From the N‐Heterocyclic Carbene‐Catalyzed Conjugate Addition of Alcohols to the Controlled Polymerization of (Meth)acrylates

Among various N‐heterocyclic carbenes (NHCs) tested, only 1,3‐bis(tert‐butyl)imidazol‐2‐ylidene (NHC^tBu) proved to selectively promote the catalytic conjugate addition of alcohols onto (meth)acrylate substrates. This rather rare example of NHC‐catalyzed 1,4‐addition of alcohols was investigated as a simple means to trigger the polymerization of both methyl methacrylate and methyl acrylate (MMA and MA, respectively). Well‐defined α‐alkoxy poly(methyl (meth)acrylate) (PM(M)A) chains, the molar masses of which could be controlled by the initial [(meth)acrylate]₀/[ROH]₀ molar ratio, were ultimately obtained in N,N‐dimethylformamide at 25 °C. A hydroxyl‐terminated poly(ethylene oxide) (PEO‐OH) macro‐initiator was also employed to directly access PEO‐b‐PMMA amphiphilic block copolymers. Investigations into the reaction mechanism by DFT calculations revealed the occurrence of two competitive concerted pathways, involving either the activation of the alcohol or that of the monomer by NHC^tBu.     

Nonparabolic Asymptotic Limits of Solutions of the Heat Equation on $${\mathbb{R}}^N$$

In this paper, we construct solutions u(t,x) of the heat equation on such that has nontrivial limit points in as t → ∞ for certain values of μ > 0 and β > 1/2. We also show the existence of solutions of this type for nonlinear heat equations.      

Synthesis of N-Benzoyl-4-oxo-1,2,3,4-Tetrahydropyridine and its Ethylene Ketal

Recently we had need for large quantities of N-benzoyl-4-oxo-1,2,3,4-tetrahydropyridine (1), its ethylene ketal derivative 7, and potentially other N-acyl derivatives. Prior to our initial studies, the N-carboethoxy derivative 2 had been prepared by sodium borohydride reduction of N-carboethoxy-4-pyridone.¹.     

Charge Site Mass Spectra: Conformation-Sensitive Components of the Electron Capture Dissociation Spectrum of a Protein

A conventional electron capture dissociation (ECD) spectrum of a protein is uniquely characteristic of the first dimension of its linear structure. This sequence information is indicated by summing the primary c ^m+ and z ^m+? products of cleavage at each of its molecular ion’s inter-residue bonds. For example, the ECD spectra of ubiquitin (M?+?nH)ⁿ⁺ ions, n?=?7–13, provide sequence characterization of 72 of its 75 cleavage sites from 1843 ions in seven c ^(1–7)+ and eight z ^(1–8)+? spectra and their respective complements. Now we find that each of these c/z spectra is itself composed of “charge site (CS)” spectra, the c ^m+ or z ^m+? products of electron capture at a specific protonated basic residue. This charge site has been H-bonded to multiple other residues, producing multiple precursor ion forms; ECD at these residues yields the multiple products of that CS spectrum. Closely similar CS spectra are often formed from a range of charge states of ubiquitin and KIX ions; this indicates a common secondary conformation, but not the conventional α-helicity postulated previously. CS spectra should provide new capabilities for comparing regional conformations of gaseous protein ions and delineating ECD fragmentation pathways.

Nucleophilic Addition of Nitrogen to Aryl Cations: Mimicking Titan Chemistry

The reactivity of aryl cations toward molecular nitrogen is studied systematically in an ion trap mass spectrometer at 10² Pascal of nitrogen, the pressure of the Titan main haze layer. Nucleophilic addition of dinitrogen occurs and the nature of aryl group has a significant influence on the reactivity, through inductive effects and by changing the ground state spin multiplicity. The products of nitrogen activation, aryldiazonium ions, react with typical nitriles, aromatic amines, and alkynes (compounds that are relevant as possible Titan atmosphere constituents) to form covalently bonded heterocyclic products. Theoretical calculations at the level [DFT(B3LYP)/6-311++G(d,p)] indicate that the N₂ addition reaction is exothermic for the singlet aryl cations but endothermic for their triplet spin isomers. The –OH and –NH₂ substituted aryl ions are calculated to have triplet ground states, which is consistent with their decreased nitrogen addition reactivity. The energy needed for the generation of the aryl cations from their protonated precursors (ca. 340 kJ/mol starting with protonated aniline) is far less than that required to directly activate the nitrogen triple bond (the lowest energy excited state of N₂ lies ca. 600 kJ/mol above the ground state). The formation of aza-aromatics via arene ionization and subsequent reactions provide a conceivable route to the genesis of nitrogen-containing organic molecules in the interstellar medium and Titan haze layers.

Strategic oscillation for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to different tasks when their ability to cooperate may affect the results. Strategic oscillation (SO) is a search strategy that operates in relation to a critical boundary associated with important solution features (such as feasibility). Originally proposed in the context of tabu search, it has become widely applied as an efficient memory-based methodology. We apply strategic oscillation to the quadratic multiple knapsack problem, disclosing that SO effectively exploits domain-specific knowledge, and obtains solutions of particularly high quality compared to those obtained by current state-of-the-art algorithms.     

A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.