https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31692 k(z) := Σ^∞_n=0 z^kn (1 − z^kn)⁻¹ is transcendental for all algebraic numbers z with |z| < 1. We give a similar result for F_k(z) := Σ^∞n=0 z^kn)(1 + z^kn)⁻¹. These results were known to Mahler, though our proofs of the function transcendence are new and elementary; no linear algebra or differential calculus is used.]]> Wed 11 Apr 2018 15:07:27 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44607 Tue 18 Oct 2022 08:37:52 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:2372 Sat 24 Mar 2018 08:27:54 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13725 2, b not a proper power, a b-ary Machin-type BBP arctangent formula for κ is a formula of the form κ = ∑_m a_m arctan(−b^−m), a_m ∈ ℚ, while when b = 2 , we also allow terms of the form a_m arctan(1/(1 − 2^m)). Of particular interest, we show that π has no Machin-type BBP arctangent formula when b ≠ 2 . To the best of our knowledge, when there is no Machin-type BBP formula for a constant then no BBP formula of any form is known for that constant.]]> Sat 24 Mar 2018 08:22:57 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14075 Sat 24 Mar 2018 08:22:34 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14076 Sat 24 Mar 2018 08:22:34 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14071 Sat 24 Mar 2018 08:22:33 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14067 g(x) for all x, there is a continuous mapping h: X → ℝ with f(x) > h(x) > g(x). This is due to Dowker [Str], [Du]. In this paper we allow f and g to take extended values in a partially ordered vector space (Y,S) where S is an ordering convex cone, and give versions of Hahn's theorem and of Dowker's theorem in this setting. To do this we make appropriate definitions of semicontinuity for functions and for multifunctions. We are then able to apply Michael's selection theorem to the lower semicontinuous multifunction H(x) := [f(x) — S] ⋂ [g(x) + S] to obtain Hahn-type results. We provide a similar selection result for strongly lower semicontinuous multifunctions which we apply to K(x) := [f(x) — IntS] ⋂ [g(x) + IntS] to obtain Dowker-type results. In each case we place restrictions on S to insure that the selection theorem applies.]]> Sat 24 Mar 2018 08:22:31 AEDT ]]> https://nova.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 ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13151 1(µ) has a weak Hadamard differentiable renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if µ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L₁.]]> Sat 24 Mar 2018 08:18:08 AEDT ]]> https://nova.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 ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13143 Sat 24 Mar 2018 08:18:07 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13175 Sat 24 Mar 2018 08:16:07 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13164 Sat 24 Mar 2018 08:16:06 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13127 Sat 24 Mar 2018 08:15:42 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13055 0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.]]> Sat 24 Mar 2018 08:15:39 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13080 Sat 24 Mar 2018 08:15:38 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13094 Sat 24 Mar 2018 08:15:35 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10018 Sat 24 Mar 2018 08:12:18 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11904 Sat 24 Mar 2018 08:08:57 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10330 Sat 24 Mar 2018 08:07:00 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17809 Sat 24 Mar 2018 07:57:36 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16446 Sat 24 Mar 2018 07:56:02 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16140 Sat 24 Mar 2018 07:55:17 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:26176 Sat 24 Mar 2018 07:30:07 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:3866 Sat 24 Mar 2018 07:23:11 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:22533 1, then A² = 0.]]> Sat 24 Mar 2018 07:15:42 AEDT ]]>