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The PAIVGLOSS MARK I MAT system

The goal of the PANGLOSS projecd is to develop a system which will, from the very beginning, produce highquality translations of unconstrained text. This can only be attained currently by keeping the human in the translation loop, in our case via a software module called the A U O ~ R . The main measure of progress in the development of the Pangloss system will therefore be the gradual decrease...

I , Mycorrhizal Mat Communities in 3 Forest Soils

The role of ectomycorrhizal (EM) fungi in forest soil function and tree productivity has become an increasingly important topic for research in light of possible direct large-scale degradation of EM populations in the forests of Europe (Arnolds, 1991). Although there is a rapidly growing body of information being assembled from laboratory studies using pure culture syntheses, there is relativel...

Mat 320-Linear Algebra I Summary of Lectures

Mat 201b Recap

4. Let (Ω,Σ, μ) be a measure space. If f : Ω → R, then we say that f is a measurable function if for every t ∈ R, the level set: Sf (t) = {x ∈ Ω|f(x) > t} is measurable. f : Ω→ C is measurable if and only if both Re(f) and Im(f) are measurable. 5. A real function f : Ω → R is lower semicontinuous on Ω if Sf (t) is open, and is upper semicontinuous if {x ∈ Ω|f(x) < t} is open. Equivalently, f is...

Mat 215a Recap

(a) D: α0 = 1, α1 = 1, α2 = 1. χ(D ) = 1. (b) S: α0 = 1, α1 = 0, α2 = 1. χ(S ) = 2. (c) Möbius band: α0 = 1, α1 = 2, α2 = 1. χ(M) = 0. (d) Mg of genus g: α0 = 1, α1 = 2g, α2 = 1. χ(Mg) = 2− 2g. 6. RP n = (R − {0})/{z ∼ λz} = S/{z ∼ −z} = S/Z2 RP n = σ ∪ RP n−1 implies RP n = σ ∪ σn−1 ∪ · · · ∪ σ χ(RP ) = 1 for n even and 0 for n odd. 7. CP n = (C − {0})/{z ∼ λz} = S/{z ∼ λz||λ| = 1} CP n = σ ∪ ...