Global stability, periodic solutions and optimal control in a nonlinear differential delay model
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2010
- Type: Text , Conference proceedings
- Relation: Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, 2010
- Full Text: false
- Description: A nonlinear differential equation with delay serving as a mathematical model of several applied problmes is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsay. An optimization problem for a maximal consumption is stated and solved for the latter.
Integral cohomology algebras : The algebras of cohomology groups with integer coefficients and primary operations
- Authors: Percy, Andrew
- Date: 2010
- Type: Text , Book
- Full Text: false
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- Description: Summary "'Integral cohomology algebras' explores the algebraic objects consisting of cohomology groups with integer coefficients and the primary cohomology operations acting on them. These cohomology algebras are contrasted with their Eckmann-Hilton dual of homotopy groups and primary homotopy operations. They are also shown to generalize the Steenrod algebra structures for cohomology over finite fields. Several examples are given using the cohomology algebra structure to distinguish between topological spaces. The earlier chapters provide a comprehensive summary of the Eckmann-Hilton duality of integral cohomology and homotopy groups and the natural primary operations on them. A final chapter discusses directions for future research."--Back cover.
Internet security applications of Grobner-Shirvov bases
- 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
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Internet security applications of the Munn rings
- 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
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- 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
- 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
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Alternative route : from van Schooten to Ptolemy
- 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
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An algorithm for the optimization of multiple classifers in data mining based on graphs
- 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
- 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
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- 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
A generalization of the Remez algorithm to a class of linear spline approximation problems with constraints on spline parameters
- 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
- 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
- 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
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Decomposability of polytopes
- 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
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- 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
- 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
- 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
- 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
Iwasawa's local splitting theorem for pro-Lie groups
- Authors: Hofmann, Karl , Morris, Sidney
- Date: 2008
- Type: Text , Journal article
- Relation: Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629
- Full Text:
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- Description: If the nilradical () of the Lie algebra of a pro-Lie group G is finite dimensional modulo the center (), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. © Walter de Gruyter 2008.
- Description: C1
Metric regularity and systems of generalized equations
- Authors: Dmitruk, Andrei , Kruger, Alexander
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 342, no. 2 (2008), p. 864-873
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- Description: The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity and metric multi-regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. The criteria are applied to systems of generalized equations producing some "error bound" type estimates. © 2007 Elsevier Inc. All rights reserved.
Monotonic analysis over cones : III
- Authors: Dutta, J. , Martinez-Legaz, Juan , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 15, no. 3 (2008), p. 561-579
- Full Text: false
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- Description: This paper studies the class of increasing and co-radiant (ICR) functions over a cone equipped with an order relation which agrees with the conic structure. In particular, a representation of ICR functions as abstract convex functions is provided. This representation suggests the introduction of some polarity notions between sets. The relationship between ICR functions and increasing positively homogeneous functions is also shown.
- Description: C1