Spatially Directed Pyrolysis via Thermally Morphing Surface Adducts

Combustion is often difficult to spatially direct or tune associated kinetics—hence a run-away reaction. Coupling pyrolytic chemical transformation to mass transport and reaction rates (Damköhler number), however, we spatially directed ignition with concomitant switch from combustion to pyrolysis (low oxidant). A ‘surface-then-core’ order in ignition, with concomitant change in burning rate,is therefore established. Herein, alkysilanes grafted onto cellulose fibers are pyrolyzed into non-flammable SiO₂ terminating surface ignition propagation, hence stalling flame propagating. Sustaining high temperatures, however, triggers ignition in the bulk of the fibers but under restricted gas flow (oxidant and/or waste) hence significantly low rate of ignition propagation and pyrolysis compared to open flame (Liñán's equation). This leads to inside-out thermal degradation and, with felicitous choice of conditions, formation of graphitic tubes. Given the temperature dependence, imbibing fibers with an exothermically oxidizing synthon (MnCl₂) or a heat sink (KCl) abets or inhibits pyrolysis leading to tuneable wall thickness. We apply this approach to create magnetic, paramagnetic, or oxide containing carbon fibers. Given the surface sensitivity, we illustrate fabrication of nm- and μm-diameter tubes from appropriately sized fibers.     

Spanning 3-colourable subgraphs of small bandwidth in dense graphs

A conjecture by Bollobás and Komlós states the following: For every γ>0 and integers r2 and Δ, there exists β>0 with the following property. If G is a sufficiently large graph with n vertices and minimum degree at least and H is an r-chromatic graph with n vertices, bandwidth at most βn and maximum degree at most Δ, then G contains a copy of H.This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r=3.     

Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups

We prove that group (co)homology can be computed up to bounded torsion using certain generalized projective resolutions. We investigate the notion of dimension obtained using this kind of resolutions and its relationship with the existence of torsion in both ordinary and complete cohomology groups.     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

Computational Homogenisation using Reduced-Order Modelling applied to Hyperelasticity

Within this study nonlinear reduced-order modelling for hyperelastic material is applied for the boundary value problem on the micro-scale which arises in the context of computational homogenisation. This involves the Proper Orthogonal Decomposition and the Discrete Empirical Interpolation Method for the nonlinear term. Considered error measures are the errors of the displacement field, the averaged stresses and the effective elasticity tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the difference between consecutive zeros of the Riemann zeta function

Let 0 < γ₁ ≤ γ₂ ≤ … be the imaginary part of the zeros, $\text{λ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$ and $\text{μ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$. Assuming the Riemann hypothesis, it is known that μ ≤ 0.68 and λ > 1. One suspects that μ = 0 and λ = +∞. The object of this note is to show that λ ≥ 1.9.     

Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery

In this paper, we consider a variant of the many-to-many location-routing problem, where hub facilities have to be located and customers with either pickup or delivery demands have to be combined in vehicle routes. In addition, several commodities and inter-hub transport processes are taken into account. A practical application of the problem can be found in the timber-trade industry, where companies provide their services using hub-and-spoke networks. We present a mixed-integer linear model for the problem and use CPLEX 12.4 to solve small-scale instances. Furthermore, a multi-start procedure based on a fix-and-optimize scheme and a genetic algorithm are introduced that efficiently construct promising solutions for medium- and large-scale instances. A computational performance analysis shows that the presented methods are suitable for practical application.     

Flip or flop? Students’ perspectives of a flipped lecture in mathematics

This paper describes students’ perspectives of a one-off flipped lecture in a large undergraduate mathematics service course. The focus was on calculating matrix determinants and was designed specifically to introduce debate and argumentation into a mathematics lecture. The intention was to promote a deeper learning and understanding through engagement with the added hope of instilling some passion for the subject. During the lecture, students were asked to vote with their feet, literally moving around the lecture theatre to form groups according to their shared favourite technique for calculating matrix determinants. Group discussions were then followed by a whole class debate facilitated by the lecturers, before they wrapped up the lecture by resolving the professional disagreements that had come to light during the debate. Following the lecture, data on student perspectives was gathered using both surveys and focus groups. Within this paper, we share the data and reveal the interesting results that emerged from our analysis. Despite remaining unconvinced as to whether flipped lectures are better for learning, students reported greater engagement and increased understanding of the material covered.     

Pattern formation during deformation of a confined viscoelastic layer: from a viscous liquid to a soft elastic solid

We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system [poly(dimethylsiloxane) with different degrees of cross-linking] allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation, where the fingering wavelength scales only with the film thickness, and a bulk regime called "viscoelastic," where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and present a reduced parameter describing the transition between the two regimes and allowing us to predict the observed patterns over the whole range of viscoelastic properties.