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46Miller, Mirka
24Morris, Sidney
18Kruger, Alexander
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
14Pineda-Villavicencio, Guillermo
13Baca, Martin
13Rubinov, Alex
13Ryan, Joe
11Hofmann, Karl
10Outrata, Jiri
9Kelarev, Andrei
8Mammadov, Musa
8Yost, David
7Gabriyelyan, Saak
6Balbuena, Camino
6Ugon, Julien
6Yearwood, John
5Abawajy, Jemal
5Baskoro, Edy

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220102 Applied Mathematics
12Graph theory
110802 Computation Theory and Mathematics
11Mathematics
8Antimagic labeling
6Data mining
6Metric regularity
6Normal cone
6Variational analysis
50103 Numerical and Computational Mathematics
50906 Electrical and Electronic Engineering
5Connectivity
5Metric subregularity
5Moore bound
5Number theory
5Slope
4Aubin property
4Degree/diameter problem
4Lie group

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Sigma supporting cone and optimality conditions in non-convex problems

- Hassani, Sara, Mammadov, Musa

**Authors:**Hassani, Sara , Mammadov, Musa**Date:**2014**Type:**Text , Journal article**Relation:**Far East Journal of Mathematical Sciences Vol. 91, no. 2 (2014), p. 169-190**Full Text:**false**Reviewed:****Description:**In this paper, a new supporting function for characterizing non-convex sets is introduced. The notions of Ïƒ-supporting cone and maximal conic gap are proposed and some properties are investigated. By applying these new notions, we establish the optimality conditions considered in [7] for a broader class of finite dimensional normed spaces in terms of weak subdifferentials.

Quadratic form representations via generalized continuants

- Delorme, Charles, Pineda-Villavicencio, Guillermo

**Authors:**Delorme, Charles , Pineda-Villavicencio, Guillermo**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Integer Sequences Vol. 18, no. 6 (2015), p. Article number 15.6.4**Full Text:**false**Reviewed:****Description:**H. J. S. Smith proved Fermat’s two-square theorem using the notion of palindromic continuants. In this paper we extend Smith’s approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of integers and rings of polynomials over fields of odd characteristic. Also, we present new deterministic algorithms for finding the corresponding proper representations. © 2015 University of Waterloo. All rights reserved.

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

Error bounds for vector-valued funtions on metric spaces

- Kruger, Alexander, Bednarczuk, Ewa

**Authors:**Kruger, Alexander , Bednarczuk, Ewa**Date:**2012**Type:**Text , Journal article**Relation:**Vietnam Journal of Mathematics Vol. 40, no. 2/3 (2012), p. 165-180**Full Text:****Reviewed:****Description:**In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.

**Authors:**Kruger, Alexander , Bednarczuk, Ewa**Date:**2012**Type:**Text , Journal article**Relation:**Vietnam Journal of Mathematics Vol. 40, no. 2/3 (2012), p. 165-180**Full Text:****Reviewed:****Description:**In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.

Exclusive sum labelings of trees

- Miller, Mirka, Tuga, Mauritsius, Ryan, Joe, Ryjacek, Zdenek

**Authors:**Miller, Mirka , Tuga, Mauritsius , Ryan, Joe , Ryjacek, Zdenek**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 109-121**Full Text:**false**Reviewed:****Description:**The notions of**Description:**C1**Description:**2003001406

Parallel algorithms for generalized clique transversal problems

- Miller, Mirka, Dahlhaus, Elias, Manuel, Paul

**Authors:**Miller, Mirka , Dahlhaus, Elias , Manuel, Paul**Date:**2005**Type:**Text , Journal article**Relation:**Australasian Journal of Combinatorics Vol. 33, no. (2005), p. 3-14**Full Text:**false**Reviewed:****Description:**The K ` - clique transversal problem is to locate a minimum collection of cliques of size ` in a graph G such that every maximal clique of size ` in G contains at least one member of the collection. We give an NC algorithm to solve this problem on strongly chordal graphs. Keywords: balanced graphs, strongly chordal graphs, clique transversal, k-fold clique transversal, K ` - clique transversal. 1 Introduction A 0 Gamma 1 matrix is balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of an odd cycle. A 0 Gamma 1 matrix is totally balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of any cycle. A hypergraph H is an ordered pair (V; E) where V is a set of vertices and E is a family of subsets of V . The members of E are called hyperedges of H . Let V = fv 1 ; v 2 ; : : : ; v n g and E = fE 1 ; E 2 ; : : : ; Em g. Let A(H) denote the hyperedge - vertex incidence matrix of a hypergraph H .**Description:**C1**Description:**2003001400

Super antimagic total labeling of graphs

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

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 76, no. (2008), p. 161-171**Full Text:**false**Reviewed:****Description:**Let G = (V, E) be a simple, finite and undirected graph with v vertices and e edges, A graph labeling is a mapping from elements of a graph to a set of numbers (usually positive integers). If the domain of the mapping is the set of vertices (or edges) then the labeling is called vertex-labeling (or edge-labeling). If the domain of the mapping is the set of vertices and edges then the labeling is called total labeling. The sum of all labels associated with a graph element is called the weight of the element. If the weights of vertices (or the weights of edges) form an arithmetic progression starting at a and with difference d, then the labeling is called (a, d)-vertex-antimagic (or (a, d)-edge-antimagic). Such a labeling is called v-super (or e-super) if the smallest labels appear on the vertices (or edges). In this paper we present new results for v-super vertex-antimagic total and e-super edge-antimagic total labeling.**Description:**C1

Typical behaviour in scalar delay differential equations

- Ivanov, Anatoli, Dzalilov, Zari, Rubinov, Alex

**Authors:**Ivanov, Anatoli , Dzalilov, Zari , Rubinov, Alex**Date:**2001**Type:**Text , Journal article**Relation:**Studies of University of Zilina, Mathematical series Vol. 14 , no. 1 (2001), p. 1-10**Full Text:**false**Reviewed:****Description:**C1**Description:**2003002564

New constructions of A-magic graphs using labeling matrices

- Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 147-151**Full Text:**false**Reviewed:**

From convergence principles to stability and optimality conditions

- Klatte, Diethard, Kruger, Alexander, Kummer, Bernd

**Authors:**Klatte, Diethard , Kruger, Alexander , Kummer, Bernd**Date:**2012**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 19, no. 4 (2012), p. 1043-1072**Full Text:****Reviewed:****Description:**We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be derived. Our most abstract models are (multi-) functions on complete metric spaces. The relevance of this approach is illustrated by deriving both classical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior of solution procedures. © Heldermann Verlag.**Description:**2003010677

**Authors:**Klatte, Diethard , Kruger, Alexander , Kummer, Bernd**Date:**2012**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 19, no. 4 (2012), p. 1043-1072**Full Text:****Reviewed:****Description:**We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes. Depending on the principle of convergence, new and intrinsic stability conditions can be derived. Our most abstract models are (multi-) functions on complete metric spaces. The relevance of this approach is illustrated by deriving both classical and new results on existence and optimality conditions, stability of feasible and solution sets and convergence behavior of solution procedures. © Heldermann Verlag.**Description:**2003010677

Hermite-Hadamard-type inequalities for increasing convex-along-rays function

- Rubinov, Alex, Dragomir, S. S, Dutta, J.

**Authors:**Rubinov, Alex , Dragomir, S. S , Dutta, J.**Date:**2004**Type:**Text , Journal article**Relation:**Analysis Vol. 24, no. 2 (2004), p. 171-181**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000933

- Baca, Martin, Lin, Yuqing, Miller, Mirka

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 72, no. (2007), p. 65-75**Full Text:**false**Reviewed:****Description:**In this paper we deal with the problem of labeling the vertices, edges and faces of a grid graph by the consecutive integers from 1 to |V| + |E| + |F| in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face weights then form an arithmetic progression with common difference d.**Description:**C1**Description:**2003004808

Teaching with CAS in a time of transition

- Kendal, Margaret, Stacey, Kaye, Pierce, Robyn

**Authors:**Kendal, Margaret , Stacey, Kaye , Pierce, Robyn**Date:**2002**Type:**Text , Journal article**Relation:**International Journal of Computer Algebra in Mathematics Education Vol. 9, no. 2 (2002), p. 113-128**Full Text:****Reviewed:****Description:**Integrating a powerful instrument such as CAS into teaching and learning mathematics requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use CAS. One teacher used CAS with the primary goal of increasing understanding but restricted students’ use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasising timesaving routines by hand and with CAS. Through these case studies we comment on the following issues related to teaching with CAS: different ways of organising the classroom, variety in approaches to teaching the use of CAS, the increased range of methods for solving problems and for teaching, the contrast between using of graphics calculators and CAS, the challenge of finding the place of by-hand skills and CAS use, and the curriculum and assessment changes required in schools.**Description:**C1**Description:**2003000120

**Authors:**Kendal, Margaret , Stacey, Kaye , Pierce, Robyn**Date:**2002**Type:**Text , Journal article**Relation:**International Journal of Computer Algebra in Mathematics Education Vol. 9, no. 2 (2002), p. 113-128**Full Text:****Reviewed:****Description:**Integrating a powerful instrument such as CAS into teaching and learning mathematics requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use CAS. One teacher used CAS with the primary goal of increasing understanding but restricted students’ use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasising timesaving routines by hand and with CAS. Through these case studies we comment on the following issues related to teaching with CAS: different ways of organising the classroom, variety in approaches to teaching the use of CAS, the increased range of methods for solving problems and for teaching, the contrast between using of graphics calculators and CAS, the challenge of finding the place of by-hand skills and CAS use, and the curriculum and assessment changes required in schools.**Description:**C1**Description:**2003000120

On the nonexistence of graphs of diameter 2 and defect 2

- Miller, Mirka, Nguyen, Minh Hoang, Pineda-Villavicencio, Guillermo

**Authors:**Miller, Mirka , Nguyen, Minh Hoang , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 5-20**Full Text:**false**Reviewed:****Description:**In 1960, Hoffman and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d² + 1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdös et al., using eigenvalue analysis, showed that, with the exception of C4, there are no graphs of diameter 2, maximum degree d and d² vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d² - 1 vertices do not exist for most values of d with d ≥ 6, and conjecture that they do not exist for any d ≥ 6.**Description:**2003007893

Moore graphs and beyond : A survey of the degree/diameter problem

**Authors:**Miller, Mirka , Siran, Jozef**Date:**2005**Type:**Text , Journal article**Relation:**Electronic Journal of Combinatorics Vol. DS14, no. (2005), p. 1-61**Full Text:**false**Reviewed:****Description:**The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds { called Moore bounds { for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bounds for the maximum possible number of vertices, given the other two parameters, and thus attacking the degree/diameter problem `from above', remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter problem `from below'. This survey aims to give an overview of the current state-of-the-art of the degree/diameter problem. We focus mainly on the above two streams of research. However, we could not resist mentioning also results on various related problems. These include considering Moore-like bounds for special types of graphs and digraphs, such as vertex-transitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.**Description:**C1**Description:**2003001407

Super edge-antimagic total labeling

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

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin**Date:**2006**Type:**Text , Journal article**Relation:**Utilitas Mathematica Vol. 71, no. (2006), p. 131-141**Full Text:**false**Reviewed:****Description:**A (p, q)-graph G is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1,2,...,p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Moreover, G is said to be super (a, d)-edge-antimagic total if f(V(G)) = {1,2,..., p}. In this paper we study the super (a,d)-edge-antimagic total properties of certain classes of graphs, including ladders, generalized prisms and antiprisrns.**Description:**C1**Description:**2003001596

On graphs of maximum degree 3 and defect 4

- Pineda-Villavicencio, Guillermo, Miller, Mirka

**Authors:**Pineda-Villavicencio, Guillermo , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008), p. 25-31**Full Text:**false**Reviewed:****Description:**It is well known that apart from the Petersen graph there are no Moore graphs of degree 3. As a cubic graph must have an even number of vertices, there are no graphs of maximum degree 3 and

On antimagic labelings of disjoint union of complete s-partite graphs

- Dafik, Miller, Mirka, Ryan, Joe, Baca, Martin

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

**Authors:**Dafik , Miller, Mirka , Ryan, Joe , Baca, Martin**Date:**2008**Type:**Text , Journal article**Relation:**Journal of combinatorial mathematics and combinatorial computing Vol. 65, no. (May 2008 2008), p. 41-49**Full Text:****Reviewed:****Description:**By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) u E(G) onto the set. { 1, 2, ... ,ǀV(C)ǀ+IE(G)I} such that the set of all the edge-weights, w(uv) ,.... f(u) + f(uv) + f(v), uv C E (G), is {a, a+ d, a+ 2d, . . . , a + (lE(G)I-1)d}, for two integers a > 0 and d

Subspaces of the free topological vector space on the unit interval

- Gabriyelyan, Saak, Morris, Sidney

**Authors:**Gabriyelyan, Saak , Morris, Sidney**Date:**2018**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 97, no. 1 (2018), p. 110-118**Full Text:**false**Reviewed:****Description:**For a Tychonoff space X, let V(X) be the free topological vector space over X, A(X) the free abelian topological group over X and I the unit interval with its usual topology. It is proved here that if X is a subspace of I, then the following are equivalent: V(X) can be embedded in V(I) as a topological vector subspace; A(X) can be embedded in A(I) as a topological subgroup; X is locally compact. © 2017 Australian Mathematical Publishing Association Inc..

Continuants and some decompositions into squares

- Delorme, Charles, Pineda-Villavicencio, Guillermo

**Authors:**Delorme, Charles , Pineda-Villavicencio, Guillermo**Date:**2015**Type:**Text , Journal article**Relation:**Integers Vol. 15, no. (2015), p. 1**Full Text:****Reviewed:****Description:**In 1855 H. J. S. Smith proved Fermat's two-square using the notion of palindromic continuants. In his paper, Smith constructed a proper representation of a prime number

**Authors:**Delorme, Charles , Pineda-Villavicencio, Guillermo**Date:**2015**Type:**Text , Journal article**Relation:**Integers Vol. 15, no. (2015), p. 1**Full Text:****Reviewed:****Description:**In 1855 H. J. S. Smith proved Fermat's two-square using the notion of palindromic continuants. In his paper, Smith constructed a proper representation of a prime number

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