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46Miller, Mirka
20Morris, Sidney
16Kruger, Alexander
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
13Baca, Martin
13Rubinov, Alex
13Ryan, Joe
11Hofmann, Karl
10Pineda-Villavicencio, Guillermo
9Kelarev, Andrei
8Mammadov, Musa
8Outrata, Jiri
6Balbuena, Camino
6Gabriyelyan, Saak
6Yearwood, John
5Abawajy, Jemal
5Baskoro, Edy
5Slamin,
5Yost, David

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190102 Applied Mathematics
12Graph theory
11Mathematics
100802 Computation Theory and Mathematics
8Antimagic labeling
6Data mining
6Variational analysis
5Metric regularity
5Moore bound
5Normal cone
5Number theory
40103 Numerical and Computational Mathematics
4Connectivity
4Degree/diameter problem
4Lie group
4Numerical methods
4Problem solving
4Slope
4Theorem proving

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(a,d)-edge-antimagic total labelings of caterpillars

- Miller, Mirka, Sugeng, Kiki Ariyanti, Slamin,, Baca, Martin

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Slamin, , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**Combinatorial Geometry and Graph Theory, LNCS 3330, Lecture Notes in Computer Science, Indonesia-Japan Joint Conference IJCCGGT 2003, Bandung, Indonesia, September 2003, Revised Selected Papers Vol. 3330, no. (2005), p. 169-180**Full Text:**false**Reviewed:****Description:**For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .**Description:**C1**Description:**2003001412

A data mining application of the incidence semirings

- Abawajy, Jemal, Kelarev, Andrei, Yearwood, John, Turville, Christopher

**Authors:**Abawajy, Jemal , Kelarev, Andrei , Yearwood, John , Turville, Christopher**Date:**2013**Type:**Text , Journal article**Relation:**Houston Journal of Mathematics Vol. 39, no. 4 (2013), p. 1083-1093**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Full Text:**false**Reviewed:****Description:**This paper is devoted to a combinatorial problem for incidence semirings, which can be viewed as sets of polynomials over graphs, where the edges are the unknowns and the coefficients are taken from a semiring. The construction of incidence rings is very well known and has many useful applications. The present article is devoted to a novel application of the more general incidence semirings. Recent research on data mining has motivated the investigation of the sets of centroids that have largest weights in semiring constructions. These sets are valuable for the design of centroid-based classification systems, or classifiers, as well as for the design of multiple classifiers combining several individual classifiers. Our article gives a complete description of all sets of centroids with the largest weight in incidence semirings.

A dual criterion for maximal monotonicity of composition operators

- Jeyakumar, Vaithilingam, Wu, Zhiyou

**Authors:**Jeyakumar, Vaithilingam , Wu, Zhiyou**Date:**2007**Type:**Text , Journal article**Relation:**Set-Valued Analysis Vol. 15, no. 3 (2007), p. 265-273**Full Text:**false**Reviewed:****Description:**In this paper we present a dual criterion for the maximal monotonicity of the composition operator T:=A* SA, where S:Y→→ Y is a maximal monotone (set-valued) operator and A: X→ Y is a continuous linear map with the adjoint A*, X and Y are reflexive Banach spaces, and the product notation indicates composition. The dual criterion is expressed in terms of the closure condition involving the epigraph of the conjugate of Fitzpatrick function associated with S, and the operator A. As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given. © 2006 Springer Science+Business Media B.V.**Description:**C1

**Authors:**Sukhorukova, Nadezda**Date:**2008**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 23, no. 5 (2008), p. 793-810**Full Text:**false**Reviewed:****Description:**The classical Remez algorithm was developed for constructing the best polynomial approximations for continuous and discrete functions in an interval [a, b]. In this paper, the classical Remez algorithm is generalized to the problem of linear spline approximation with certain conditions on the spline parameters. Namely, the spline parameters have to be nonnegative and the values of the splines at one of the borders (or both borders) of the approximation intervals may be fixed. This type of constraint occurs in some practical applications, e.g. the problem of taxation tables restoration. The results of the numerical experiments with a Remez-like algorithm developed for this class of conditional optimization problems, are presented.**Description:**C1

A Grobner-Shirshov Algorithm for Applications in Internet Security

- Kelarev, Andrei, Yearwood, John, Watters, Paul, Wu, Xinwen, Ma, Liping, Abawajy, Jemal, Pan, L.

**Authors:**Kelarev, Andrei , Yearwood, John , Watters, Paul , Wu, Xinwen , Ma, Liping , Abawajy, Jemal , Pan, L.**Date:**2011**Type:**Text , Journal article**Relation:**Southeast Asian Bulletin of Mathematics Vol. 35, no. (2011), p. 807-820**Full Text:**false**Reviewed:****Description:**The design of multiple classication and clustering systems for the detection of malware is an important problem in internet security. Grobner-Shirshov bases have been used recently by Dazeley et al. [15] to develop an algorithm for constructions with certain restrictions on the sandwich-matrices. We develop a new Grobner-Shirshov algorithm which applies to a larger variety of constructions based on combinatorial Rees matrix semigroups without any restrictions on the sandwich-matrices.

A lower bound on the order of regular graphs with given girth pair

- Balbuena, Camino, Jiang, T., Lin, Yuqing, Marcote, Xavier, Miller, Mirka

**Authors:**Balbuena, Camino , Jiang, T. , Lin, Yuqing , Marcote, Xavier , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 55, no. 2 (2007), p. 153-163**Full Text:**false**Reviewed:****Description:**The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209-218]. A (**Description:**C1**Description:**2003004727

A new recipe for the spin characters of the symmetric group

**Authors:**Plant, Allison**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Physics a-Mathematical and Theoretical Vol. 41, no. 31 (Aug 2008), p.**Full Text:**false**Reviewed:****Description:**The ring of symmetric functions is a graded ring with important applications in mathematical physics. By examining the various transition matrices between the different bases of the ring of symmetric functions, we are able to write the spin characters of the symmetric group in terms of the ordinary characters of the symmetric group. This approach allows us to describe a new, non-recursive, combinatorial algorithm for the spin characters. We also present simpler algorithms in two special cases.**Description:**C1

A problem of modal control in a linear neutral system

- Ivanov, Anatoli, Khusainov, D. Ya

**Authors:**Ivanov, Anatoli , Khusainov, D. Ya**Date:**2001**Type:**Text , Journal article**Relation:**Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm Vol. 8, no. 3 (2001), p. 395-404**Full Text:**false**Reviewed:****Description:**A problem of modal control is considered for a class of linear multidimensional differential delay systems of neutral type. The control vector is sought in the form that results in a given in advance characteristic equation of the closed system. The problem is completely solved for systems of a special form, the so-called canonical systems. A two-dimensional example is considered in full detail.

A sum labelling for the generalised friendship graph

- Fernau, Henning, Ryan, Joe, Sugeng, Kiki Ariyanti

**Authors:**Fernau, Henning , Ryan, Joe , Sugeng, Kiki Ariyanti**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 5-6 (2008), p. 734-740**Full Text:**false**Reviewed:****Description:**We provide an optimal sum labelling scheme for the generalised friendship graph, also known as the flower (a symmetric collection of cycles meeting at a common vertex) and show that its sum number is 2. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

**Authors:**Mammadov, Musa**Date:**2003**Type:**Text , Journal article**Relation:**Abstract and Applied Analysis Vol. 2003, no. 11 (2003), p. 631-650**Full Text:**false**Reviewed:****Description:**We study the turnpike property for the nonconvex optimal control problems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.**Description:**C1**Description:**2003000343

About [q]-regularity properties of collections of sets

- Kruger, Alexander, Thao, Nguyen

**Authors:**Kruger, Alexander , Thao, Nguyen**Date:**2014**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 416, no. 2 (2014), p. 471-496**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed.**Description:**We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed. (C) 2014 Elsevier Inc. All rights reserved.

**Authors:**Kruger, Alexander , Thao, Nguyen**Date:**2014**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 416, no. 2 (2014), p. 471-496**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed.**Description:**We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed. (C) 2014 Elsevier Inc. All rights reserved.

About intrinsic transversality of pairs of sets

**Authors:**Kruger, Alexander**Date:**2018**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 26, no. 1 (2018), p. 111-142**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The article continues the study of the ‘regular’ arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification conditions in optimization as well as subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. One of the main motivations for the development of the transversality theory of collections of sets comes from the convergence analysis of alternating projections for solving feasibility problems. This article targets infinite dimensional extensions of the intrinsic transversality property introduced recently by Drusvyatskiy, Ioffe and Lewis as a sufficient condition for local linear convergence of alternating projections. Several characterizations of this property are established involving new limiting objects defined for pairs of sets. Special attention is given to the convex case.

**Authors:**Kruger, Alexander**Date:**2018**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 26, no. 1 (2018), p. 111-142**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The article continues the study of the ‘regular’ arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification conditions in optimization as well as subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. One of the main motivations for the development of the transversality theory of collections of sets comes from the convergence analysis of alternating projections for solving feasibility problems. This article targets infinite dimensional extensions of the intrinsic transversality property introduced recently by Drusvyatskiy, Ioffe and Lewis as a sufficient condition for local linear convergence of alternating projections. Several characterizations of this property are established involving new limiting objects defined for pairs of sets. Special attention is given to the convex case.

About regularity of collections of sets

**Authors:**Kruger, Alexander**Date:**2006**Type:**Text , Journal article**Relation:**Set-Valued Analysis Vol. 14, no. 2 (Jun 2006), p. 187-206**Full Text:****Reviewed:****Description:**The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.**Description:**2003001526

About subdifferential calculus for abstract convex functions

**Authors:**Sharikov, Evgenii**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Nonlinear and Convex Analysis Vol. 8, no. 2 (2007), p. 257-275**Full Text:**false**Reviewed:****Description:**We introduce a stronger version of the strong globalization property of Rolewicz and examine the corresponding subdifferential calculus for abstract convex functions. In particular, we calculate a formula for the abstract subdifferential of the maximum of a finite set of abstract convex functions. We also present some examples of families of functions, which possess this new strong globalization property.**Description:**C1**Description:**2003005856

About subtransversality of collections of sets

- Kruger, Alexander, Luke, Russell, Thao, Nguyen

**Authors:**Kruger, Alexander , Luke, Russell , Thao, Nguyen**Date:**2017**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 25, no. 4 (2017), p. 701-729**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.

**Authors:**Kruger, Alexander , Luke, Russell , Thao, Nguyen**Date:**2017**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 25, no. 4 (2017), p. 701-729**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.

**Authors:**Sultanova, Nargiz**Date:**2015**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 91, no. 3 (2015), p. 523-524**Full Text:**false**Reviewed:****Description:**Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, for example in engineering, machine learning and economics. In addition, some smooth problems can be reformulated as nonsmooth optimisation problems with a simpler structure or a smaller dimension. Despite the fact that there exist many algorithms for solving nonsmooth optimisation problems, the field is still very much in development. Nonsmooth nonconvex optimisation, in particular, is far from being considered a mature branch of optimisation.

Algebraic insight underpins the use of CAS for modelling

**Authors:**Pierce, Robyn**Date:**2005**Type:**Text , Journal article**Relation:**The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117**Full Text:****Reviewed:****Description:**Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.**Description:**C1**Description:**2003001447

**Authors:**Pierce, Robyn**Date:**2005**Type:**Text , Journal article**Relation:**The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117**Full Text:****Reviewed:****Description:**Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.**Description:**C1**Description:**2003001447

All (k;g)-cages are k-edge-connected

- Lin, Yuqing, Miller, Mirka, Rodger, Chris

**Authors:**Lin, Yuqing , Miller, Mirka , Rodger, Chris**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227**Full Text:**false**Reviewed:****Description:**A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.**Description:**C1

Alternative route : from van Schooten to Ptolemy

- Percy, Andrew, Rogers, Douglas

**Authors:**Percy, Andrew , Rogers, Douglas**Date:**2009**Type:**Text , Journal article**Relation:**Normat: Nordisk Matematisk Tidskrift Vol. 57, no. 3 (2009), p. 116-128**Full Text:**false**Reviewed:**

An additive subfamily of enlargements of a maximally monotone operator

- Burachik, Regina, Martinez-Legaz, Juan, Rezaie, Mahboubeh, Thera, Michel

**Authors:**Burachik, Regina , Martinez-Legaz, Juan , Rezaie, Mahboubeh , Thera, Michel**Date:**2015**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 643-665**Full Text:****Reviewed:****Description:**We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical epsilon-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the epsilon-subdifferential enlargement.

**Authors:**Burachik, Regina , Martinez-Legaz, Juan , Rezaie, Mahboubeh , Thera, Michel**Date:**2015**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 643-665**Full Text:****Reviewed:****Description:**We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical epsilon-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the epsilon-subdifferential enlargement.

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