; (ii) preparation of graphene nanoribbons (GN) by oxidative unzipping of multi-walled carbon nanotubes; (iii) adsorptive immobilization of GNs on the surface of a screen printed carbon electrode (SPCE); (iv) covalent attachment of FAD to the nanoribbons; (v) recombination of the apo-enzyme with the covalently bound FAD to the holoenzyme; and (vi) stabilization of the bio-layer with a thin membrane of Nafion. The biosensor (referred to as GN/FAD/apo-GOx/Nafion/SPCE) is operated at a potential of +0.475 V vs Ag/AgCl/{3 M KCl} in flow-injection mode with an oxygen-free phosphate buffer (pH 7.5) acting as a carrier. The signals are linearly proportional to the concentration of glucose in the range from 50 to 2000 mg?L^?1 with a detection limit of 20 mg?L^?1. The repeatability (10 measurements, at 1000 mg?L^?1 glucose) is ±1.4% and the reproducibility (5 sensors, 1000 mg?L^?1 glucose) is ±1.8%. The biosensor was applied to the determination of glucose in human serum.

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Graphical abstract Wiring of the apo-enzyme of glucose oxidase (apo-GOx) with graphene nanoribbons (GN) bound to FAD at a screen-printed carbon electrode (SPCE). Cyclic voltammetric and amperometric responses to various glucose concentrations.

     

Exponential attractors for a class of reaction-diffusion problems with time delays

We consider a reaction-diffusion system subject to homogeneous Neumann boundary conditions on a given bounded domain. The reaction term depends on the population densities as well as on their past histories in a very general way. This class of systems is widely used in population dynamics modelling. Due to its generality, the longtime behavior of the solutions can display a certain complexity. Here we prove a qualitative result which can be considered as a common denominator of a large family of specific models. More precisely, we demonstrate the existence of an exponential attractor, provided that a bounded invariant region exists and the past history decays exponentially fast. This result will be achieved by means of a suitable adaptation of the l-trajectory method coming back to the seminal paper of Málek and Nečas. The first author was partially supported by the Italian PRIN 2006 research project Problemi a frontiera libera, transizioni di fase e modelli di isteresi. The second author was supported by the research project MŠM 0021620839 and by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling).     

Critical evaluation of a new method for quantitative determination of minerals in solid samples

The new method for the Chemical Quantitative Mineral Analysis (CQMA) is presented and critically evaluated. The percentages of minerals are calculated of the elemental bulk chemical analysis using identified minerals and their crystallochemical formulas. For this calculation an optimization procedure is used. CQMA enables also the feedback calculation of the bulk chemical analysis from CQMA calculated mineral contents. Subsequent comparison of the feedback calculated bulk chemical analysis and actual bulk chemical analysis of the same sample is used for critical evaluation of the input data. If necessary the input data are completed and/or reanalyzed and used for repeated calculation to achieve better match between the feedback calculated and actual chemical analyses, which consequently leads to more accurate mineral analysis. Moreover the feedback bulk chemical analysis can be also separately calculated from any mineral analyses determined e.g. by XRD, FTIR and/or optical method. Six German rock reference samples representing a very wide range of minerals and chemical composition of materials were selected and their mineral analyses carried out by CQMA and Rietveld X‐ray diffraction methods. The results were compared with reference mineral analyses and critically evaluated.     

An Ethanol Biosensor Based on Simple Immobilization of Alcohol Dehydrogenase on Fe3O4@Au Nanoparticles

An ethanol biosensor based on alcohol dehydrogenase (ADH) attached to Au seeds decorated on magnetic nanoparticles (Fe₃O₄@Au NPs) is presented. ADH was immobilized on Fe₃O₄@Au NPs, which were subsequently fixed by a magnet on a carbon paste electrode modified with 5 % (m : m) MnO₂. Optimum conditions for the amperometric determination of ethanol with the biosensor were as follows: working potential +0.1 V (vs. Ag/AgCl); supporting electrolyte: 0.1 M phosphate buffer solution at pH 6.8 containing 0.25 mM of the coenzyme (NAD⁺); working electrode: carbon paste with magnetically attached Fe₃O₄@Au NPs (0.012 mg ? cm^?2 electrode area) with immobilized alcohol dehydrogenase (120 units per cm² of electrode area). Linearity between signal and concentration was found for the range from 0.1 to 2.0 M ethanol (r²=0.995) with a detection limit of 0.07 M, a sensitivity of 0.02 µA ? mM^?1 ? cm^?2, a reproducibility of 4.0 % RSD, and a repeatability of 2.7 % RSD. The results for the determination of ethanol in alcoholic beverages showed good agreement with gas chromatography (GC) with recovery of 96.0 – 108.8 %.     

Remarks on the uniqueness of second order ODEs

We are concerned with the uniqueness problem for solutions to the second order ODE of the form x″+f(x, t) = 0, subject to appropriate initial conditions, under the sole assumption that f is non-decreasing with respect to x, for each t fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable.     

Organoplatinum(II) complexes containing chelating or bridging bis(N-heterocyclic carbene) ligands: formation of a platinum(II) carbonate complex by aerial CO2 fixation

The preparation of two new bis(N-heterocyclic carbene) platinum(II) complexes, in which NHC rings are joined by a CH(2) linker group, is described. While, the chelate complex [PtMe(2)(bis-NHC1)], 1, was formed with large tert-butyl wingtips, the iso-propyl N-substituent analogue favors formation of the cluster complex [Pt(2)Me(4)(μ-SMe(2))(μ-bis-NHC2)](2)(μ-Ag(2)Br(2)), 2, in which two binuclear platinum(II) complexes are linked together by an Ag(2)Br(2) unit. The chelating platinum complex 1 undergoes aerial CO(2) fixation and forms platinum(II) carbonate complex [Pt(CO(3))(bis-NHC1)], 3.     

Fish and Chips: a microfluidic perfusion platform for monitoring zebrafish development

We have developed a multi-channel microfluidic perfusion platform for culturing zebrafish embryos and capturing live images of various tissues and organs inside the embryo. The Fish and Chips was micro-fabricated in silicon and glass for reproducibility and accuracy of the microfluidic structure. The microfluidic platform consists of three parts: a microfluidic gradient generator, a row of eight fish tanks, in which the fish embryos are individually placed, and eight output channels. The fluidic gradient generator supports dose-dependent drug and chemical studies. A unique perfusion system ensures a uniform and constant flow of media to the fish tank while the wastes are efficiently removed. The fish tanks restrict the embryo movements, except rotationally, for live imaging of internal tissues and organs. The embryos showed developmental abnormalities under the influence of the drug valproic acid (VPA).     

On Perfectly Generating Projective Classes in Triangulated Categories

We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd-style representability theorem, we give a new proof of Brown Representability Theorem.