Mechanistic Aspects of a Highly Active Dinuclear Zinc Catalyst for the Co‐polymerization of Epoxides and CO2

The dinuclear zinc complex reported by us is to date the most active zinc catalyst for the co‐polymerization of cyclohexene oxide (CHO) and carbon dioxide. However, co‐polymerization experiments with propylene oxide (PO) and CO₂ revealed surprisingly low conversions. Within this work, we focused on clarification of this behavior through experimental results and quantum chemical studies. The combination of both results indicated the formation of an energetically highly stable intermediate in the presence of propylene oxide and carbon dioxide. A similar species in the case of cyclohexene oxide/CO₂ co‐polymerization was not stable enough to deactivate the catalyst due to steric repulsion.     

Facile non‐lithographic route to highly aligned silica nanopatterns using unidirectionally aligned polystyrene‐block‐polydimethylsiloxane films

Thin films (monolayer and bilayer) of cylinder forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS) were shear aligned by the swelling and deswelling of a crosslinked PDMS pad that was physically adhered to the film during solvent vapor annealing. The nanostructures formed by self‐assembly were exposed to ultraviolet‐ozone to partially oxidize the PDMS, followed by calcination in air at 500 °C. In this process, the PS segments were fully decomposed, while the PDMS yielded silica nanostructures. The highly aligned PDMS cylinders were thus deposited as silica nanolines on the silicon substrate. Using a bilayer film, the center‐to‐center distance of these features were effectively halved from 38 to 19 nm. Similarly, by sequential shear‐alignment of two distinct layers, a rhombic array of silica nanolines was fabricated. This methodology provides a facile route to fabricating complex topographically patterned nanostructures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1058–1064     

Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

Nitrostyrene Derivatives of Adenosine 5′-Glutarates Modified with an Alkyl Spacer and their inhibitory activity on epidermal growth factor receptor protein tyrosine kinase

β-Nitrostyrene derivatives of adenosine 5′-glutarates are potent and selective bisubstrate-type inhibitors of the epidermal growth factor receptor protein tyrosine kinase (EGF-R PTK). In an attempt to improve the inhibitory activity, this type of compounds was modified with alkyl spacers of varying length between the nitrostyrene and the glutaryl units. The spacers consisted of 1, 3, 4, and 5 atoms to give compounds of the benzyl, oxyethyl, oxypropyl, and oxybutyl series, respectively (Schemes 1 and 2). Adenosine 5′-esters were prepared in the benzyl and oxypropyl series only. Compared to the compounds in the parent series without spacer (IC₅₀ = 0.7–12 μM ), most of the modified compounds inhibited the EGF-R PTK only marginally or were inactive (IC₅₀ ≥ 100 μM ). The only exceptions were the free acids 19 and 20 with IC₅₀ values of ca. 5 μM . It is noteworthy that esterification of these two hydrogen glutarates with either MeOH or adenosine yielded inactive compounds, which is in contrast to the corresponding substances without spacers.     

The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.