Qa := ∫ Qa ⊗ P (xj|b,b ′,x, a,y) dxj [Symbolic Substitution] For all bi in Qa Qa := [ Qa ⊗ P (bi|b,x, a,y) ] |b′i=1 ⊕ [ Qa ⊗ P (bi|b,x, a,y) ] |b′i=0 [Case ⊕] Compute final Q-Value (discount and add reward): Qa := R(b,x, a,y)⊕ (γ ⊗Qa) Note that ∫ f (xj)⊗δ[xj−h(z)]dxj = f (xj){xj/h(z)}where the latter operation indicates that any occurrence of xj in f (x ′ j) is symbolically substituted with the...

Theorem 9.7 of Lieb and Loss [Analysis, AMS, Providence, RI, 2000] is an extended version of Newton’s theorem and was cited in the authors’ previously published paper [SIAM J. Math. Anal., 43 (2011), pp. 1975–1994]. However, the statement of this theorem is incorrect for dimensions d ≤ 2. A couple of comments and, in particular, Figure 1 in the authors’ paper [SIAM J. Math. Anal., 43 (2011), pp...

abd allah b.sa’d, believed in islam and for a short time recorded divine revelations; but then he lost his faith. historical studies prove that his apostasy has no relation to writing celestial words. but story-writers who often lack an analytical mind, perhaps credulously or tendentiously connect his blaspheme to the act of recording sacred verses. these unfounded stories have entered history ...

i Statement of Funding and Purpose This report incorporates data collected during implementation of the Agency for Healthcare Research and Quality (AHRQ) Healthcare Horizon Scanning System by ECRI Institute under contract to AHRQ, Rockville, MD (Contract No. HHSA290201000006C). The findings and conclusions in this document are those of the authors, who are responsible for its content, and do no...

In this article we study the strength of Σ 1 3 absoluteness (with real parameters) in various types of generic extensions, correcting and improving some results from [2]. We shall also make some comments relating this work to the bounded forcing axioms BMM, BPFA and BSPFA. The statement " Σ 1 3 absoluteness holds for ccc forcing " means that if a Σ 1 3 formula with real parameters has a solutio...

Statman's 1-Section Theorem [17] is an important but little-known result in the model theory of the simplytyped λ-calculus. The λ-Section Theorem states a necessary and sufficient condition on models of the simplytyped λ-calculus for determining whether βη-equational reasoning is complete for proving equations that hold in a model. We review the statement of the theorem, give a detailed proof, ...