Given an arbitrary sequence of elements ξ = { n } ∈ N $\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ a Hilbert space ( H , ⟨ · ⟩ ) $(\mathcal {H},\langle \cdot ,\cdot \rangle )$ the operator T $T_\xi$ is defined as associated to sesquilinear form Ω f g ∑ $\Omega _\xi (f,g)=\sum {N}} \langle _n\rangle _n g\rangle$ for h : | 2 < ∞ $f,g\in \lbrace h\in \mathcal {H}: \sum {N}}|\langle |^2<\infty ...

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow one to hide irrelevant parts of the state during verification, whereas the anti-frame rule allows one to hide local state from the context. We give the first sound model for Charguéraud and Pottier’s type and capability system including both frame and anti-frame rules. The model ...

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow one to hide irrelevant parts of the state during verification, whereas the anti-frame rule allows one to hide local state from the context. We discuss the semantic foundations of frame and anti-frame rules, and present the first sound model for Charguéraud and Pottier’s type and ...

Spectral indices from models of inflation which incorporate a Generalized Einstein Theory (GET) gravity sector are calculated to first order in a slow-roll expansion. By quantizing a suitably-generalized measure of the intrinsic curvature perturbation, the spectral indices as calculated in the Jordan frame now match those as calculated following a conformal transformation, in the Einstein frame...

Generalized fusion frame and some of their properties in tensor product Hilbert spaces are described. Also, the canonical dual g-fusion is considered. Finally, operator for a pair Bessel sequences presented.