An organocatalytic asymmetric formal [3+2] cycloaddition of isatin-derived 3-indolylmethanol with 3-methyl-2-vinylindole has been established, leading to highly stereoselective construction of a spiro[cyclopenta[b]indole-1,3'-oxindole] scaffold with the concomitant creation of three contiguous stereogenic centers (72-99% yield, all >95 : 5 dr, 90-98% ee), one of which is an all-carbon quaternary stereogenic center.

C(sp 3 )À H bond coupling with carbon electrophiles remains rarely explored under thermo-driven hydrogen atom transfer (HAT) conditions due to the challenge of integrating oxidation and reduction in a single operation. We report here a Ni-catalyzed arylation and alkylation of C(sp 3 )À H bonds with organohalides to forge C(sp 3 )À C bonds by merging economical Zn and tBuOOtBu (DTBP) as the external reductant and oxidant. The mild and easy-to-operate protocol enables facile carbofunctionalization of N-/O-α-and cyclohexane CÀ H bonds, and preparation of a few intermediates of bioactive compounds and drug derivatives. Preliminary mechanistic studies implied addition of an alkyl radical to a Ni II salt.

We present an isogeometric boundary element method (IGABEM) capable of delivering accurate and efficient solutions in the heat transfer analysis of 2D coated structures such as those commonly found in turbomachinery. Although we consider very thin coatings (of thickness down to 10 −7 m), they are modelled explicitly as BEM zones, and this is made possible by the development of a new integration scheme (sinh +) aimed particularly at the challenging nearly singular integrals that arise. Sinh + is a hybrid of adaptive and sinh transformation approaches, and we make further extensions to the latter to improve its robustness. The scheme is tuned to deliver results of engineering accuracy in an optimal time. The scheme is adaptable, by changing a tolerance, to enable engineers to achieve a different balance between accuracy and computational efficiency as may be required for different applications. A set of numerical examples demonstrates the ability of the scheme to produce accurate temperature distributions efficiently in the presence of very thin coatings.

Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with thek-Fibonacci andk-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011).