Assume that κ and λ are respectively strong weakly compact cardinals with λ>κ. Fix Θ≥λ a cardinal cof(Θ)>κ cof(δ)=δ<κ. Assuming the GCH≥κ holds, we construct generic extension of universe where is limit cardinal, cof(κ)=δ, 2κ=Θ TP(κ++) holds. This extends main result [5] for uncountable cofinalities.

3.5 Consistency of approximate M-estimators of ψ type. As in Sec. 3.3, let (X, A, P) be a probability space and Θ a locally compact separable metric space. Let ψ(θ, x) be a function of x in X and θ ∈ Θ with values in a Euclidean space R m. Let X 1 , X 2 ,. .. be independent with values in X and distribution P. A sequence of estimators T n := T n (X 1 ,. .. , X n) with values in Θ will be called...

Abstract The work is devoted to FSW of cold rolled AA2519. non-uniform distribution all second phase precipitates (including coherent θ″ and non-coherent θ) was shown via the TEM-technique. nucleation stable θ-phase, along with decreased dislocation density, led a drop (∼60 HV 0.2 ) in microhardness nugget zone.

If we do gradient descent with η * (t), then almost surely, the algorithm converges (for the quadratic model). To prove that, we follow classical techniques based on Lyapunov stability theory (Bucy, 1965). Notice that the expected loss follows E J θ (t+1) | θ (t) = 1 2 h · E (1 − η * h)(θ (t) − θ *) + η * hσξ 2 + σ 2 = 1 2 h (1 − η * h) 2 (θ (t) − θ *) 2 + (η *) 2 h 2 σ 2 + σ 2 = 1 2 h σ 2 (θ (...