Combined experimental and theoretical studies of the elimination kinetic of 2‐methoxytetrahydropyran in the gas phase

The products formed in 2‐methoxytetrahydropyran elimination reaction in the gas phase are 3, 4‐dihydro‐2H‐pyran and methanol. The kinetic study was carried out in a static system, with the vessels deactivated with allyl bromide, and the presence of the free radical suppressor toluene. Temperature and pressure ranges were 400–450 °C and 25–83 Torr, respectively. The process is homogeneous, unimolecular, and follows a first‐order rate law. The observed rate coefficient is represented by the following equation: log k (s^?1) = (13.95 ± 0.15) ? (223.1 ± 2.1) (kJ mol^?1) (2.303RT)^?1. The reactant exists mainly in two low energy chair‐like conformations, with the 2‐methoxy group in axial or equatorial position. However, the transition state (TS) for the elimination of the two conformers is the same. Theoretical calculations of this reaction were carried for two possible mechanisms from these conformations by using DFT functionals B3LYP, MPW1PW91, and PBE with the basis set 6‐31G(d,p) and 6‐31G++(d,p). The calculation results demonstrate that 2‐methoxytetrahydropyran exists mainly in two conformations, with the 2‐methoy group in axial or equatorial position, that are thermal in equilibrium. The average thermodynamic and kinetic parameters, taking into account the populations of the conformers in the equilibrium, are in good agreement with experimental values at B3LYP/6‐31++(d,p) level of theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras–McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras–McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we obtain complete agreement with the results obtained in intrinsic coordinates. We have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.     

Solitary waves in the granular chain

Solitary waves are lumps of energy. We consider the study of dynamical solitary waves, meaning cases where the energy lumps are moving, as opposed to topological solitary waves where the lumps may be static. Solitary waves have been studied in some form or the other for nearly 450 years. Subsequently, there have been many authoritative works on solitary waves. Nevertheless, some of the most recent studies reveal that these peculiar objects are far more complex than what we might have given them credit for. In this review, we introduce the physics of solitary waves in alignments of elastic beads, such as glass beads or stainless steel beads. We show that any impulse propagates as a new kind of highly interactive solitary wave through such an alignment and that the existence of these waves seems to present a need to re-examine the very definition of the concept of equilibrium. We further discuss the possibility of exploiting nonlinear properties of granular alignments to develop exciting technological applications.     

Surface Acoustic Wave Nebulization Produces Ions with Lower Internal Energy than Electrospray Ionization

Surface acoustic wave nebulization (SAWN) has recently been reported as a novel method to transfer non-volatile analytes directly from solution to the gas phase for mass spectrometric analysis. Here we present a comparison of the survival yield of SAWN versus electrospray ionization (ESI) produced ions. A series of substituted benzylpyridinium (BzPy) compounds were utilized to measure ion survival yield from which ion energetics were inferred. We also estimated bond dissociation energies using higher level quantum chemical calculations than previously reported for BzPy ions. Additionally, the effects on BzPy precursor ion survival of SAWN operational parameters such as inlet capillary temperature and solution flow-rate were investigated. Under all conditions tested, SAWN-generated BzPy ions displayed a higher tendency for survival and thus have lower internal energies than those formed by ESI.     

Delaunay Refinement for Piecewise Smooth Complexes

We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size and to satisfy a Lipschitz-like property. A Delaunay refinement algorithm using the weighted Voronoi diagram is shown to terminate with the recovery of the topology of the input. Guaranteed bounds on the aspect ratios, normal variation, and dihedral angles are also provided. To this end, we present new concepts and results including a new definition of local feature size and a proof for a generalized topological ball property.     

Inducing the Cosmological Constant from Five-Dimensional Weyl Space

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following the approach of the space-time-matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant Λ, or more generally, it may generate a time-dependent cosmological parameter Λ(t). As an application, we construct a simple cosmological model in which Λ(t) has some interesting properties.     

On counting subring-submodules of free modules over finite commutative frobenius rings

Let \(\texttt {R}\) be a finite commutative Frobenius ring and \(\texttt {S}\) a Galois extension of \(\texttt {R}\) of degree m. For positive integers k and \(k'\), we determine the number of free \(\texttt {S}\)-submodules \(\mathcal {B}\) of \(\texttt {S}^\ell \) with the property \(k=\texttt {rank}_\texttt {S}(\mathcal {B})\) and \(k'=\texttt {rank}_\texttt {R}(\mathcal {B}\cap \texttt {R}^\ell )\). This corrects the wrong result (Bill in Linear Algebr Appl 22:223–233, 1978, Theorem 6) which was given in the language of codes over finite fields.     

Additive cyclic codes over finite commutative chain rings

Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples.     

Holomorphic approximation on compact, holomorphically convex, real-analytic varieties

Every continuous function on a compact, holomorphically convex, real-analytic subset of can be approximated uniformly by functions holomorphic on the set.