Responsive Copolymer Brushes of Poly[(2‐(Methacryloyloxy)Ethyl) Trimethylammonium Chloride] (PMETAC) and Poly(1H,1H,2H,2H‐Perfluorodecyl acrylate) (PPFDA) to Modulate Surface Wetting Properties

Polymer brushes have a large potential for controlling properties such as surface lubrication or wetting through facile functionalization. Polymer chemistry, chain density, and length impact on the wetting properties of brushes. This study explores the use of diblock copolymer brushes with different block length and spatial arrangement of the blocks to tune surface wettability. Block copolymer brushes of the polyelectrolyte [2‐(methacryloyloxy)ethyl] trimethylammonium chloride (PMETAC) with a contact angle of 17° and a hydrophobic block of ¹H, ¹H, ²H, ²H‐perfluorodecyl Acrylate (PPFDA) with a contact angle of 130° are synthesized by RAFT polymerization. By changing the sequence of polymerization either block is synthesized as top or bottom block. By varying the concentration of initiator the length of the blocks is varied. Contact angle values with intermediate values between 17° and 130° are measured. In addition, by changing solvent pH and in presence of a different salt the contact angle of the copolymer brushes can be fine tuned. Brushes are characterized by atomic force microscopy, Raman confocal microscopy, and X‐ray photoelectron spectroscopy.

     

On p-logistic equations of equidiffusive type

We consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter \(\lambda >0\) varies. In the case of a unique positive solution \(u_{\lambda }\), we investigate the monotonicity and continuity properties of the map \(\lambda \rightarrow u_{\lambda }\).     

Bounds tightening based on optimality conditions for nonconvex box-constrained optimization

First-order optimality conditions have been extensively studied for the development of algorithms for identifying locally optimal solutions. In this work, we propose two novel methods that directly exploit these conditions to expedite the solution of box-constrained global optimization problems. These methods carry out domain reduction by application of bounds tightening methods on optimality conditions. This scheme is implicit and avoids explicit generation of optimality conditions through symbolic differentation, which can be memory and time intensive. The proposed bounds tightening methods are implemented in the global solver BARON. Computational results on a test library of 327 problems demonstrate the value of our proposed approach in reducing the computational time and number of nodes required to solve these problems to global optimality.     

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).     

Gluing Eguchi‐Hanson Metrics and a Question of Page

In 1978, Gibbons‐Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small Eguchi‐Hanson manifolds that all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun‐Singer, and Donaldson. In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi‐Hanson manifolds. This is a subtle question: if successful, this construction would produce Einstein metrics that are neither Kähler nor self‐dual. In this paper, we focus on a configuration of maximal symmetry involving eight small Eguchi‐Hanson manifolds of each orientation that are arranged according to a chessboard pattern. By analyzing the interactions between Eguchi‐Hanson manifolds with opposite orientation, we identify a nonvanishing obstruction to the gluing problem, thereby destroying any hope of producing a metric of zero Ricci curvature in this way. Using this obstruction, we are able to understand the dynamics of such metrics under Ricci flow as long as the Eguchi‐Hanson manifolds remain small. In particular, for the configuration described above, we obtain an ancient solution to the Ricci flow with the property that the maximum of the Riemann curvature tensor blows up at a rate of , while the maximum of the Ricci curvature converges to 0.© 2016 Wiley Periodicals, Inc.     

Special issue of FOA10 in honor of our colleagues in Japan and New Zealand

Tribute

Special issue of FOA10 in honor of our colleagues in Japan and New Zealand     

Determination of pesticide residues in honey by single-drop microextraction and gas chromatography

A novel, simple, and rapid single-drop microextraction (SDME) procedure combined with GC has been developed, validated, and applied for the determination of multiclass pesticide residues in honey samples. The SDME was optimized using a Plackett-Burman screening design considering all parameters that may influence an SDME procedure and a consequent central composite design to control the parameters that were found to significantly influence the pesticide determination. The developed analytical method required minimal volumes of organic solvents and exhibited good analytical characteristics with enrichment factors ranging from 3 for alpha-endosulfan to 10 for lindane, procymidone, and captan and method quantification limits ranging from 0.03 microg/kg for phosalone to 10.6 microg/kg for diazinon. The relative recoveries obtained ranged from 70.8% for captan to 120% for fenarimol, and the precision (RSD) ranged from 3 to 15%. The proposed SDME procedure followed by GC with an electron capture detector for quantification and GC/MS for identification was applied with success to the analysis of 17 honey samples. Monitoring results indicated a low level of honey contamination by diazinon, chlorpyrifos-ethyl, procymidone, bromopropylate, and endosulfan (alpha-, beta-, and endosulfan sulfate) residues that were far below the maximum residue limit values specified by the European Union for endosulfan (10 microg/kg) and bromopropylate (100 microg/kg) in honey samples.     

Synthesis of glycerol carbonate from glycerol and urea with gold-based catalysts

The reaction of glycerol with urea to form glycerol carbonate is mostly reported in the patent literature and to date there have been very few fundamental studies of the reaction mechanism. Furthermore, most previous studies have involved homogeneous catalysts whereas the identification of heterogeneous catalysts for this reaction would be highly beneficial. This is a very attractive reaction that utilises two inexpensive and readily available raw materials in a chemical cycle that overall, results in the chemical fixation of CO(2). This reaction also provides a route to up-grade waste glycerol produced in large quantities during the production of biodiesel. Previous reports are largely based on the utilisation of high concentrations of metal sulfates or oxides, which suffer from low intrinsic activity and selectivity. We have identified heterogeneous catalysts based on gallium, zinc, and gold supported on a range of oxides and the zeolite ZSM-5, which facilitate this reaction. The addition of each component to ZSM-5 leads to an increase in the reaction yield towards glycerol carbonate, but supported gold catalysts display the highest activity. For gold-based catalysts, MgO is the support of choice. Catalysts have been characterised by XRD, TEM, STEM and XPS, and the reaction has been studied with time-on-line analysis of products via a combination of FT-IR spectroscopy, HPLC, (13)C NMR and GC-MS analysis to evaluate the reaction pathway. Our proposed mechanism suggests that glycerol carbonate forms via the cyclization of a 2,3-dihydroxypropyl carbamate and that a subsequent reaction of glycerol carbonate with urea yields the carbamate of glycerol carbonate. Stability and reactivity studies indicate that consecutive reactions of glycerol carbonate can limit the selectivity achieved and reaction conditions can be selected to avoid this. The effect of the catalyst in the proposed mechanism is discussed.