With k an infinite field and τ1,τ2 endomorphisms of km, we provide a dimension bound on open locus determinantal scheme, under which, for general subspace V⊆km n≤m/2, v1,v2∈V have τ1(v1)=τ2(v2) only if v1=v2. Specializing to permutations composed by coordinate projections, obtain abstract proof the theorem [10].

Conditional Equi-concentration of Types on I-projections is presented. It provides an extension of Conditioned Weak Law of Large Numbers to the case of several I-projections. Also a multiple I-projections extension of Gibbs Conditioning Principle is developed. A resemblance between the probabilistic equi-concentration phenomenon and thermodynamic coexistence of phases is noted. μ-projection var...

In the paper, we discuss on the egg domains: Ω a = ξ = (z, w) ∈ C n+m : z ∈ C n , w ∈ C m , |z| 2 + |w| 2/a < 1 , 0 < a ≤ 2. We show that Gleason's problem can be solved in the weight Bergman space on the egg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier th...

The universal order 1 invariant f of immersions of a closed orientable surface into R, whose existence has been established in [N3], takes values in the group GU = K⊕Z/2⊕Z/2 where K is a countably generated free Abelian group. The projections of f to K and to the first and second Z/2 factors are denoted f , M, Q respectively. An explicit formula for the value of Q on any embedding has been give...

Abstract We propose a Bayesian approach to Local Projections that optimally addresses the empirical bias-variance trade-off intrinsic in choice between direct and iterative methods. (BLP) regularise LP regressions via informative priors, estimate impulse response functions capture properties of data more accurately than VARs. BLPs preserve flexibility LPs while retaining degree estimation uncer...