A type III porous-thermo-elastic problem with quasi-static microvoids

Meccanica - In this work we study, from the numerical point of view, a one-dimensional thermoelastic problem where the thermal law is of type III. Quasi-static microvoids are also assumed within...     

A methodology to select suppliers to increase sustainability within supply chains

Central European Journal of Operations Research - Sustainability practice within supply chains remains in an early development phase. Enterprises still need tools that support the integration of...     

Continuous Newton-like Inertial Dynamics for Monotone Inclusions

Set-Valued and Variational Analysis - In a Hilbert framework ℌ, we study the convergence properties of a Newton-like inertial dynamical system governed by a general maximally monotone...     

The influence of the first integrals and the rolling resistance model on tippe top inversion

Nonlinear Dynamics - In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is...     

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.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Synthesis of Highly Substituted γ‐Butyrolactones by a Gold‐Catalyzed Cascade Reaction of Benzyl Esters

Easily accessible benzylic esters of 3‐butynoic acids in a gold‐catalyzed cyclization/rearrangement cascade reaction provided 3‐propargyl γ‐butyrolactones with the alkene and the carbonyl group not being conjugated. Crossover experiments showed that the formation of the new C?C bond is an intermolecular process. Initially propargylic–benzylic esters were used, but alkyl‐substituted benzylic esters worked equally well. In the case of the propargylic–benzylic products, a simple treatment of the products with aluminum oxide initiated a twofold tautomerization to the allenyl‐substituted γ‐butyrolactones with conjugation of the carbonyl group, the olefin, and the allene. The synthetic sequence can be conducted stepwise or as a one‐pot cascade reaction with similar yields. Even in the presence of the gold catalyst the new allene remains intact.