The rank of a difference of matrices and associated generalized inverses

Various representations are given to characterize the rank of A-S in terms of rank A+k where A and S are arbitrary complex matrices and k is a function of A and S. It is shown that if S=AMA for some matrix M, and if G is any matrix satisfying A=AGA, then

$\text{rank(A-S) = rankA-nullity (I-SG)}$

. Several alternative forms of this result are established, as are many equivalent conditions to have

$\text{rank(A-S) = rankA-rankS}$

. General forms for the Moore-Penrose inverse of matrices A-S are developed which include as special cases various results by Penrose, Wedin, Hartwig and others.     

Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.     

A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.     

On elevated RMS levels in wall-bounded turbulent flows when measured by laser Doppler velocimetry

Several recent studies have shown elevated RMS velocities in laser Doppler measurements of wall bounded shear flows. We show here, through a simple model, that vibration of the probe volume is a likely contributor to these elevated values.     

Note on an extension of the Moore-Penrose inverse

The defining equations for the Moore-Penrose inverse of a matrix are extended to give a unique type of generalized inverse for matrices over arbitrary fields.     

Flux independent tests of neutrino oscillations

Zeitschrift für Physik C Particles and Fields - We discuss reactor and accelerator experiments which could provide further confirmation of neutrino oscillations. We address tests which are...     

A mackey imprimitivity theory for algebraic groups

Mathematische Zeitschrift -     

Synthesis and Bergman cyclization of a beta-extended porphyrenediyne

Condensation of a porphyrin-2,3-dione with a 1,2-diaminoarenediyne affords a [small beta]-extended porphyrinic-enediyne: upon thermal Bergman cyclization the quinoxaline spacer positioned between the macrocycle and the enediyne prevents tandem radical cyclization to a picenoporphyrin.