https://novaprd-lb.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 Computation and experimental evaluation of Mordell-Tornheim-Witten sum derivatives https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:36036 Wed 29 Jan 2020 16:32:09 AEDT ]]> Stability and regular points of inequality systems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14074 Wed 27 Jul 2022 15:07:29 AEST ]]> Norm duality for convex processes and applications https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14072 Wed 27 Jul 2022 15:07:06 AEST ]]> A C¹-function that is even on a sphere and has no critical points in the ball https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13082 Wed 24 Jul 2013 22:25:34 AEST ]]> Convex spectral functions of compact operators https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13058 Wed 24 Jul 2013 22:25:33 AEST ]]> Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13147 Wed 24 Jul 2013 22:24:52 AEST ]]> Partially monotone operators and the generic differentiability of convex-concave and biconvex mappings https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13163 Wed 24 Jul 2013 22:24:14 AEST ]]> Second order cones for maximal monotone operators via representative functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12937 Wed 11 Apr 2018 17:28:03 AEST ]]> On supportless convex sets https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13005 Wed 11 Apr 2018 17:03:15 AEST ]]> Pi, Euler numbers and asymptotic expansions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14226 Wed 11 Apr 2018 16:43:35 AEST ]]> Partially-finite programming in L₁ and the existence of maximum entropy estimates https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13008 Wed 11 Apr 2018 16:41:49 AEST ]]> Advances in the theory of box integrals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:11249 Wed 11 Apr 2018 16:29:26 AEST ]]> Strong rotundity and optimization https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13010 p norms, such properties are termed "strong rotundity." A very simple characterization of strongly rotund integral functionals on L1 is presented that shows, for example, that the Boltzmann-Shannon entropy ∫ x log x is strongly rotund. Examples are discussed, and the existence of everywhere- and densely-defined strongly rotund functions is investigated.]]> Wed 11 Apr 2018 16:19:45 AEST ]]> Assessment of the performance of reconstruction processes for computed tomography https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12995 Wed 11 Apr 2018 16:16:02 AEST ]]> Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:7552 Wed 11 Apr 2018 16:00:04 AEST ]]> Giuja's conjecture on primality https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14231 n-1 ≡ -1 mod n, then n must be a prime. We survey what is known about this interesting and now fairly old conjecture. Giuga proved that n is a counterexample to his conjecture if and only if each prime divisor p of n satisfies (p - 1) | (n/p - 1) and p | (n/p - 1). Using this characterization, he proved computationally that any counterexample has at least 1,000 digits; equipped with more computing power, E. Bedocchi later raised this bound to 1,700 digits. By improving on their method, we determine that any counterexample has at least 13,800 digits. We also give some new results on the second of the above conditions. This leads, in our opinion, to some interesting questions about what we call Giuga numbers and Giuga sequences.]]> Wed 11 Apr 2018 15:58:03 AEST ]]> On the convergence of moment problems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13029 p norm (1 < p < ∞) is used as the objective, the estimates actually converge in norm. These results provide theoretical support to the growing popularity of such methods in practice.]]> Wed 11 Apr 2018 15:40:11 AEST ]]> More quadratically converging algorithms for π https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14224 Wed 11 Apr 2018 15:34:56 AEST ]]> Direct reconstruction of functional parameters for dynamic SPECT https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13013 Wed 11 Apr 2018 15:30:30 AEST ]]> The way of all means https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14222 Wed 11 Apr 2018 15:28:16 AEST ]]> Some cubic modular identities of Ramanujan https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13009 n2+nm+m2)³ = ([formula cannot be replicated] ωn-mqn²+nm+m²)³ + ([formula cannot be replicated] q(n+1/3)²+(n+1/3)(m+1/3)+(m+1/3)²)³. Here ω = exp(2π i/3). In this note we provide an elementary proof of this identity and of a related identity due to Ramanujan. We also indicate how to discover and prove such identities symbolically.]]> Wed 11 Apr 2018 15:27:13 AEST ]]> Strange series and high precision fraud https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14227 Wed 11 Apr 2018 14:43:01 AEST ]]> Banach spaces that admit support sets https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13003 Wed 11 Apr 2018 14:25:24 AEST ]]> Duality relationships for entropy-like minimization problems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13031 p space, subject to a finite number of linear equality constraints. Such problems arise in spectralestimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constraint qualification, the primal and dual values are equal, with dual attainment. Examples show the primal value may not be attained. Conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum. These conditions are satisfied in many examples.]]> Wed 11 Apr 2018 14:04:12 AEST ]]> The converse of the mean value theorem may fail generically https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13498 Wed 11 Apr 2018 14:00:32 AEST ]]> A fast heuristic method for polynomial moment problems with Boltzmann-Shannon Entropy https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13038 m given some of its algebraic or trigonometric moments. Using the special structure of this kind of problem, a useful linear relationship among the moments is derived. A simple algorithm then provides a fairly good estimate of x̅ by just solving a couple of linear systems. Numerical computations make the algorithm seem reasonable although the theoretical convergence is still an open problem. Some notes about the error bounds are given at the end of the paper.]]> Wed 11 Apr 2018 13:50:46 AEST ]]> On the Bartle-Graves theorem https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12983 Wed 11 Apr 2018 13:43:16 AEST ]]> Super efficiency in vector optimization https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13007 Wed 11 Apr 2018 13:42:16 AEST ]]> A cubic counterpart of Jacobi's identity and the AGM https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13030 n+1 := an + 2bn / 3 and bn+1 := [formula cannot be replicated]. The limit of this iteration is identified in terms of the hypergeometric function ₂F₁ (1/3, 2/3; 1 ; ·), which supports a particularly simple cubic transformation.]]> Wed 11 Apr 2018 13:39:27 AEST ]]> Nonsmooth calculus in finite dimensions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13086 Wed 11 Apr 2018 13:17:03 AEST ]]> On Fan's minimax theorem https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13161 Wed 11 Apr 2018 13:11:46 AEST ]]> Subgradient representation of multifunctions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13032 Wed 11 Apr 2018 13:02:14 AEST ]]> Convergence of best entropy estimates https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13006 1-if Yn converges weakly to ̅y and I(yn) converges to I( ̅y ), then ynn converges to ̅y in norm. As a corollary, it is obtained that, as the number of given moments increases, the best entropy estimates converge in L1 norm to the best entropy estimate of the limiting problem, which is simply ̅ x in the determined case. Furthermore, for classical moment problems on intervals with ̅ x strictly positive and sufficiently smooth, error bounds and uniform convergence are actually obtained.]]> Wed 11 Apr 2018 12:55:45 AEST ]]> An integral characterization of Euclidean space https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13034 Wed 11 Apr 2018 12:43:43 AEST ]]> On the continuity of biconjugate convex functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12985 **, thus also answering a question raised by S. Simons. Related characterizations and examples are given.]]> Wed 11 Apr 2018 12:30:30 AEST ]]> Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13020 Wed 11 Apr 2018 12:17:03 AEST ]]> Second order differentiability of convex functions in Banach spaces https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13012 Wed 11 Apr 2018 11:34:45 AEST ]]> A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13097 Wed 11 Apr 2018 11:21:34 AEST ]]> The quest for pi https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14691 Wed 11 Apr 2018 10:46:10 AEST ]]> Surprise maximization https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12962 Wed 11 Apr 2018 09:54:55 AEST ]]> Automatic continuity and openness of convex relations https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13083 Wed 11 Apr 2018 09:33:13 AEST ]]> On the complexity of familiar functions and numbers https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13093 Wed 11 Apr 2018 09:31:47 AEST ]]> Distinct differentiable functions may share the same Clarke subdifferential at all points https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13021 Wed 11 Apr 2018 09:23:03 AEST ]]> The proximal normal formula in Banach space https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13084 Wed 11 Apr 2018 09:14:15 AEST ]]> A dual approach to multidimensional Lp spectral estimation problems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13096 p spectral estimation problem. The authors use a new constraint qualification (BWCQ) for infinite-dimensional convex programs with linear type constraints recently introduced in [Borwein and Wolkowicz, Math. Programming, 35 (1986), pp. 83-96]. This allows direct derivation of the explicit optimal solution of the problem as presented in [Goodrich and Steinhardt, SIAM J. Appl. Math., 46 (1986), pp. 417-426], and establishment of the existence of a simple and computationally tractable unconstrained Lagrangian dual problem. Moreover, the results illustrate that (BWCQ) is more appropriate to spectral estimation problems than the traditional Slater condition (which may only be applied after transformation of the problem into an Lp space [Goodrich and Steinhardt, op. cit.] and which therefore yields only necessary conditions).]]> Tue 28 May 2019 16:25:49 AEST ]]> Fast heuristic methods for function reconstruction using derivative information https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14065 Thu 01 May 2014 14:44:22 AEST ]]> High-precision numerical integration: progress and challenges https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13523 Sat 24 Mar 2018 10:37:19 AEDT ]]> Lattice sums arising from the Poisson equation https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12924 n(r₁,...,rn) = 1/π²[formula could not be replicated]. By virtue of striking connections with Jacobi ϑ-function values, we are able to develop new closed forms for certain values of the coordinates rk, and extend such analysis to similar lattice sums. A primary result is that for rational x, y, the natural potential ⏀²(x, y) is 1/π log A where A is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20,000-digit arithmetic.]]> Sat 24 Mar 2018 10:37:10 AEDT ]]> Box integrals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13095 where →/r runs over the unit n-cube, with →/q and s fixed, explicitly: ∫₀¹...∫₀¹((r₁-q₁)²+...+(rn-qn)²)s/2dr₁...drn. The study of box integrals leads one naturally into several disparate fields of analysis. While previous studies have focused upon symbolic evaluation and asymptotic analysis of special cases (notably s = 1), we work herein more generally—in interdisciplinary fashion—developing results such as: (1) analytic continuation (in complex s), (2) relevant combinatorial identities, (3) rapidly converging series, (4) statistical inferences, (5) connections to mathematical physics, and (6) extreme-precision quadrature techniques appropriate for these integrals. These intuitions and results open up avenues of experimental mathematics, with a view to new conjectures and theorems on integrals of this type.]]> Sat 24 Mar 2018 10:35:17 AEDT ]]> Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13513 Sat 24 Mar 2018 10:34:54 AEDT ]]> Hypergeometric forms for Ising-class integrals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:10012 Sat 24 Mar 2018 10:33:33 AEDT ]]> Integrals of the Ising Class https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6447 Sat 24 Mar 2018 10:23:28 AEDT ]]> Convergence of Lipschitz regularizations of convex functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14233 Sat 24 Mar 2018 08:24:44 AEDT ]]> Uniform convergence for moment problems with Fermi-Dirac type entropies https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14232 Sat 24 Mar 2018 08:24:44 AEDT ]]> Conjugate convex operators https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14051 . = F ∪ {+∞} are considered, where F is an ordered topological vector space and + ∞ an arbitrary greatest element adjoined to F. In view of applications to the polarity theory of convex operators, the possibility is investigated of representing a convex mapping taking values in F. as a supremum of continuous affine mappings.]]> Sat 24 Mar 2018 08:22:37 AEDT ]]> Generalized linear complementarity problems treated without fixed-point theory https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14050 Sat 24 Mar 2018 08:22:37 AEDT ]]> On the generating function of the integer part: [nα + γ] https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14077 n and qn are the numerators and denominators of the convergents of the continued fraction expansion of α and t**n and s**n are particular algorithmically generated sequences of best approximates for the non-homogeneous diophantine approximation problem of minimizing |nα + γ − m|. This generalizes results of Böhmer and Mahler, who considered the special case where γ = 0. This representation allows us to easily derive various transcendence results. For example, ∑∞n=1 [ne +1/2 ]/2n is a Liouville number. Indeed the first series is Liouville for rational z, w∈ [−1, 1] with |zw| ≠ 1 provided α has unbounded continued fraction expansion. A second application, which generalizes a theorem originally due to Lord Raleigh, is to give a new proof of a theorem of Fraenkel, namely [nα + γ]∞n=1 and [nα′ + γ′]∞n=1 partition the non-negative integers if and only if 1/α + 1/α′ = 1 and γ/α + γ′/α′ = 0 (provided some sign and integer independence conditions are placed on α, β, γ, γ′). The analysis which leads to the results is quite delicate and rests heavily on a functional equation for G. For this a natural generalization of the simple continued fraction to Kronecker′s forms |nα + γ − m| is required.]]> Sat 24 Mar 2018 08:22:34 AEDT ]]> Super efficiency in convex vector optimization https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14078 Sat 24 Mar 2018 08:22:34 AEDT ]]> Proximal analysis and boundaries of closed sets in Banach space, Part I: theory https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14076 Sat 24 Mar 2018 08:22:34 AEDT ]]> Dykstra's alternating projection algorithm for two sets https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14063 Sat 24 Mar 2018 08:22:33 AEDT ]]> On some trigonometric and exponential lattice sums https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14062 Sat 24 Mar 2018 08:22:33 AEDT ]]> Decomposition of multivariate functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14071 Sat 24 Mar 2018 08:22:33 AEDT ]]> Partially finite convex programming, part I: quasi relative interiors and duality theory https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14069 Sat 24 Mar 2018 08:22:33 AEDT ]]> Tangential approximations https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14070 Sat 24 Mar 2018 08:22:33 AEDT ]]> Partially finite convex programming, part II: explicit lattice models https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:14073 1 approximation, constrained approximation and interpolation, spectral estimation, semi-infinite transportation problems and the generalized market area problem of Lowe and Hurter (1976). As in Part I, we shall use lattice notation extensively, but, as we illustrated there, in concrete examples lattice-theoretic ideas can be avoided, if preferred, by direct calculation.]]> Sat 24 Mar 2018 08:22:32 AEDT ]]> Sandwich theorems for semicontinuous operators https://novaprd-lb.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 ]]> High-precision computation: mathematical physics and dynamics https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:12913 Sat 24 Mar 2018 08:18:17 AEDT ]]> On generic second-order Gateaux differentiability https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13141 ’(x), h) is continuous. Recall that a convex Gateaux differentiable function is strictly Gateaux differentiable. In the case of a locally Lipschitz function our definition coincides with more standard ones: it requires that f’ be norm to weak-star continuous.]]> Sat 24 Mar 2018 08:18:08 AEDT ]]> On the convergence of von Neumann's alternating projection algorithm for two sets https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13150 Sat 24 Mar 2018 08:18:08 AEDT ]]> Class number three Ramanujan type series for 1/π https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13145 Sat 24 Mar 2018 08:18:07 AEDT ]]> Absolute norms on vector lattices https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13142 Sat 24 Mar 2018 08:18:07 AEDT ]]> Cubic and higher order algorithms for π https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13144 Sat 24 Mar 2018 08:18:07 AEDT ]]> Directionally Lipschitzian mappings on Baire spaces https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13137 Sat 24 Mar 2018 08:18:06 AEDT ]]> On the mean iteration (a,b) ← (a+3b/4, √ab+b/2) https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13173 n = (an + 3bn/4, bn+1 =(√anbn+bn)/2 is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these nontrivial identifications, is highlighted.]]> Sat 24 Mar 2018 08:16:07 AEDT ]]> The hypertangent cone https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13172 Sat 24 Mar 2018 08:16:07 AEDT ]]> Proximal analysis and boundaries of closed sets in Banach space Part II: applications https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13164 Sat 24 Mar 2018 08:16:06 AEDT ]]> The differentiability of real functions on normed linear space using generalized subgradients https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13166 Sat 24 Mar 2018 08:16:06 AEDT ]]> A simple constraint qualification in infinite dimensional programming https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13162 Sat 24 Mar 2018 08:16:06 AEDT ]]> Analysis of certain lattice sums* https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13171 Sat 24 Mar 2018 08:16:05 AEDT ]]> Energy of static electron lattices https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13170 Sat 24 Mar 2018 08:16:05 AEDT ]]> Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13169 Sat 24 Mar 2018 08:16:05 AEDT ]]> An explicit cubic iteration for π https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13160 Sat 24 Mar 2018 08:16:05 AEDT ]]> Approximate subgradients and coderivatives in R<sup>n</sup> https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13131 Sat 24 Mar 2018 08:15:42 AEDT ]]> The range of the gradient of a continuously differentiable bump https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13067 Sat 24 Mar 2018 08:15:39 AEDT ]]> On the construction of Hölder and proximal subderivatives https://novaprd-lb.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 ]]> Local Lipschitz-constant functions and maximal subdifferentials https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13079 X* is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its ‘local Lipschitz-constant’ function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.]]> Sat 24 Mar 2018 08:15:37 AEDT ]]> Duality inequalities and sandwiched functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13074 Sat 24 Mar 2018 08:15:37 AEDT ]]> Antiproximinal norms in Banach spaces https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13078 0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the convex point of continuity property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]> Convex functions of Legendre type in general Banach spaces https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13070 n is given.]]> Sat 24 Mar 2018 08:15:36 AEDT ]]> The range of the gradient of a Lipschitz C¹-smooth bump in infinite dimensions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13071 Sat 24 Mar 2018 08:15:35 AEDT ]]> The stability analysis of dynamic SPECT systems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13101 Sat 24 Mar 2018 08:15:13 AEDT ]]> Entropy minimization, DAD problems, and doubly stochastic kernels https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13121 Sat 24 Mar 2018 08:15:05 AEDT ]]> On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13117 Sat 24 Mar 2018 08:15:05 AEDT ]]> Maximum entropy reconstruction using derivative information, part I: Fisher information and convex duality https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:13124 Sat 24 Mar 2018 08:15:04 AEDT ]]> The evaluation of character Euler double sums https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:10334 Sat 24 Mar 2018 08:07:00 AEDT ]]> The life of Simon Fitzpatrick, 1953-2004 https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6598 Sat 24 Mar 2018 07:45:48 AEDT ]]> Maximal monotone inclusions and Fitzpatrick functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:27998 gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrate how naturally this gap function arises from the Fitzpatrick function, which is a convex function, used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.]]> Sat 24 Mar 2018 07:38:40 AEDT ]]> Crandall's computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet L-series https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:26172 Sat 24 Mar 2018 07:30:05 AEDT ]]> Computation and theory of Mordell-Tornheim-Witten sums II https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:28248 Sat 24 Mar 2018 07:28:33 AEDT ]]> Computation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:26179 Sat 24 Mar 2018 07:24:10 AEDT ]]>