Let M be the collection of the multipliers of the Drury-Arveson space H2n, n ≥ 2. In a recent paper [Adv. Math. 335 (2018), pp. 372-404], Aleman et al. showed that for ƒ ∈ H2n, the condition sup|z|<1 Re(ƒ,K_zƒ) < ∞ is sufficient for the membership ƒ ∈ M. We show that this condition is not necessary for ƒ ∈ M. Moreover, we show that the condition sup|z|<1 Re(ƒ,Kzƒ) < ∞ only captures a nowhere dense subset of M. [ABSTRACT FROM AUTHOR]
This paper proposes a class of one parameter conjugate gradient methods, which can be regarded as some kinds of convex combinations of some modified form of PRP and HS methods. The scalar β k has the form of ϕ k ϕ k − 1 μ k . The convergence of the given methods is analyzed by some unified tools which show the global convergence of the proposed methods. Numerical experiments with the CUTE collections show that the proposed methods are promising. [ABSTRACT FROM AUTHOR]
Benjamin Wardhaugh starts this section with an examination of the use of marks and more deliberate marginalia in 366 copies of eighteenth-century mathematical books; he finds approximately 85% of books bore varying evidence of use, which is likely an I under i count, particularly with respect to heavily annotated books, which are less likely to have been preserved than cleaner books. Together, these chapters expand our understanding of how university students and scholars - particularly those who would not go on to become professional mathematicians - encountered mathematics and engaged with mathematical books during the early modern period. Overall, this book is a thought-provoking collection of case studies that fulfills its subtitle's promise to explore the production, collection, and - most of all - use of early modern mathematical books. [Extracted from the article]