A Lax type operator for quantum finite W-algebras

Selecta Mathematica - For a reductive Lie algebra $$\mathfrak {g}$$ , its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients...     

Enantioselective Synthesis of α-Thiocarboxylic Acids by Nitrilase Biocatalysed Dynamic Kinetic Resolution of α-Thionitriles

The enantioselective synthesis of α-thiocarboxylic acids by biocatalytic dynamic kinetic resolution (DKR) of nitrile precursors exploiting nitrilase enzymes is described. A panel of 35 nitrilase biocatalysts were screened and enzymes Nit27 and Nit34 were found to catalyse the DKR of racemic α-thionitriles under mild conditions, affording the corresponding carboxylic acids with high conversions and good-to-excellent ee. The ammonia produced in situ during the biocatalytic transformation favours the racemization of the nitrile enantiomers and, in turn, the DKR without the need of any external additive base.     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.     

High Activity and Selective Fischer–Tropsch Catalysts for Use in a Microchannel Reactor

Each process configuration for practicing the Fischer–Tropsch synthesis places demands particular to that configuration on the catalyst to be used. We discuss how a particular catalyst, prepared by the OMX (organic matrix combustion) method, when used in conjunction with the Velocys microchannel reactor system, results in a very stable, high performance Fischer–Tropsch synthesis system. With the ability to remove heat far more effectively than a conventional reactor system, this microchannel reactor requires a catalyst with much higher volumetric reactive site density. Further, with such a high volumetric reaction rate, mass transfer effects will be important in both the observed activity and selectivity of the operating catalyst. Nevertheless, the catalyst prepared using the OMX method exhibits an apparent turnover frequency which is considerably higher than reported for other catalysts in the literature. In addition to high activity, an economically useful catalyst must exhibit a stable, high selectivity for liquid products and be able to recover near-fresh performance using a regeneration approach which can be carried out with the catalyst in-place. An example of such a stable, multiply regenerated catalyst is given. Finally, further development has focused on a catalyst with even higher C₅₊ selectivity.     

Synthesis and Biological Evaluation of RGD Peptidomimetic–Paclitaxel Conjugates Bearing Lysosomally Cleavable Linkers

Two small‐molecule–drug conjugates (SMDCs, 6 and 7 ) featuring lysosomally cleavable linkers (namely the Val–Ala and Phe–Lys peptide sequences) were synthesized by conjugation of the α_vβ₃‐integrin ligand cyclo[DKP–RGD]‐CH₂NH₂ ( 2 ) to the anticancer drug paclitaxel (PTX). A third cyclo[DKP–RGD]–PTX conjugate with a nonpeptide “uncleavable” linker ( 8 ) was also synthesized to be tested as a negative control. These three SMDCs were able to inhibit biotinylated vitronectin binding to the purified α_Vβ₃‐integrin receptor at nanomolar concentrations and showed good stability at pH 7.4 and pH 5.5. Cleavage of the two peptide linkers was observed in the presence of lysosomal enzymes, whereas conjugate 8 , which possesses a nonpeptide “uncleavable” linker, remained intact under these conditions. The antiproliferative activities of the conjugates were evaluated against two isogenic cell lines expressing the integrin receptor at different levels: the acute lymphoblastic leukemia cell line CCRF‐CEM (α_Vβ₃?) and its subclone CCRF‐CEM α_Vβ₃ (α_Vβ₃+). Fairly effective integrin targeting was displayed by the cyclo[DKP–RGD]–Val–Ala–PTX conjugate ( 6 ), which was found to differentially inhibit proliferation in antigen‐positive CCRF‐CEM α_Vβ₃ versus antigen‐negative isogenic CCRF‐CEM cells. The total lack of activity displayed by the “uncleavable” cyclo[DKP–RGD]–PTX conjugate ( 8 ) clearly demonstrates the importance of the peptide linker for achieving the selective release of the cytotoxic payload.     

Poly(ionic liquid)s derived from 3‐octyl‐1‐vinylimidazolium bromide and N‐isopropylacrylamide with tunable properties

A new series of linear and crosslinked copolymers, obtained from 3‐octyl‐1‐vinylimidazolium bromide (VImBr) and N‐isopropylacrylamide (NIPAAm), were prepared by radical polymerization. Namely, VImBr was synthesized from 1‐bromooctane and an ionic liquid such as 1‐vinylimidazole. NIPAAm was used because it gives raise to well known thermoresponsive (co‐)polymers. The copolymers were thoroughly characterized by means of ¹H NMR and ¹³C NMR spectroscopies. Besides, differential scanning calorimetry, Fourier transform infrared spectroscopy, and scanning electron microscopy were also used. Moreover, the swelling behavior and the thermoresponsive properties of the corresponding hydrogels were studied. It was found that the VImBr incorporation into the copolymers does have a dramatic influence on both the thermal properties of the dried materials and the lower critical solution temperature of the corresponding hydrogels. In detail, the glass transition temperature was dependent on the monomer ratios, and ranged from 5 to 155 °C. Analogously, the lower critical solution temperature of the resulting hydrogels ranged from less than 10 up to 38 °C, thus including the physiological temperature. NMR spectroscopies, which were performed on the linear polymers, indicated that the monomers exhibit an alternating tendency resulting in a microstructure in which blocks are not present, at least when the two monomers are in equimolar amounts. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3521–3532     

Asset prices in an ambiguous economy

Models with ambiguity averse preferences have the potential to explain some pricing anomalies on financial markets. However, the models used in applications make additional assumptions, beyond ambiguity aversion, on the structure of the investor’s preferences. Therefore, it is not clear how to disentangle the effect of ambiguity aversion from other features of preferences on equilibrium prices. This paper offers a general theory of asset pricing assuming only ambiguity aversion. Price indeterminacy may result in equilibrium when preferences are not smooth. A set of priors, which is identifiable in all the models used in applications, contains the relevant information to price assets. Ambiguity enriches the standard pricing formula by an additional stochastic discount factor and we calculate its explicit form for various models.