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40Miller, Mirka
18Morris, Sidney
14Lin, Yuqing
14Sugeng, Kiki Ariyanti
11Ryan, Joe
10Baca, Martin
10Rubinov, Alex
9Hofmann, Karl
6Balbuena, Camino
6Kelarev, Andrei
6Mammadov, Musa
5Baskoro, Edy
5Gabriyelyan, Saak
5Slamin,
4Hantoute, Abderrahim
4López, Marco
4Nguyen, Minh Hoang
4Outrata, Jiri
4Percy, Andrew
4Pineda-Villavicencio, Guillermo

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12Graph theory
100102 Applied Mathematics
8Antimagic labeling
70802 Computation Theory and Mathematics
6Mathematics
5Data mining
5Moore bound
5Number theory
40103 Numerical and Computational Mathematics
4Connectivity
4Lie group
4Numerical methods
4Problem solving
4Theorem proving
30906 Electrical and Electronic Engineering
3Abstract convexity
3Convex functions
3Degree/diameter problem
3Duality

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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

**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

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:**

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

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

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..

Open mapping theorem for topological groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 31, no. 2 (2007), p. 533-551**Full Text:**false**Reviewed:****Description:**We survey sufficient conditions that force a surjective continuous homomorphism between topological groups to be open. We present the shortest proof yet of an open mapping theorem between projective limits of finite dimensional Lie groups.**Description:**C1**Description:**2003005915

Attracting sets for increasing co-radiant and topical operators

- Kloeden, Peter, Rubinov, Alex

**Authors:**Kloeden, Peter , Rubinov, Alex**Date:**2002**Type:**Text , Journal article**Relation:**Mathematische Nachrichten Vol. 243, no. (2002), p. 134-145**Full Text:**false**Reviewed:****Description:**A generalization of the Perron-Frobenius theorem to increasing positively homogeneous of degree one operators is extended to increasing co-radiant and topical operators, which are of interest in mathematical economics. In particular, small attracting sets containing the limit points of all sequences generated by iteration of such operators are determined.**Description:**C1**Description:**2003000150

The structure of almost connected pro-lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2011**Type:**Text , Journal article**Relation:**Journal of Lie Theory Vol. 21, no. 2 (2011), p. 347-383**Full Text:**false**Reviewed:****Description:**Recalling that a topological group G is said to be almost connected if the quotient group G=G0 is compact, where G0 is the connected component of the identity, we prove that for an almost connected pro-Lie group G, there exists a compact zero-dimensional, that is, profinite, subgroup D of G such that G = G0D. Further for such a group G, there are sets I , J , a compact connected semisimple group S , and a compact connected abelian group A such that G and ℝI × (ℤ=2ℤ)J × S × A are homeomorphic. En route to this powerful structure theorem it is shown that the compact open topology makes the automorphism group Aut g of a semisimple pro-Lie algebra g a topological group in which the identity component (Aut g)0 is exactly the group Inn g of inner automorphisms. In this situation, Inn(G) has a totally disconnected semidirect complement

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.

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