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46Miller, Mirka
22Morris, Sidney
17Kruger, Alexander
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
13Baca, Martin
13Rubinov, Alex
13Ryan, Joe
12Pineda-Villavicencio, Guillermo
11Hofmann, Karl
9Kelarev, Andrei
9Outrata, Jiri
7Gabriyelyan, Saak
7Mammadov, Musa
6Balbuena, Camino
6Yearwood, John
6Yost, David
5Abawajy, Jemal
5Baskoro, Edy
5López, Marco

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210102 Applied Mathematics
12Graph theory
110802 Computation Theory and Mathematics
11Mathematics
8Antimagic labeling
6Data mining
6Variational analysis
50103 Numerical and Computational Mathematics
5Metric regularity
5Moore bound
5Normal cone
5Number theory
40906 Electrical and Electronic Engineering
4Connectivity
4Degree/diameter problem
4Lie group
4Numerical methods
4Problem solving
4Slope

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The weights of closed subgroups of a locally compact group

- Hernández, Salvador, Hofmann, Karl, Morris, Sidney

**Authors:**Hernández, Salvador , Hofmann, Karl , Morris, Sidney**Date:**2012**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 15, no. 5 (2012), p. 613-630**Full Text:**false**Reviewed:****Description:**Let G be an infinite locally compact group and let n be a cardinal satisfying n 0 ≤ n ≤ w(G) for the weight w(G) of G. It is shown that there is a closed subgroup N of G with w(N) = n. Sample consequences are: (1) Every infinite compact group contains an infinite closed metric subgroup. (2) For a locally compact group G and n a cardinal satisfying n 0 ≤ n ≤ w**Description:**2003010570

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.

Global asymptotic stability in a class of nonlinear differential delay equations

- Ivanov, Anatoli, Mammadov, Musa

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2011**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.**Full Text:****Reviewed:****Description:**An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.**Description:**2003009358

**Authors:**Ivanov, Anatoli , Mammadov, Musa**Date:**2011**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.**Full Text:****Reviewed:****Description:**An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.**Description:**2003009358

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

Error bounds : Necessary and sufficient conditions

- Fabian, Marian, Henrion, René, Kruger, Alexander, Outrata, Jiri

**Authors:**Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri**Date:**2010**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149**Full Text:****Reviewed:****Description:**The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. Â© 2010 Springer Science+Business Media B.V.

**Authors:**Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri**Date:**2010**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149**Full Text:****Reviewed:****Description:**The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. Â© 2010 Springer Science+Business Media B.V.

Internet security applications of Grobner-Shirvov bases

- Kelarev, Andrei, Yearwood, John, Watters, Paul

**Authors:**Kelarev, Andrei , Yearwood, John , Watters, Paul**Date:**2010**Type:**Text , Journal article**Relation:**Asian-European Journal of Mathematics Vol. 3, no. 3 (2010), p. 435-442**Relation:**http://purl.org/au-research/grants/arc/DP0211866**Full Text:**false**Reviewed:**

Internet security applications of the Munn rings

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

**Authors:**Kelarev, Andrei , Yearwood, John , Watters, Paul , Wu, Xinwen , Abawajy, Jemal , Pan, L.**Date:**2010**Type:**Text , Journal article**Relation:**Semigroup Forum Vol. 81, no. 1 (2010), p. 162-171**Full Text:****Reviewed:****Description:**Effective multiple clustering systems, or clusterers, have important applications in information security. The aim of the present article is to introduce a new method of designing multiple clusterers based on the Munn rings and describe a class of optimal clusterers which can be obtained in this construction.

**Authors:**Kelarev, Andrei , Yearwood, John , Watters, Paul , Wu, Xinwen , Abawajy, Jemal , Pan, L.**Date:**2010**Type:**Text , Journal article**Relation:**Semigroup Forum Vol. 81, no. 1 (2010), p. 162-171**Full Text:****Reviewed:****Description:**Effective multiple clustering systems, or clusterers, have important applications in information security. The aim of the present article is to introduce a new method of designing multiple clusterers based on the Munn rings and describe a class of optimal clusterers which can be obtained in this construction.

Some examples of relations between non-stable integral cohomology operations

**Authors:**Percy, Andrew**Date:**2010**Type:**Text , Journal article**Relation:**Bulletin of the Korean Mathematical Society Vol. 47, no. 2 (2010), p. 275-286**Full Text:**false**Reviewed:****Description:**The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups with and into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.

Topology of interconnection networks with given degree and diameter

- Pineda-Villavicencio, Guillermo

**Authors:**Pineda-Villavicencio, Guillermo**Date:**2010**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 81, no. 2 (2010), p. 350-352**Full Text:****Reviewed:**

**Authors:**Pineda-Villavicencio, Guillermo**Date:**2010**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 81, no. 2 (2010), p. 350-352**Full Text:****Reviewed:**

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 algorithm for the optimization of multiple classifers in data mining based on graphs

- Kelarev, Andrei, Ryan, Joe, Yearwood, John

**Authors:**Kelarev, Andrei , Ryan, Joe , Yearwood, John**Date:**2009**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 71, no. (2009), p. 65-85**Full Text:**false**Reviewed:****Description:**This article develops an efficient combinatorial algorithm based on labeled directed graphs and motivated by applications in data mining for designing multiple classifiers. Our method originates from the standard approach described in [37]. It defines a representation of a multiclass classifier in terms of several binary classifiers. We are using labeled graphs to introduce additional structure on the classifier. Representations of this sort are known to have serious advantages. An important property of these representations is their ability to correct errors of individual binary classifiers and produce correct combined output. For every representation like this we develop a combinatorial algorithm with quadratic running time to compute the largest number of errors of individual binary classifiers which can be corrected by the combined multiple classifier. In addition, we consider the question of optimizing the classifiers of this type and find all optimal representations for these multiple classifiers.**Description:**2003007563

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

**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 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 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

Boris Mordukhovich, the never tiring traveller, celebrates his sixtieth birthday

- Henrion, René, Kruger, Alexander, Outrata, Jiri

**Authors:**Henrion, René , Kruger, Alexander , Outrata, Jiri**Date:**2008**Type:**Text , Journal article**Relation:**Set-Valued Analysis Vol. 16, no. 2-3 (2008), p. 125-127**Full Text:****Reviewed:**

**Authors:**Henrion, René , Kruger, Alexander , Outrata, Jiri**Date:**2008**Type:**Text , Journal article**Relation:**Set-Valued Analysis Vol. 16, no. 2-3 (2008), p. 125-127**Full Text:****Reviewed:**

Decomposability of polytopes

- Przeslawski, Krzysztof, Yost, David

**Authors:**Przeslawski, Krzysztof , Yost, David**Date:**2008**Type:**Text , Journal article**Relation:**Discrete & Computational Geometry Vol. 39, no. 1-3 (Mar 2008), p. 460-468**Full Text:****Reviewed:****Description:**A known characterization of the decomposability of polytopes is reformulated in a way which may be more computationally convenient, and a more transparent proof is given. New sufficient conditions for indecomposability are then deduced, and illustrated with some examples.**Description:**C1

**Authors:**Przeslawski, Krzysztof , Yost, David**Date:**2008**Type:**Text , Journal article**Relation:**Discrete & Computational Geometry Vol. 39, no. 1-3 (Mar 2008), p. 460-468**Full Text:****Reviewed:****Description:**A known characterization of the decomposability of polytopes is reformulated in a way which may be more computationally convenient, and a more transparent proof is given. New sufficient conditions for indecomposability are then deduced, and illustrated with some examples.**Description:**C1

Enumerations of vertex orders of almost Moore digraphs with selfrepeats

- Baskoro, Edy, Cholily, Yus Mochamad, Miller, Mirka

**Authors:**Baskoro, Edy , Cholily, Yus Mochamad , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 1 (2008), p. 123-128**Full Text:**false**Reviewed:****Description:**An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r (u) = v, such that there are two walks of length ≤ k from u to v. The smallest positive integer p such that the composition rp (u) = u is called the order of u. If the order of u is 1 then u is called a selfrepeat. It is known that if G is an almost Moore digraph of diameter k ≥ 3 then G contains exactly k selfrepeats or none. In this paper, we propose an exact formula for the number of all vertex orders in an almost Moore digraph G containing selfrepeats, based on the vertex orders of the out-neighbours of any selfrepeat vertex. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

Graphs of order two less than the Moore bound

- Miller, Mirka, Simanjuntak, Rinovia

**Authors:**Miller, Mirka , Simanjuntak, Rinovia**Date:**2008**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 308, no. 13 (2008), p. 2810-2821**Full Text:**false**Reviewed:****Description:**The Moore bound for a directed graph of maximum out-degree d and diameter k is Md,k=1+d+d2++dk. It is known that digraphs of order Md,k (Moore digraphs) do not exist for d>1 and k>1. Similarly, the Moore bound for an undirected graph of maximum degree d and diameter k is . Undirected Moore graphs only exist in a small number of cases. Mixed (or partially directed) Moore graphs generalize both undirected and directed Moore graphs. In this paper, we shall show that all known mixed Moore graphs of diameter k=2 are unique and that mixed Moore graphs of diameter k3 do not exist.**Description:**C1

HSAGA and its application for the construction of near-Moore digraphs

- Tang, Jianmin, Miller, Mirka, Lin, Yuqing

**Authors:**Tang, Jianmin , Miller, Mirka , Lin, Yuqing**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Discrete Algorithms Vol. 6, no. 1 (2008), p. 73-84**Full Text:**false**Reviewed:****Description:**The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. This paper deals with directed graphs. General upper bounds, called Moore bounds, exist for the largest possible order of such digraphs of maximum degree d and given diameter k. It is known that simulated annealing and genetic algorithm are effective techniques to identify global optimal solutions. This paper describes our attempt to build a Hybrid Simulated Annealing and Genetic Algorithm (HSAGA) that can be used to construct large digraphs. We present our new results obtained by HSAGA, as well as several related open problems. © 2007 Elsevier B.V. All rights reserved.**Description:**C1

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