If ν is a positive linear functional then sν is its support projection, the smallest orthogonal projection P such that ν (1 − P ) = 0.
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Quantum hypothesis testing is set with respect to a sequence of ﬁnite dimensional orthogonal projections pn on h such that s − limn pn = 1.
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
It follows that s′ω = J sω J ∈ M′ is the orthogonal projection on the closure of MΩω .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Therefore, as t ↑ ∞, the states ωt are concentrating exponentially fast along the projections s(ωt−ω−t )+ while the states ω−t are concentrating exponentially fast along the orthogonal complement 1 − s(ωt−ω−t )+ .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
The orthogonal projection 1R onto hR coincide with the projection onto the absolutely continuous part of h0 .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Let P j : J → J (e j , 1) be the orthogonal projection on J (e j , 1).
Maximal Invariants Over Symmetric Cones
In this study, we have devised an orthogonal fault classiﬁcation scheme and calculated their frequencies over seven open source Java projects.
Towards a better understanding of testing if conditionals
In the sequel, (cid:98)Πk stands for the orthogonal projection in Rn onto the reason, we propose a Fisher-type statistic. space generated by the ˆkKL columns of W.
Minimax adaptive tests for the Functional Linear model
Furthermore the orthogonal projection of S near y on any coordinate line xj contains a neighborhood of yj .
Sampling From A Manifold
Let ΠSF f and ΠS c f be the orthogonal projections of a function f ∈ Σ on span(cid:0){ϕl }l∈SF (cid:1) and span(cid:0){ϕl }l∈S c F (cid:1) respectively.
Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression
Let P be an orthogonal projection, rankP = k .
John decompositions: selecting a large part
Let P be an orthogonal projection, rankP = k .
John decompositions: selecting a large part
For any set A ∈ Ed , A|F denotes the (orthogonal) projection of A onto F ∈ Lj,d.
Radii of regular polytopes
Moreover the optimal projections take place in orthogonal subspaces.
Radii of regular polytopes
Let IK : L2 (G\G) ⊗ Vg → L2 (M , V (g)) denote the orthogonal projection.
On quantum ergodicity for vector bundles
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