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.     

Change of evaporation rate of single monocomponent droplet with temperature using time-resolved phase rainbow refractometry

Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28$\times {10}^{?8}$ m²/s at atmospheric 293 K to a range of (?1.5, ?8)$\times {10}^{?8}$ m²/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions.     

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.