Given a complex matrix H, we consider the decomposition H=QRP∗ where Q and P have orthonormal columns, and R is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of H. This decomposition, which we call the geometric mean decomposition, has application to signal processing and to the design of telecommunication networks. The unitary...

Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a, b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometr...

An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| ...

physical and mechanical properties of alfalfa (medicago sativa, l.) grind are required for optimum design of equipment used in transporting, processing and storage of the material. this study was conducted to determine the effect of particle size (2.38, 3.36 and 4.76 mm) and moisture content (8, 9.3 and 11% wb) on some physical and mechanical properties of alfalfa grind. these properties includ...

A statistical synthesis of marine aerosol measurements from experiments in four different oceans is used to evaluate a global aerosol microphysics model (GLOMAP). We compare the model against observed size resolved particle concentrations, probability distributions, and the temporal persistence of different size particles. We attempt to explain the observed sub-micrometre size distributions in ...

The number of particles and their size distributions were measured in a rural area, during the summer, using a PCASP-X. The aim was to study the influence of wildfires on particle size distributions. The comparative studies carried out reveal an average increase of around ten times in the number of particles in the fine mode, especially in sizes between 0.10 and 0.14 μm, where the increase is o...

Abstract The Reynolds-averaged general dynamic equation (RAGDE) for the nanoparticle size distribution function is derived, including contribution to particle coagulation resulting from fluctuating concentration. together with that of a turbulent gas flow solved numerically in ventilation chamber jet on wall based proposed model relating gradient mean Some results are compared experimental data...

-Andersen cascade impactors are widely used to assess airborne particle size distributions. Two forms (MkI and MklI) have been calibrated using solid and liquid aerosols, measured by microscopy, fluorimetry, and aerodynamic particle sizer. A fluorescent tracer was used to examine qualitatively the details of the wall loss deposition patterns when using greased and ungreased plates, and to quant...