On several classes of monographs
- Authors: Sugeng, Kiki Ariyanti , Ryan, Joe
- Date: 2007
- Type: Text , Journal article
- Relation: Australasian Journal of Combinatorics Vol. 37, no. (2007), p. 277-284
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- Description: C1
- Description: 2003004943
Open mapping theorem for topological groups
- Authors: Hofmann, Karl , Morris, Sidney
- Date: 2007
- Type: Text , Journal article
- Relation: Topology Proceedings Vol. 31, no. 2 (2007), p. 533-551
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- 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
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
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- 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
Best approximation by downward sets with applications
- Authors: Rubinov, Alex , Mohebi, Hossein
- Date: 2006
- Type: Text , Journal article
- Relation: Analysis in Theory and Applications Vol. 22, no. 1 (2006), p. 20-40
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- Description: We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.
- Description: C1
- Description: 2003001535
Calculating the extremal number ex (v ; {C3, C4, ..., Cn})
- Authors: Tang, Jianmin , Lin, Yuqing , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 27, no. (2006), p. 101-102
- Full Text: false
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- Description: This paper introduces and analyzes a parallel method of simulated annealing. Borrowing from genetic algorithms, an effective combination of simulated annealing and genetic algorithms, called parallel recombinative simulated annealing, is developed. This new algorithm strives to retain the desirable asymptotic convergence properties of simulated annealing, while adding the populations approach and recombinative power of genetic algorithms. The algorithm iterates a population of solutions rather than a single solution, employing a binary recombination operator as well as a unary neighborhood operator. Proofs of global convergence are given for two variations of the algorithm. Convergence behavior is examined, and empirical distributions are compared to Boltzmann distributions. Parallel recombinative simulated annealing is amenable to straightforward implementation on SIMD, MIMD, or shared-memory machines. The algorithm, implemented on the CM-5, is run repeatedly on two deceptive problems to demonstrate the added implicit parallelism and faster convergence which can result from larger population sizes.
- Description: C1
Characterization of eccentric digraphs
- Authors: Gimbert, Joan , Lopez, Nacho , Miller, Mirka , Ryan, Joe
- Date: 2006
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 306, no. 2 (2006), p. 210-219
- Full Text: false
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- Description: The eccentric digraph ED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G=ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement graph G is either self-centered of radius two or it is the union of complete graphs. As a consequence, we obtain that all trees except those with diameter 3 are eccentric digraphs. We also determine when ED(G) is symmetric in the cases when G is a graph or a digraph that is not strongly connected. Crown Copyright © 2006 Published by Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001601
Colocality and twisted sums of Banach spaces
- Authors: Jebreen, H. M. , Jamjoom, F. B. H. , Yost, David
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 323, no. 2 (2006), p. 864-875
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- Description: Using the relation between subspaces of Banach spaces and quotients of their duals, we introduce the concept of colocality to give a new method that guarantees the existence of nontrivial twisted sums in which finite quotients play a major role (Theorem 1.7). An interesting point is that no restrictions are imposed on the quotients, only on the various subspaces. New examples of nontrivial twisted sums are given.
- Description: C1
- Description: 2003001831
Conical decomposition and vector lattices with respect to several preorders
- Authors: Baratov, Rishat , Rubinov, Alex
- Date: 2006
- Type: Text , Journal article
- Relation: Taiwanese Journal of Mathematics Vol. 10, no. 2 (2006), p. 265-298
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- Description: The decomposition set-valued mapping in a Banach space E with cones K i,i = 1,..., n describes all decompositions of a given element on addends, such that addend i belongs to the i-th cone. We examine the decomposition mapping and its dual. We study conditions that provide the additivity of the decomposition mapping. For this purpose we introduce and study the Riesz interpolation property and lattice properties of spaces with respect to several preorders. The notion of 2-vector lattice is introduced and studied. Theorems that establish the relationship between the Riesz interpolation property and lattice properties of the dual spaces are given.
- Description: C1
- Description: 2003001553
Consecutive magic graphs
- Authors: Balbuena, Camino , Barker, Ewan , Lin, Yuqing , Miller, Mirka , Sugeng, Kiki Ariyanti
- Date: 2006
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 306, no. 16 (2006), p. 1817-1829
- Full Text: false
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- Description: Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1, 2, ..., n + e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is { a + 1, a + 2, ..., a + n }, and is b-edge consecutive magic if the set of labels of the edges is { b + 1, b + 2, ..., b + e }. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n - 1)
- Description: C1
- Description: 2003001604
Divisibility conditions in almost Moore digraphs with selfrepeats
- Authors: Teska, Jakub , Kuzel, Roman , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 24, no. (2006), p. 161-163
- Full Text: false
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- Description: Moore digraph is a digraph with maximum out-degree d, diameter k and order Md, k = 1 + d + ... + dk. Moore digraphs exist only in trivial cases if d = 1 (i.e., directed cycle Ck) or k = 1 (i.e., complete symmetric digraph). Almost Moore digraphs are digraphs of order one less than Moore bound. We shall present new properties of almost Moore digraphs with selfrepeats from which we prove nonexistence of almost Moore digraphs for some k and d. © 2006 Elsevier B.V. All rights reserved.
- Description: C1
Enhancing the image of mathematics by association with simple pleasures from real world contexts
- Authors: Pierce, Robyn , Stacey, Kaye
- Date: 2006
- Type: Text , Journal article
- Relation: ZDM Zentralblatt fur Didaktik der Mathematik Vol. 38, no. 3 (2006), p. 214-225
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- Description: Those who market people or products choose their images very carefully. They create positive associations in the public's mind by photographing their clients with sporting heroes or national icons. In this paper we present a variety of evidence to show that a major and overlooked reason for teachers' use and choice of real world problems is to take advantage of this ‘halo effect’ to improve studients' attitude towards learning mathematics. Analysis of interviews, reports, and results of a brief survey from teachers of middle secondary school classes indicate that they place a very high priority on positive attitudes and hence both choose and enhance real world problems to promote studients' affective engagement through simple pleasures. Pleasant sensory stimuli, generally non-cognitive and peripheral to the situation to be modelled, are used to promote a positive view of mathematics. This is a good strategy for creating enjoyable and memorable lessons, but there is a danger that it may override more substantive learning goals.
- Description: C1
- Description: 2003001563
Face antimagic labelings of prisms
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2006
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 71, no. (Nov 2006), p. 269-286
- Full Text: false
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- Description: This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and labels of vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every number s, the s-sided face weights form an arithmetic progression of difference d. In this paper, we investigate d-antimagic labelings for prism for d is an element of {7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 26,27,30,36).
- Description: C1
Multipartite Moore digraphs
- Authors: Fiol, M. A. , Gimbert, Joan , Miller, Mirka
- Date: 2006
- Type: Text , Journal article
- Relation: Linear Algebra and Its Applications Vol. 419, no. 1 (2006), p. 234-250
- Full Text: false
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- Description: We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, under the assumption that every vertex of a given partite set is adjacent to the same number δ of vertices in each of the other independent sets. We determine when a multipartite Moore digraph is weakly distance-regular. Within this framework, some necessary conditions for the existence of a r-partite Moore digraph with interpartite outdegree δ > 1 and diameter k = 2m are obtained. In the case δ = 1, which corresponds to almost Moore digraphs, a necessary condition in terms of the permutation cycle structure is derived. Additionally, we present some constructions of dense multipartite digraphs of diameter two that are vertex-transitive.
- Description: C1
- Description: 2003002157
Necessary and sufficient conditions for stable conjugate duality
- Authors: Burachik, Regina , Jeyakumar, Vaithilingam , Wu, Zhiyou
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Nonlinear Analysis Vol. 64, no. 9 (2006), p. 1998-2005
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- Description: The conjugate duality, which states that infx∈X φ(x, 0) = maxv∈Y ' −φ∗(0,v), whenever a regularity condition on φ is satisfied, is a key result in convex anal¬ysis and optimization, where φ : X × Y → IR ∪{+∞} is a convex function, X and Y are Banach spaces, Y ' is the continuous dual space of Y and φ∗ is the Fenchel-Moreau conjugate of φ. In this paper, we establish a necessary and sufficient condition for the stable conjugate duality, ∗ ∗ ∈ X' inf {φ(x, 0) + x ∗(x)} = max {−φ ∗(−x ,v)}, ∀x, x∈Xv∈Y ' and obtain a new global dual regularity condition, which is much more general than the popularly known interior-point type conditions, for the conjugate duality. As a consequence we present an epigraph closure condition which is necessary and sufficient for a stable Fenchel-Rockafellar duality theorem. In the case where one of the functions involved in the duality is a polyhedral convex function, we also provide generalized interior-point conditions for the epigraph closure condition. Moreover, we show that a stable Fenchel’s duality for sublinear functions holds whenever a subdifferential sum formula for the functions holds. As applications, we give general sufficient conditions for a minimax theorem, a subdifferential composition formula and for duality results of convex programming problems.
- Description: C1
- Description: 2003003596
New largest graphs of diameter 6. (Extended Abstract)
- Authors: Pineda-Villavicencio, Guillermo , Gomez, Jose , Miller, Mirka , Pérez-Rosés, Hebert
- Date: 2006
- Type: Text , Journal article
- Relation: Electronic Notes in Discrete Mathematics Vol. 24, no. (2006), p. 153-160
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- Description: In the pursuit of obtaining largest graphs of given degree and diameter, many construction techniques have arisen. Compounding of graphs is one such technique. In this paper, by means of the compounding of complete graphs into the bipartite Moore graph of diameter 6, we obtain two families of (
- Description: C1
On optimum summable graphs
- Authors: Miller, Mirka , Koh, K. M. , Smyth, W. F. , Wang, Yan
- Date: 2006
- Type: Text , Journal article
- Relation: AKCE International Journal of Graphs and Combinatorics Vol. 3, no. 1 (2006), p. 45-57
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001922
On the degrees of a strongly vertex-magic graph
- Authors: Balbuena, Camino , Barker, Ewan , Das, K. C. , Lin, Yuqing , Miller, Mirka , Ryan, Joe , Slamin, , Sugeng, Kiki Ariyanti , Tkac, M.
- Date: 2006
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 306, no. 6 (2006), p. 539-551
- Full Text: false
- Reviewed:
- Description: Let G=(V,E) be a finite graph, where |V|=n≥2 and |E|=e≥1. A vertex-magic total labeling is a bijection λ from V∪E to the set of consecutive integers {1,2,...,n+e} with the property that for every v∈V, λ(v)+∑w∈N(v)λ(vw)=h for some constant h. Such a labeling is strong if λ(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e≥10n2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs. © 2006 Elsevier B.V. All rights reserved
- Description: C1
- Description: 2003001603
Star-shaped separability with applications
- Authors: Rubinov, Alex , Sharikov, Evgenii
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 13, no. 3-4 (2006), p. 849-860
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- Description: We discuss the notion of a support collection to a star-shaped set at a certain boundary point and a weak separability of two star-shaped sets. Applications to some problems, including the minimization of a star-shaped distance, are given. © Heldermann Verlag.
- Description: C1
- Description: 2003001592
Statistical limit inferior and limit superior for sequences of fuzzy numbers
- Authors: Aytar, Salih , Mammadov, Musa , Pehlivan, Serpil
- Date: 2006
- Type: Text , Journal article
- Relation: Fuzzy Sets and Systems Vol. 157, no. 7 (2006), p. 976-985
- Full Text: false
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- Description: In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers. © 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001832
Structure of repeat cycles in almost Moore digraphs with selfrepeats and diameter 3
- Authors: Miller, Mirka , Baskoro, Edy , Cholily, Yus Mochamad
- Date: 2006
- Type: Text , Journal article
- Relation: Bulletin of the Institute of Combinatorics and its Applications Vol. 46, no. (2006), p. 99-109
- Full Text: false
- Reviewed:
- Description: C1
- Description: 2003001829