A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Surplus division and investment incentives in supply chains: A biform-game analysis

In this paper, we use a biform-game approach for analyzing the impact of surplus division in supply chains on investment incentives. In the first stage of the game, firms decide non-cooperatively on investments. In the second stage, the surplus is shared according to the Shapley value. We find that all firms have inefficiently low investment incentives which, however, depend on their position in the supply chain. Cross-subsidies for investment costs can mitigate, but not eliminate the underinvestment problem. Vertical integration between at least some firms.yields efficient investments, but may nevertheless reduce the aggregated payoff of the firms. We show how the size of our effects depends on the structure of the supply chain and the efficiency of the investment technology. Various extensions demonstrate that our results are qualitatively robust.     

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Intramolecular [2+2] Photocycloaddition of 3‐ and 4‐(But‐3‐enyl)oxyquinolones: Influence of the Alkene Substitution Pattern,Photophysical Studies,and Enantioselective Catalysis by a Chiral Sensitizer

The intramolecular [2+2] photocycloaddition of four 4‐(but‐3‐enyl)oxyquinolones (substitution pattern at the terminal alkene carbon atom: CH₂, Z‐CHEt, E‐CHEt, CMe₂) and two 3‐(but‐3‐enyl)oxyquinolones (substitution pattern: CH₂, CMe₂) was studied. Upon direct irradiation at λ=300 nm, the respective cyclobutane products were formed in high yields (83–95 %) and for symmetrically substituted substrates with complete diastereoselectivity. Substrates with a Z‐ or E‐substituted terminal double bond showed a stereoconvergent reaction course leading to mixtures of regio‐ and diastereomers with almost identical composition. The mechanistic course of the photocycloaddition was elucidated by transient absorption spectroscopy. A triplet intermediate was detected for the title compounds, which–in contrast to simple alkoxyquinolones such as 3‐butyloxyquinolone and 4‐methoxyquinolone–decayed rapidly (τ≈1 ns) through cyclization to a triplet 1,4‐diradical. The diradical can evolve through two reaction channels, one leading to the photoproduct and the other leading back to the starting material. When the photocycloaddition was performed in the presence of a chiral sensitizer (10 mol %) upon irradiation at λ=366 nm in trifluorotoluene as the solvent, moderate to high enantioselectivities were achieved. The two 3‐(but‐3‐enyl)oxyquinolones gave enantiomeric excesses (ees) of 60 and 64 % at ?25 °C, presumably because a significant racemic background reaction occurred. The 4‐substituted quinolones showed higher enantioselectivities (92–96 % ee at ?25 °C) and, for the terminally Z‐ and E‐substituted substrates, an improved regio‐ and diastereoselectivity.     

A NEW SYNTHETIC ROUTE TO SULFINIC ACID ESTERS

Abstract

Dialkylsulfoxylates undergo reactions with alkylhalides and other alkylating agents to give sulfinic acid esters, which were characterized by IR-, ¹H-NMR- and mass-spectra.     

Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties

This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate.     

Epimerization,transacylation and bromination of dihydroquercetin acetates; synthesis of 8-bromodihydroquercetin

Dihydroquercetin (dhq) and its 3-acetate react with acetic anhydride in the absence of a base catalyst to yield mixtures of partially acetylated products. Three new esters were characterized by NMR spectroscopy as dhq 3,7,3′-triacetate, 3,7,4′-triacetate and 5,7,3′,4′-tetraacetate. At its melting point neat dhq 3,7,3′,4′-tetraacetate is partially converted to dhq 3,3′,4′-triacetate and dhq pentaacetate by intermolecular acetyl transfer. Dhq 7,3′,4′-triacetate yields exclusively dhq 3′,4′-di- and 3,7,3′,4′-tetraacetate under these conditions. The acetylation/deacetylation reactions are accompanied by partial epimerization: 3 new acetates with 2,3-cis stereochemistry (dhq 3-, 3,7,3′,4′-tetra- and penta-) were identified. Dhq and its 3,7,3′,4′-tetraacetate undergo regiospecific dibromination at C-6 and C-8 with excess N-bromosuccinimide in polar solvents, and 6,8-dibromo-dhq can be regioselectively debrominated to 8-bromo-dhq with sodium sulfite.