Accurate computation of the smallest eigenvalue of a diagonally dominant -matrix

If each off-diagonal entry and the sum of each row of a diagonally dominant -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.

     

Entrywise relative perturbation theory for nonsingularM-matrices and applications

This paper establishes a new entrywise relative perturbation result for the inverse of a nonsingularM-matrixA. It is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx =b, whereb is nonnegative, with small entrywise relative error. IfA is tridiagonal, the Gaussian elimination alone suffices.     

Blockwise perturbation theory for block p-cyclic stochastic matrices

Summary. Let P be a block p-cyclic stochastic matrix with stationary distribution , which is partitioned conformally in the form . This paper establishes the relative error bound for when each block of P gets a small relative perturbation. Received May 10, 1997 / Revised version October 21, 1997 / Published online November 17, 1999     

Formation of six- versus five-membered cyclic sulfones by C-H insertion

Selectivity of six- versus five- membered ring formation in C-H insertion on alkylsulfonyl diazoacetates is sensitive to the substrate structure and catalyst used.     

THE SENSITIVITY OF THE EXPONENTIAL OF AN ESSENTIALLY NONNEGATIVE MATRIX

This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation. For a general essentially nonnegative matrix, we obtain an upper bound for the relative error in 2-norm, which is sharper than the existing perturbation results. For a triangular essentially nonnegative matrix, we obtain an upper bound for the relative error in entrywise sense. This bound indicates that, if the spectral radius of an essentially nonnegative matrix is not large, then small entrywise relative perturbations cause small relative error in each entry of its exponential. Finally, we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.     

Synthetically Useful Intermediates by Diazosulfone and Sulfonate C–H Insertion

Intramolecular C–H insertion on diazosulfone and diazosulfonate substrates was used to prepare synthetically useful intermediates from easily available starting materials.     

Asymmetric intramolecular C–H insertion of sulfonyldiazoacetates catalyzed by Rh(II)

The asymmetric C–H insertion of alkyldiazosulfones has been studied. High selectivity was achieved using a combination of a chiral catalyst and a chiral auxiliary (Rh₂(S-pttl)₄ and menthyl ester).     

Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue

We consider a MAP/PH/1 queue with two priority classes and nonpreemptive discipline, focusing on the asymptotic behavior of the tail probability of queue length of low-priority customers. A sufficient condition under which this tail probability decays asymptotically geometrically is derived. Numerical methods are presented to verify this sufficient condition and to compute the decay rate of the tail probability.     

Perturbation Analysis of Structured Least Squares Problems and Its Application in Calibration of Interest Rate Term Structure

A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.     

Practical Preparation of Resveratrol 3-O-β-D-Glucuronide

Abstract

A practical synthesis of resveratrol 3-O-β-D-glucuronide, suitable for preparation of large quantities, was developed using selective deacetylation of resveratrol triacetate with ammonium acetate. A simplified procedure for large-scale preparation of resveratrol is also reported.