Circle Maps,Measured Laminations,and Free Group Actions on IR-trees

This paper explores the connection between homeomorphisms of the unit circle, codimension-1 measured laminations on closed surfaces, and free actions of surface groups on IR-trees.     

Conformal Families of Measures for Fibred Systems

In this paper, we give sufficient conditions for the existence of (pseudo) weakly conformal and conformal families of measures for fibred systems. We describe a general construction principle for these families, modelled on the one developed by Denker and Urbanski for conformal measures. For those systems that are fibrewise local homeomorphisms, the constructed families are (pseudo) conformal. If a system is, moreover, weakly topologically exact along fibres, then each measure in the associated family is supported on the whole fibre where it is naturally defined.     

Folding of the Tau Protein on Microtubules

Microtubules are regulated by microtubule‐associated proteins. However, little is known about the structure of microtubule‐associated proteins in complex with microtubules. Herein we show that the microtubule‐associated protein Tau, which is intrinsically disordered in solution, locally folds into a stable structure upon binding to microtubules. While Tau is highly flexible in solution and adopts a β‐sheet structure in amyloid fibrils, in complex with microtubules the conserved hexapeptides at the beginning of the Tau repeats two and three convert into a hairpin conformation. Thus, binding to microtubules stabilizes a unique conformation in Tau.     

Influence of the soft segment length on the properties of water‐cured poly(carbonate‐urethane‐urea)s

Poly(carbonate‐urethane‐urea)s (PCUU) based on oligocarbonate diols (M_n ≈ 2000) with different length of the hydrocarbon chain as soft segments were synthesized and investigated. Carbonate oligomerols were obtained in a two‐step method from dimethyl carbonate (DMC) and linear α,ω‐diols (1,4‐butanediol, 1,5‐pentanediol, 1,6‐hexanediol, 1,9‐nonanediol, 1,10‐dekanediol and 1,12‐dodecanediol). Oligo(trimethylene carbonate) diol was synthesized using ring‐opening polymerization of trimethylence carbonate. PCUUs were obtained by prepolymer method using isophorone diisocyanate (IPDI) and water as a chain extender. Changes in polymers properties with increase of methylene group number between carbonate linkages were investigated by differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), tensile strength and hardness measurements. The thermal stability was also analyzed by means of thermogravimetric analysis (TGA). Based on FTIR analysis influence of methylene groups number between carbonate linkages on phase separation and concentration of allophanate and biuret groups in the samples were investigated. The obtained poly(carbonate‐urethane‐urea)s exhibited very good mechanical properties. Tensile strength and elongation at break were 40 MPa and 400–600%, respectively, depending on the oligocarbonate used. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.     

Liquid-phase epitaxy of multicomponent layer-based porous coordination polymer thin films of [M(L)(P)0.5] type: importance of deposition sequence on the oriented growth

The progressive liquid-phase layer-by-layer (LbL) growth of anisotropic multicomponent layer-based porous coordination polymers (PCPs) of the general formula [M(L)(P)(0.5)] (M: Cu(2+), Zn(2+); L: dicarboxylate linker; P: dinitrogen pillar ligand) was investigated by using either pyridyl- or carboxyl-terminated self-assembled monolayers (SAMs) on gold substrates as templates. It was found that the deposition of smooth, highly crystalline, and oriented multilayer films of these PCPs depends on the conditions at the early growth cycles. In the case of a two-step process with an equimolar mixture of L and P, growth along the [001] direction is strongly preferred. However, employing a three-step scheme with full separation of all components allows deposition along the [100] direction on carboxyl-terminated SAMs. Interestingly, the growth of additional layers on top of previously grown oriented seeding layers proved to be insensitive to the particular growth scheme and full retention of the initial orientation, either along the [001] or [100] direction, was observed. This homo- and heteroepitaxial LbL growth allows full control over the orientation and the layer sequence, including introduction of functionalized linkers and pillars.     

Comparison of silica gel modified with three different functional groups with C-18 and styrene-divinylbenzene adsorbents for the analysis of selected volatile flavor compounds

A comparison of SPE cartridges produced in authors laboratory containing silica modified by addition of three functional moieties with standard C-18 and SDVB cartridges was made in terms of their applicability for the isolation of flavor compounds. Compounds found in wine and grapes were used for model mixture, which was spiked into a grape juice. Functionalized phases for SPE were prepared modifying silica gel with alkoxysilanes with different functional groups: (3-(phenylamino)-propyltrimethoxysilane, octyltriethoxysilane and octadecyl-silane. The functionalization was carried out by the dry method, which resulted 5, 10 and 20 weight parts of initial support. Functionalized phases were characterized using FT-IR, elemental analysis and NMR.Performance for new phases compared to “standard” ones (C-18 and SDVB (styrene–divinylbenzene) varied, depending on the group or type of analyzed compound. They were more efficient in extraction of methyl anthranilate and vanilins. For extraction of terpenes, C-6 alcohols, isoprenoids, benzene derivatives and phenols their efficiency was comparable to that of C-18.Functionalized laboratory-made mixed phases are suitable for extraction of flavor compounds from grape juice. They are suitable for extraction of compounds belonging to different chemical classes with the efficiency comparable to C-18 and SDVB phases. The production of such functionalized phases can be easily performed in the laboratory, at a very low cost, comparing to C-18 or SDVB cartridges. This makes the proposed functionalized phases an interesting alternative, in sample preparation for analysis and particularly in preparative/flash chromatography.     

Stability studies of clonazepam, diazepam, haloperidol, and doxepin with diverse polarities in an acidic environment

Stability of clonazepam, diazepam, haloperidol, and doxepin was determined in acidic solutions. In addition, determination of the kinetic and thermodynamic properties of this stability was carried out. Reaction rate constants (k), half-life times (t(0.1) and t(0.5)), and activation energy (Ea) were estimated for the drugs, which differed in polarity expressed with log P values. It was observed that estimated Ea values increased from 42.13 to 125.03 kJ/mol with an increase of lipophilicity (log P) beginning from the most hydrophilic drug (clonazepam, 2.70 log P) to the most lipophilic drug (doxepin, 4.10 log P). All degradation products were studied using an HPLC/electrospray ionization-MS technique in the positive ionization mode.     

Mixed phosphine and group-13 metal ligator complexes [(PR3)(a)M(ECp*)b] (M = Mo, Ni; E = Ga, Al; R = C6H5, cyclo-C6H11, CH3)

Treatment of [Mo(N(2))(PMe(3))(5)] with two equivalents GaCp* (Cp* = η(5)-C(5)(CH(3))(5)) leads to the formation of cis-[Mo(GaCp*)(2)(PMe(3))(4)] (1), while AlCp* did not react with this precursor. In addition, [Ni(GaCp*)(2)(PPh(3))(2)] (2a), [Ni(AlCp*)(2)(PPh(3))(2)] (2b), [Ni(GaCp*)(2)(PCy(3))(2)] (3a), [Ni(GaCp*)(2)(PMe(3))(2)] (3b), [Ni(GaCp*)(3)(PCy(3))] (4) and [Ni(GaCp*)(PMe(3))(3)] (5) have been prepared in high yields by a direct synthesis from [Ni(COD)(2)] and stoichiometric amounts of the ligands PR(3) and ECp* (E = Al, Ga), respectively. All compounds have been fully characterized by (1)H, (13)C, and (31)P NMR spectroscopy, elemental analysis and single crystal X-ray diffraction studies.