https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 Symmetry and the monotonicity of certain Riemann sums https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:42654 Wed 31 Aug 2022 13:02:35 AEST ]]> Structure theory for maximally monotone operators with points of continuity https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:16127 Wed 27 Jul 2022 14:01:20 AEST ]]> Ramanujan and Pi https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13168 Wed 24 Jul 2013 22:24:13 AEST ]]> On the binary expansions of algebraic numbers https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13492 1,then the number #(|y|,N) of 1-bits in the expansion of |y| through bit position N satisfies #(|y|,N) > CN1/D for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals ∑n≥o 1/2f(n) where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner–Mahler number ∑n≥o 1/22n, yet we can also handle numbers with a substantially denser occurrence of 1’s. Though the number z = ∑n≥o 1/2n2 has too high a 1’s density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z2.]]> Wed 11 Apr 2018 17:14:51 AEST ]]> Maximality of sums of two maximal monotone operators https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10022 Wed 11 Apr 2018 17:09:47 AEST ]]> The Brezis–Browder Theorem in a general Banach space https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12912 Wed 11 Apr 2018 16:03:52 AEST ]]> Maximum entropy and feasibility methods for convex and nonconvex inverse problems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12942 Wed 11 Apr 2018 15:51:14 AEST ]]> Uniformly convex functions on Banach Spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:7553 Wed 11 Apr 2018 15:33:04 AEST ]]> Surprising sinc sums and integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12939 Wed 11 Apr 2018 15:17:28 AEST ]]> Variational methods in the presence of symmetry https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13495 Wed 11 Apr 2018 15:11:05 AEST ]]> Mosco convergence and the Kadec property https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13027 Wed 11 Apr 2018 15:10:01 AEST ]]> Special values of generalized log-sine integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13512 Wed 11 Apr 2018 14:56:45 AEST ]]> Ramanujan and Pi https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12976 Wed 11 Apr 2018 14:52:58 AEST ]]> Recent results on Douglas-Rachford methods https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20518 Wed 11 Apr 2018 14:50:28 AEST ]]> The evaluation of Bessel functions via exp-arc integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10019 Wed 11 Apr 2018 14:35:23 AEST ]]> Null sets and essentially smooth Lipschitz functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13022 Wed 11 Apr 2018 14:18:53 AEST ]]> On projection algorithms for solving convex feasibility problems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13019 Wed 11 Apr 2018 14:14:13 AEST ]]> Separable determination of integrability and minimality of the Clarke subdifferential mapping https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12996 Wed 11 Apr 2018 14:03:41 AEST ]]> Three-step and four-step random walk integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12926 4(± 1) are given and two new conjectures are recorded.]]> Wed 11 Apr 2018 13:49:54 AEST ]]> Hilbert's inequality and Witten's zeta-function https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12936 Wed 11 Apr 2018 13:47:17 AEST ]]> Maths matters: exploratory experimentation: digitally-assisted discovery and proof https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12977 Wed 11 Apr 2018 13:41:27 AEST ]]> Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13018 Wed 11 Apr 2018 13:41:04 AEST ]]> Lipschitz functions with maximal Clarke subdifferentials are generic https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12997 Wed 11 Apr 2018 13:40:53 AEST ]]> Lp norms and the sinc function https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11528 Wed 11 Apr 2018 13:27:07 AEST ]]> Special values of multiple polylogarithms https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12998 Wed 11 Apr 2018 13:18:11 AEST ]]> Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:22219 Wed 11 Apr 2018 12:44:31 AEST ]]> Organic mathematics: then and now https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13510 Wed 11 Apr 2018 12:43:27 AEST ]]> The Princeton companion to mathematics (book review) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:7551 Wed 11 Apr 2018 12:35:57 AEST ]]> Mosco convergence and reflexivity https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13028 M are useful notions only in the reflexive setting. Specifically, we prove that each of the following conditions is necessary and sufficient for a Banach space X to be reflexive: (1) whenever A , A₁, A₂, A₃, ... are nonempty closed convex subsets of X with A = τM — lim An , then A° = τM — lim A°/n ; (2) τM is a Hausdorff topology on the nonempty closed convex subsets of X ; (3) the arg min multifunction ∫ ⇉ {x ∈ X : ∫(x) = infx ∫} on the proper lower semicontinuous convex functions on X , equipped with τM , has closed graph.]]> Wed 11 Apr 2018 12:35:09 AEST ]]> Symbolic computation of multidimensional Fenchel conjugates https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13545 n, extending earlier work to the non-separable multi-dimensional case. It also explores the potential application of the developed algorithms to automatic inequality proving.]]> Wed 11 Apr 2018 12:25:11 AEST ]]> Integer powers of arcsin https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13491 Wed 11 Apr 2018 12:14:43 AEST ]]> On the Hahn-Banach extension property https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13035 Wed 11 Apr 2018 12:09:01 AEST ]]> Stability of closedness of convex cones under linear mappings II https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11145 Wed 11 Apr 2018 11:16:27 AEST ]]> Nonnormality of Stoneham constants https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12923 b,c = Σn≥1 1/(cnbcn), for coprime integers b ≥ 2 and c ≥ 2. These are of interest because, according to previous studies, αb,c is known to be b-normal, meaning that every m-long string of base-b digits appears in the base-b expansion of the constant with precisely the limiting frequency b-m. So, for example, the constant α2,3 = Σn≥1 1/(3n23n) is 2-normal. More recently it was established that αb,c is not bc-normal, so, for example,α2,3 is provably not 6-normal. In this paper, we extend these findings by showing that αb,c is not B-normal, where B = bpcq r, for integers b and c as above, p, q, r ≥ 1, neither b nor c divide r, and the condition D=cq/pr1/p/bc-1 < 1 is satisfied. It is not known whether or not this is a complete catalog of bases to which αb,c is nonnormal. We also show that the sum of two B-nonnormal Stoneham constants as defined above, subject to some restrictions, is B-nonnormal.]]> Wed 11 Apr 2018 10:56:19 AEST ]]> Log-sine evaluations of Mahler measures https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12988 Wed 11 Apr 2018 10:48:30 AEST ]]> Necessary conditions for constrained optimization problems with semicontinuous and continuous data https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13014 Wed 11 Apr 2018 10:31:15 AEST ]]> On formulas for π experimentally conjectured by Jauregui–Tsallis https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12972 Wed 11 Apr 2018 10:04:16 AEST ]]> The computation of previously inaccessible digits of π² and Catalan's constant https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13722 Wed 11 Apr 2018 09:55:47 AEST ]]> Log-Sine Evaluations of Mahler Measures, II https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12973 Wed 11 Apr 2018 09:50:53 AEST ]]> Ten problems in experimental mathematics https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10339 Wed 11 Apr 2018 09:34:30 AEST ]]> Lipschitz functions with maximal Clarke subdifferentials are staunch https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12980 Wed 11 Apr 2018 09:29:42 AEST ]]> On the Khintchine constant https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13500 Wed 11 Apr 2018 09:19:32 AEST ]]> Some arithmetic properties of short random walk integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12247 Wed 11 Apr 2018 09:16:08 AEST ]]> On an intriguing integral and some series related to ζ (4) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13011 Wed 11 Apr 2018 09:15:09 AEST ]]> The Douglas-Rachford algorithm in the absence of convexity https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13520 Sat 24 Mar 2018 10:37:19 AEDT ]]> On difference convexity of locally Lipschitz functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13522 Sat 24 Mar 2018 10:37:19 AEDT ]]> Walking on real numbers https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12958 Sat 24 Mar 2018 10:37:17 AEDT ]]> Mahler measures, short walks and log-sine integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12927 Sat 24 Mar 2018 10:37:10 AEDT ]]> Thirty-two Goldbach variations https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13088 Sat 24 Mar 2018 10:35:18 AEDT ]]> Proximality and Chebyshev sets https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13090 Sat 24 Mar 2018 10:35:17 AEDT ]]> Infimal convolutions and lipschitzian properties of subdifferentials for prox-regular functions in hilbert spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:9909 Sat 24 Mar 2018 10:31:59 AEDT ]]> Loving and Hating Mathematics by Reuben Hersh & Vera John-Steiner (book review) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11718 Sat 24 Mar 2018 10:31:22 AEDT ]]> Higher-dimensional box integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10329 Sat 24 Mar 2018 10:31:09 AEDT ]]> Maximal monotonicity via convex analysis https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:6507 Sat 24 Mar 2018 10:24:22 AEDT ]]> Stability of closedness of convex cones under linear mappings https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:7182 Sat 24 Mar 2018 08:34:13 AEDT ]]> Variational analysis in nonreflexive spaces and applications to control problems with L1 perturbations https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14234 Sat 24 Mar 2018 08:24:44 AEDT ]]> Normal Numbers and Pseudorandom Generators https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:15946 0, every m-long string of digits in the base-b expansion of α appears, in the limit, with frequency b-m. Although almost all reals in [0, 1] are b-normal for every b, it has been rather difficult to exhibit explicit examples. No results whatsoever are known, one way or the other, for the class of “natural” mathematical constants, such as π,e,2√ and log2. In this paper, we summarize some previous normality results for a certain class of explicit reals and then show that a specific member of this class, while provably 2-normal, is provably not 6-normal. We then show that a practical and reasonably effective pseudorandom number generator can be defined based on the binary digits of this constant and conclude by sketching out some directions for further research.]]> Sat 24 Mar 2018 08:23:41 AEDT ]]> On the existence of Pareto efficient points https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14046 Sat 24 Mar 2018 08:22:36 AEDT ]]> Mosco and slice convergence of level sets and graphs of linear functionals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14079 Sat 24 Mar 2018 08:22:31 AEDT ]]> Lipschitz functions with prescribed derivatives and subderivatives https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14689 Sat 24 Mar 2018 08:19:10 AEDT ]]> On Eulerian log-gamma integrals and Tornheim–Witten zeta functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12922 n = ∫₀¹lognΓ(x)dx for 1≤n≤4 and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right]]> Sat 24 Mar 2018 08:18:13 AEDT ]]> Symbolic Fenchel conjugation https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12940 n. These algorithms are realized in the form of the Maple package SCAT.]]> Sat 24 Mar 2018 08:17:39 AEDT ]]> Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13046 Sat 24 Mar 2018 08:16:32 AEDT ]]> Two-point step size gradient methods https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13167 Sat 24 Mar 2018 08:16:05 AEDT ]]> Proximal analysis in smooth spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13130 Sat 24 Mar 2018 08:15:42 AEDT ]]> Partially smooth variational principles and applications https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13052 Sat 24 Mar 2018 08:15:41 AEDT ]]> Legendre functions and the method of random Bregman projections https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13051 Sat 24 Mar 2018 08:15:41 AEDT ]]> On the equivalence of some basic principles in variational analysis https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13053 Sat 24 Mar 2018 08:15:40 AEDT ]]> Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13054 Sat 24 Mar 2018 08:15:40 AEDT ]]> Limiting convex examples for nonconvex subdifferential calculus https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13056 Sat 24 Mar 2018 08:15:39 AEDT ]]> The SIAM 100-digit challenge a study in high-accuracy numerical computing (book review) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13085 Sat 24 Mar 2018 08:15:38 AEDT ]]> Some remarkable properties of sinc and related integrals https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13072 ∞0 n∏k=0 sin(akx)―akxdx. We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.]]> Sat 24 Mar 2018 08:15:38 AEDT ]]> The (digital) life of Pi https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13089 Sat 24 Mar 2018 08:15:37 AEDT ]]> Multi-variable sinc integrals and volumes of polyhedra https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13069 Sat 24 Mar 2018 08:15:36 AEDT ]]> Inequalities for compound mean iterations with logarithmic asymptotes https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13119 Sat 24 Mar 2018 08:15:05 AEDT ]]> Response to "Experimental approaches to theoretical thinking: artefacts and proofs" https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12416 Sat 24 Mar 2018 08:14:54 AEDT ]]> Uniform bounds for the complementary incomplete gamma function https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12968 c|a − 1|} with a real and z complex. Our results show that within the hyperboloid, |Г(a, z)| is of order |z|a−1e−Re(z), and extends an upper estimate of Natalini and Palumbo to complex values of z.]]> Sat 24 Mar 2018 08:14:42 AEDT ]]> Parametric Euler sum identities https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10011 Sat 24 Mar 2018 08:12:20 AEDT ]]> Variational methods in convex analysis https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10016 Sat 24 Mar 2018 08:12:17 AEDT ]]> Techniques of variational analysis https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:9774 Sat 24 Mar 2018 08:09:05 AEDT ]]> Legendre-type integrands and convex integral functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20926 Sat 24 Mar 2018 08:06:12 AEDT ]]> On lattice sums and Wigner limits https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20817 Sat 24 Mar 2018 08:05:54 AEDT ]]> Random walks in the plane. https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:16327 Sat 24 Mar 2018 07:58:01 AEDT ]]> On the solution of linear mean recurrences https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19133 Sat 24 Mar 2018 07:55:54 AEDT ]]> Pseudo-mathematics and financial charlatanism: the effects of backtest overfitting on out-of-sample performance https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:20685 Sat 24 Mar 2018 07:55:38 AEDT ]]> Some results on the convexity of the closure of the domain of a maximally monotone operator https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19191 Sat 24 Mar 2018 07:55:02 AEDT ]]> Monotone operators and "bigger conjugate" functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:16166 Sat 24 Mar 2018 07:52:27 AEDT ]]> Sum theorems for maximally monotone operators of type (FPV) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:21030 A + B provided that A and B are maximally monotone operators such that star(dom A) ∩ int dom B ≠ ∅, and A is of type (FPV). We show that when also dom A is convex, the sum operator A + B is also of type (FPV). Our result generalizes and unifies several recent sum theorems.]]> Sat 24 Mar 2018 07:50:34 AEDT ]]> Recent progress on monotone operator theory https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:26270 Sat 24 Mar 2018 07:40:16 AEDT ]]> The cyclic Douglas-Rachford method for inconsistent feasibility problems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28000 Sat 24 Mar 2018 07:38:40 AEDT ]]> Reproducibility in computational science: a case study: randomness of the digits of pi https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:31017 computational and experimental mathematics. is now a full-fledged discipline with mathematics, and the larger field of computational science is now taking its place as an experimental discipline on a par with traditional experimental fields. In this new realm, reproducibility comes to the forefront as an essential part of the computational research enterprise, and establishing procedures to ensure and facilitate reproducibility is now a central focus of researchers in the field. In this study, we describe our attempts to reproduce the results of a recently published article by Reinhard Ganz, who concluded that the decimal expansion of p is not statistically random, based on an analysis of several trillion decimal digits provided by Yee and Kondo. While we are able to reproduce the specific findings of Ganz, additional statistical analysis leads us to reject his overall conclusion.]]> Sat 24 Mar 2018 07:34:53 AEDT ]]> Norm convergence of realistic projection and reflection methods https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:26750 Sat 24 Mar 2018 07:24:44 AEDT ]]> Recent results on Douglas-Rachford methods for combinatorial optimization problems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28771 Sat 24 Mar 2018 07:23:45 AEDT ]]> The legacy of Kurt Mahler https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:23671 Sat 24 Mar 2018 07:16:51 AEDT ]]> Nearest points and delta convex functions in Banach spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24006 C in a Banach space (X, || · ||), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ||x - z||, where dC is the distance of x from C. We survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta convex functions and indicate how it is related to finding nearest points.]]> Sat 24 Mar 2018 07:16:42 AEDT ]]> Some remarks on convex analysis in topological groups https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:25161 Sat 24 Mar 2018 07:14:30 AEDT ]]> I prefer pi: a brief history and anthology of articles in the American Mathematical Monthly https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:23028 Sat 24 Mar 2018 07:13:51 AEDT ]]> Relations for Nielsen polylogarithms https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:22781 Sat 24 Mar 2018 07:12:17 AEDT ]]> On Eulerian log-gamma integrals and Tornheim-Witten zeta functions https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:22779 Sat 24 Mar 2018 07:12:15 AEDT ]]> Monotone operators without enlargements https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:18770 Fri 24 Jul 2015 11:10:13 AEST ]]>