https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Some modular identities of Ramanujan useful in approximating π https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13037 Wed 11 Apr 2018 14:54:35 AEST ]]> Local boundedness of monotone operators under minimal hypotheses https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13026 Wed 11 Apr 2018 09:23:38 AEST ]]> Dual Kadec-Klee norms and the relationships between Wijsman, slice, and Mosco convergence https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13882 Sat 24 Mar 2018 08:25:50 AEDT ]]> Examples of convex functions and classifications of normed spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14061 Sat 24 Mar 2018 08:22:33 AEDT ]]> Convex functions on Banach spaces not containing ℓ<sub>1</sub> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14688 1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.]]> Sat 24 Mar 2018 08:19:10 AEDT ]]> Cubic analogues of the Jacobian theta function θ(z,q) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13148 2/3 1,) analogous to the classical θ₂(q),θ₃(q),θ₄(q) and the hypergeometric function ₂F₁(1/2,1/2 1,)• We give elliptic function generalizations of a(q), b(q), c(q) analogous to the classical theta-function θ(z,q). A number of identities are proved. The proofs are self-contained, relying on nothing more than the Jacobi triple product identity.]]> Sat 24 Mar 2018 08:18:07 AEDT ]]> Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13076 o(x;v):=[formula cannot be replicated], and the Clarke subdifferential is defined by ∂cf(x) = {⏀∈X*:⏀(v) ≤ fo(x;v) for all v∈X}. This subdifferential has been widely used as a powerful tool in nonsmooth analysis with applications in diverse areas of optimization. Recently, substantial progress has been made on understanding the limitations of the Clarke derivative. Among other things, it is shown that on any Banach space X, the 1-Lipschitz functions for which ∂cf(x)=Bx* for all x∈X, is a residual set among all the 1-Lipschitz functions on X (where Bx* denotes the dual unit ball). That is, even though the Clarke derivative is an effective tool in a wide variety of both theoretical and applied optimization problems, just like the classical derivative, the class of pathological Lipschitz functions for which it provides no additional information is larger in the category sense. In this note, we begin by considering the following related question, which asks how profuse (from the point of view of extensions) the functions in the aforementioned result are.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]>