Copper‐Catalyzed Amidation of Primary and Secondary Alkyl Boronic Esters

The oxidative copper‐catalyzed cross‐coupling of functionalized alkyl boronic esters with primary amides is reported. Through the identification of appropriate diketimine ligands, conditions for efficient coupling of both primary and secondary alkyl boronic esters with diverse primary amides, including acetamide, have been developed.     

Phenalenannulations: Three-Point Double Annulation Reactions that Convert Benzenes into Pyrenes

3-Point annulations, or phenalenannulations, transform a benzene ring directly into a substituted pyrene by “wrapping” two new cycles around the perimeter of the central ring at three consecutive carbon atoms. This efficient, modular, and general method for π-extension opens access to non-symmetric pyrenes and their expanded analogues. Potentially, this approach can convert any aromatic ring bearing a -CH₂Br or a -CHO group into a pyrene moiety. Depending upon the workup choices, the process can be directed towards either tin- or iodo-substituted product formation, giving complementary choices for further various cross-coupling reactions. The two-directional bis-double annulation adds two new polyaromatic extensions with a total of six new aromatic rings at a central core.     

Solubilization of silica nanoparticles in alkanes and poly(α-olefin)s by functionalized polyisobutylene oligomers

Covalent and noncovalent chemical methods that use oligomeric lipophilic agents to solubilize silica nanoparticles in heptane and poly(α-olefin) (EPAO) solvents are described. While only modest solubilization efficiencies are seen with an octadecyl group, a variety of terminally functionalized polyisobutylene (PIB) derivatives are more efficient. Both covalent and noncovalent chemistry was found to be effective. Covalent modification solubilized up to 34 wt% of silica nanoparticles (SiNPs) as stable solutions in heptane or PAOs. Noncovalent modification was however more effective, solubilizing up to 70% of SiNPs in heptane or PAOs. The most successful covalent approach used PIB oligomers containing terminal triethoxysilane groups to covalently modify SiNPs. Alternatively, SiNPs that were first functionalized with amine groups could be solubilized in heptane or PAOs with polyisobutylene containing sulfonic acid groups using acid–base chemistry. Studies of these and other solubilization chemistry was also carried out using fluorescent labels, studies that confirmed the gravimetric analyses of the heptane-solubilized SiNPs. Transmission electron microscopy of a PAO solution of these solutions showed that these SiNPs were present as small aggregates dispersed in the PAOs.     

A Buchwald–Hartwig Protocol to Enable Rapid Linker Exploration of Cereblon E3-Ligase PROTACs**

A palladium-catalysed Buchwald–Hartwig amination for lenalidomide-derived aryl bromides was optimised using high throughput experimentation (HTE). The substrate scope of the optimised conditions was evaluated for a range of alkyl- and aryl- amines and functionalised aryl bromides. The methodology allows access to new cereblon-based bifunctional proteolysis targeting chimeras with a reduced step count and improved yields.     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

Tandem Chemoselective Suzuki–Miyaura Cross‐Coupling Enabled by Nucleophile Speciation Control

Control of boronic acid speciation is presented as a strategy to achieve nucleophile chemoselectivity in the Suzuki–Miyaura reaction. Combined with simultaneous control of oxidative addition and transmetalation, this enables chemoselective formation of two C? C bonds in a single operation, providing a method for the rapid preparation of highly functionalized carbogenic frameworks.     

Metal-acetylide addition to tetracyanoethylene

Two push-pull chromophores that have shown utility in the field of molecular electronics and non-linear optics are DDMEBT (1, 2-(4-dimethylamino)phenyl)-3-((4-(dimethylamino)phenyl)ethynyl)buta-1,3-diene-1,1,4,4-tetracarbonitrile) and TDMEE (2, 4-(4-dimethylamino)phenyl)but-1-en-3-yne-1,1,2-tricarbonitrile). Unfortunately, the methods reported for their synthesis give variable yields, use toxic solvents, and only provide small amounts of material. We report improved synthetic protocols, providing access to larger quantities of material. By investigating multiple metal-acetylides of 4-ethynyl-N,N-dimethylaniline and their subsequent addition to TCNE, we obtained various products depending on the identity of the metal ion. This led to the simple synthesis of push-pull chromophoric compounds.     

Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).     

Fully three-dimensional direct numerical simulation of a plunging breakerSimulation numérique directe tridimensionnelle du déferlement plongeant

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).