1c:I[419806,["/_next/static/chunks/bb923814e1f4d2e9.js","/_next/static/chunks/dd3ee9f5b7716ca6.js","/_next/static/chunks/4204a0ae82542ca8.js","/_next/static/chunks/30036bedc5269936.js","/_next/static/chunks/6e1aa89a642f40be.js","/_next/static/chunks/cd5e572bc3e4eb92.js","/_next/static/chunks/8ffd0b71567920d8.js","/_next/static/chunks/67ea6dfd21f16c5f.js","/_next/static/chunks/24eb4379f68013fd.js","/_next/static/chunks/b8cd775ffdf935bd.js","/_next/static/chunks/983103cd9eb7b428.js","/_next/static/chunks/d4ac9dcf27f6ff52.js","/_next/static/chunks/294b9525248c8e5f.js"],"default"] 1d:T447,For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix Γ _p = Φ ^1/2 Λ _p 'Ψ _p^-1 Λ _p Φ ^1/2. This matrix increases with the number of observable variables p. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of Γ _p or, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors.1e:T40f,Screening of the topological charge due to fermion-induced interactions is an important phenomenon, closely related with the resolution of the strong CP and U(1) problems. We study the mechanism of such screening in a ``correlated instanton vacuum,'' as opposed to the ``random'' one. Both scalar and pseudoscalar gluonic correlators are analyzed by means of an observable that minimizes finite size effects. Screening of the topological charge is established. This allows us to calculate the \ensuremath{\eta}' mass without having to invert the Dirac operator. We suggest that this method might be used in lattice QCD calculations as well. Our results for the screening of the topological charge are in agreement with the chiral Ward identities, and the scalar gluonic correlator satisfies a low energy theorem first derived by Novikov et al. We also propose a modified Witten-Veneziano formula, in which the topological susceptibility is not defined for an infinite box in a world without fermions, but for a small box in the real world.

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