Acetone promoted 1,4-migration of an alkoxycarbonyl group on a syn-1,2-diamine

A 2-protected cis-amino mitosene undergoes an irreversible acetone promoted isomerization and converts to the 1-isomer. Kinetic studies and DFT calculations of the reaction are reported. An organocatalytic mechanism is proposed, involving a covalent intermediate formed by reaction of the mitosene and acetone.     

Quadpack computation of Feynman loop integrals

The paper addresses a numerical computation of Feynman loop integrals, which are computed by an extrapolation to the limit as a parameter in the integrand tends to zero. An important objective is to achieve an automatic computation which is effective for a wide range of instances. Singular or near singular integrand behavior is handled via an adaptive partitioning of the domain, implemented in an iterated/repeated multivariate integration method. Integrand singularities possibly introduced via infrared (IR) divergence at the boundaries of the integration domain are addressed using a version of the Dqags algorithm from the integration package Quadpack, which uses an adaptive strategy combined with extrapolation. The latter is justified for a large class of problems by the underlying asymptotic expansions of the integration error. For IR divergent problems, an extrapolation scheme is presented based on dimensional regularization.     

A local instructional theory for the guided reinvention of the quotient group concept

In this paper we describe a local instructional theory for supporting the guided reinvention of the quotient group concept. This local instructional theory takes the form of a sequence of key steps in the process of reinventing the quotient group concept. We describe these steps and frame them in terms of the theory of Realistic Mathematics Education. Each step of the local instructional theory is illustrated using example instructional tasks and either samples of students’ written work or excerpts of discussions.     

Film junction effect on foam drainage

Foam drainage is modelled by the flow of liquid through Plateau borders (PBs) that are the liquid channels resulting from the merging of three liquid films separating the gas bubbles. Available models generally neglect the influence of these films. Yet, within drainage conditions, experimental observations indicate a strong coupling of these films with the channels. We consider the influence of films on foam drainage through their effect on the cross-section geometry of the channels. More precisely, we assume that the Plateau border cross-section is enclosed by three circular arcs that are not always tangent but instead exhibit a non-zero contact angle θ as it has been observed experimentally. The liquid flow through the channels is studied using numerical simulations whose parameters are θ and the Boussinesq number, Bo, that reflects the surface shear viscosity of the interface. We show that, for values of Bo relevant for foam drainage conditions, a slight increase of θ results in a strong decrease of the average liquid velocity.     

Access to novel bicyclic fused γ-butyrolactone using [3,3]-sigmatropic rearrangement and acid-lactonization sequence as key transformation

In this Letter, we wish to disclose a new strategy for the construction of substituted γ-butyrolactones. The latter might not only be of potential interest in terms of biological activity and synthesis but also allow access to original heterocyclic scaffolds. According to previous study, efficient two-step sequence involving Eschenmoser-Claisen rearrangement and acid-lactonization reaction was successfully applied for the construction of original fused bicyclic γ-butyrolactones based on an 1,4-oxazine core.