Carbonyl ylide reactions of α-benzylidene-β-dicarbonyl compounds: competitive formation of dihydrofurans and dihydrobenzoxepines

α-Benzylidene-β,β′-biscarbonyl compounds were reacted with dimethyl diazomalonate using Cu(II) acetylacetonate as a catalyst. Dihydrofurans or mixtures of dihydrofurans and dihydrobenzoxepines were obtained depending on the nature of the carbonyl group present in the starting material.     

Reactions of α,β‐Enones with Diazo Compounds,Part 3

Carbonyl ylides arising from ethyl acetodiazoacetate/dimethyl diazomalonate and α,β‐enones with mainly s‐cis conformations underwent disrotatory cyclization to produce dihydrofuran derivatives. This process proved to be sensitive to steric effects. The corresponding ylides arising from rather s‐trans α,β‐enals yielded dioxole derivatives. The mechanisms of the reactions are discussed.     

Sequential testing of simple hypotheses about compound Poisson processes

One of two simple hypotheses for the unknown arrival rate and jump distribution of a compound Poisson process is correct. We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision. We find a Bayes-optimal sequential decision rule and describe completely how to calculate its parameters without any restrictions on the arrival rate and the jump distribution.     

Approximate solution of multi-pantograph equation with variable coefficients

This paper deals with the approximate solution of multi-pantograph equation with nonhomogenous term in terms of Taylor polynomials. The technique we have used is based on a Taylor matrix method. In addition, some numerical examples are presented to show the properties of the given method and the results are discussed.     

The effect of support locations on the steady-state response of viscoelastically point-supported rectangular orthotropic plates

The vibration of orthotropic rectangular plates having viscoelastic point supports symmetrically located on its diagonals is analyzed. The plate is under the effect of a sinusoidally varying force at its center. The Lagrange equations are used in the solution process. To apply the Lagrange equations, the trial function denoting the deflection of the plate is expressed in polynomial form. By using the Lagrange equations, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties, the damping of the supports and the locations of point supports on the steady-state response of the viscoelastically point-supported rectangular plates is investigated numerically for the concentrated load at center for various values of the mechanical properties characterizing the anisotropy of the plate material and for various values of damping and location of the supports for a certain stiffness value of the supports. The results are given for the considered frequency range of the external force. Convergence studies are made. The validity of the obtained results is demonstrated by comparing them with other solutions based on the Kirchhoff–Love plate theory.     

Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

In this study, a practical matrix method based on Laguerre polynomials is presented to solve the higher‐order linear delay differential equations with constant coefficients and functional delays under the mixed conditions. Also, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity and applicability of the method. In addition, an algorithm written in Matlab is given for the method. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of moisture content in fibre laser cutting of pine wood

This paper reports a statistical analysis of the multiple-pass laser cutting of wet and dry pine wood with a Ytterbium fibre laser. As multiple factors affect the laser wood cutting process, finding the optimal combination of process parameters is necessary to achieve good quality and high process efficiency. Design of experiments (DOE) and statistical modelling were used in this study to investigate the significant process parameters and their interactions. A high brightness, 1 kW IPG single mode, continuous wave Ytterbium doped fibre laser was employed to cut wet and dry pine wood samples. The parameters investigated are laser power, traverse speed, focal plane position (f.p.p.), gas pressure, number of passes, direction of cut (normal or parallel to wood's tracheids) and the moisture content. The experimental results were compared against process responses defining the efficiency (i.e. kerf depth and energy consumption) and quality of the cut section (i.e. kerf width, heat affected zone—HAZ, edge surface roughness and perpendicularity). It has been found that the laser cutting process was mainly affected by the moisture content and the cut direction with respect to the wood's tracheids, followed by traverse speed, laser power and the number of passes. The effect of moisture content on energy consumption in the laser cutting process of both wet and dry wood is analysed. The wood cutting results with fibre laser are compared with those from a CO₂ laser.     

Constructing modular separating invariants

We consider a finite dimensional modular representation V of a cyclic group of prime order p. We show that two points in V that are in different orbits can be separated by a homogeneous invariant polynomial that has degree one or p and that involves variables from at most two summands in the dual representation. Simultaneously, we describe an explicit construction for a separating set consisting of polynomials with these properties.     

Finding transition pathways using the string method with swarms of trajectories

An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.