Observations on the Hantzsch Reaction: Synthesis of N-tBoc-S-Dolaphenine

An understanding of the mechanism by which racemization occurs in the Hantzsch reaction preparation of 2-(1-aminoalkyl)thiazoles has enabled the development of a methodology to prevent racemization. N-^tBoc-S-dolaphenine (3) is then synthesized using this methodology.     

Numerical prediction of turbulent flows using Reynolds‐averaged Navier–Stokes and large‐eddy simulation with uncertain inflow conditions

Numerous comparisons between Reynolds‐averaged Navier–Stokes (RANS) and large‐eddy simulation (LES) modeling have already been performed for a large variety of turbulent flows in the context of fully deterministic flows, that is, with fixed flow and model parameters. More recently, RANS and LES have been separately assessed in conjunction with stochastic flow and/or model parameters. The present paper performs a comparison of the RANS k ? ε model and the LES dynamic Smagorinsky model for turbulent flow in a pipe geometry subject to uncertain inflow conditions. The influence of the experimental uncertainties on the computed flow is analyzed using a non‐intrusive polynomial chaos approach for two flow configurations (with or without swirl). Measured quantities including an estimation of the measurement error are then compared with the statistical representation (mean value and variance) of their RANS and LES numerical approximations in order to check whether experiment/simulation discrepancies can be explained within the uncertainty inherent to the studied configuration. The statistics of the RANS prediction are found in poor agreement with experimental results when the flow is characterized by a strong swirl, whereas the computationally more expensive LES prediction remains statistically well inside the measurement intervals for the key flow quantities.Copyright © 2012 John Wiley & Sons, Ltd.     

Schensted-Type Correspondences and Plactic Monoids for Types B n and D n

We use Kashiwara's theory of crystal bases to study plactic monoids for U _q(so _2n+1) and U _q(so _2n ). Simultaneously we describe a Schensted type correspondence in the crystal graphs of tensor powers of vector and spin representations and we derive a Jeu de Taquin for type B from the Sheats sliding algorithm.     

Mackey Formula in Type A

The statement (and the proof) of Theorem 4.1.1 of the paper‘Mackey formula in type A’ [Proc. London. Math.Soc. (3) 80 (2000) 545–574] is false. In this corrigendumwe provide a correct statement (and a correct proof). As a consequence,we see that Corollary 4.1.2 of the paper holds. So all the otherstatements in the paper are correct (up to minor misprints...).2000 Mathematical Subject Classification: 20G05, 20G40.     

New exact penalty function for solving constrained finite min-max problems

This paper introduces a new exact and smooth penalty function to tackleconstrained min-max problems.By using this new penalty function and adding justone extra variable,a constrained min-max problem is transformed into an unconstrainedoptimization one.It is proved that,under certain reasonable assumptions and when thepenalty parameter is sufficiently large,the minimizer of this unconstrained optimizationproblem is equivalent to the minimizer of the original constrained one.Numerical resultsdemonstrate that this penalty function method is an effective and promising approach forsolving constrained finite min-max problems.     

Evaluating American put options on zero-coupon bonds by a penalty method

In this paper, American put options on zero-coupon bonds are priced under a single factor model of short-term rate. The linear complementarity problem of the option value is solved numerically by a penalty method, by which the problem is transformed into a nonlinear PDE by adding a power penalty term. The solution of the penalized problem converges to that of the original problem. A numerical scheme is established by using the finite volume method and the corresponding stability and convergence are discussed. Numerical results are presented to show the usefulness of the method.     

Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies. Based on the concept of invariant pairs, a theoretically sound and reliable numerical continuation procedure is developed. Particular attention is paid to the situation when the procedure approaches a singularity, that is, when eigenvalues included in the invariant pair collide with other eigenvalues. For the real generic case, it is proven that such a singularity only occurs when two eigenvalues collide on the real axis. It is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair. The viability of our continuation procedure is illustrated by a numerical example.     

Inherent Reactivity of Spiro-Activated Electrophilic Cyclopropanes

The kinetics of the ring-opening reactions of thiophenolates with geminal bis(acceptor)-substituted cyclopropanes in DMSO at 20 °C was monitored by photometric methods. The determined second-order rate constants of the S_N2 reactions followed linear relationships with Mayr nucleophilicity parameters (N/s_N) and Brønsted basicities (pK_aH) of the thiophenolates as well as with Hammett substituent parameters (σ) for groups attached to the thiophenolates. Phenyl-substituted cyclopropanes reacted by up to a factor of 15 faster than their unsubstituted analogues, in accord with the known activating effect of adjacent π-systems in S_N2 reactions. Variation of the electronic properties of substituents at the phenyl groups of the cyclopropanes gave rise to parabolic Hammett relationships. Thus, the inherent S_N2 reactivity of electrophilic cyclopropanes is activated by electron-rich π-systems because of the more advanced C1−C2 bond polarization in the transition state. On the other hand, electron-poor π-systems also lower the energetic barriers for the attack of anionic nucleophiles owing to attractive electrostatic interactions.