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46Miller, Mirka
25Morris, Sidney
24Kruger, Alexander
17Pineda-Villavicencio, Guillermo
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
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13Rubinov, Alex
13Ryan, Joe
11Hofmann, Karl
11Outrata, Jiri
10Yost, David
9Kelarev, Andrei
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8Ugon, Julien
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270102 Applied Mathematics
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60103 Numerical and Computational Mathematics
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50906 Electrical and Electronic Engineering
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The non-smooth and bi-objective team orienteering problem with soft constraints

- Estrada-Moreno, Alejandro, Ferrer, Albert, Juan, Angel, Panadero, Javier, Bagirov, Adil

**Authors:**Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil**Date:**2020**Type:**Text , Journal article**Relation:**Mathematics Vol. 8, no. 9 (2020), p.**Full Text:****Reviewed:****Description:**In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. © 2020 by the authors.**Description:**This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).

**Authors:**Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil**Date:**2020**Type:**Text , Journal article**Relation:**Mathematics Vol. 8, no. 9 (2020), p.**Full Text:****Reviewed:****Description:**In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. © 2020 by the authors.**Description:**This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).

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

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

On Fréchet subdifferentials

**Authors:**Kruger, Alexander**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 116, no. 3 (2003), p. 3325-3358**Full Text:****Reviewed:****Description:**2003002852

**Authors:**Kruger, Alexander**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 116, no. 3 (2003), p. 3325-3358**Full Text:****Reviewed:****Description:**2003002852

Star-shaped separability with applications

- Rubinov, Alex, Sharikov, Evgenii

**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**Full Text:****Reviewed:****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

**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**Full Text:****Reviewed:****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

Convex along lines functions and abstract convexity. Part i

- Crespi, G. P., Ginchev, I., Rocca, M., Rubinov, Alex

**Authors:**Crespi, G. P. , Ginchev, I. , Rocca, M. , Rubinov, Alex**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 14, no. 1 (2007), p. 185-204**Full Text:**false**Reviewed:****Description:**The present paper investigates the property of a function f : Rn → R+∞ := R U {+∞} with f(0) < +∞ to be Ln-subdifferentiable or Hn-convex. The Ln-subdifferentiability and Hnn-convexity are introduced as in Rubinov [9]. Some refinements of these properties lead to the notions of Ln0-subdifferentiability and Hn0-convexity. Their relation to the convex-along (CAL) functions is underlined in the following theorem proved in the paper (Theorem 5.6): Let the function f : Rn → R+∞ be such that f(0) < +∞ and f is Hn-convex at the points at which it is infinite. Then if f is Ln0-subdifferentiable, it is CAL and globally calm at each x0 ∈ dom f. Here the notions of local and global calmness are introduced after Rockafellar, Wets [8] and play an important role in the considerations. The question is posed for the possible reversal of this result. In the case of a positively homogeneous (PH) and CAL function such a reversal is proved (Theorem 6.2). As an application conditions are obtained under which a CAL PH function is Hn0-convex (Theorems 6.3 and 6.4). © Heldermann Verlag.**Description:**C1

**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

All (k;g)-cages are k-edge-connected

- Lin, Yuqing, Miller, Mirka, Rodger, Chris

**Authors:**Lin, Yuqing , Miller, Mirka , Rodger, Chris**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227**Full Text:**false**Reviewed:****Description:**A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.**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

On d-antimagic labelings of prisms

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

**Authors:**Lin, Yuqing , Slamin, , Baca, Martin , Miller, Mirka**Date:**2004**Type:**Text , Journal article**Relation:**Ars Combinatoria: A Canadian Journal of Combinatorics Vol. 72, no. (2004), p. 65-76**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000907

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.

On the degrees of a strongly vertex-magic graph

- Balbuena, Camino, Barker, Ewan, Das, K. C., Lin, Yuqing, Miller, Mirka, Ryan, Joe, Slamin,, Sugeng, Kiki Ariyanti, Tkac, M.

**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

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:**

On non-polynomiality of XOR over Zn2

- Grosek, Otokar, Miller, Mirka, Ryan, Joe

**Authors:**Grosek, Otokar , Miller, Mirka , Ryan, Joe**Date:**2004**Type:**Text , Journal article**Relation:**Tatra Mountains Mathematical Publications Vol. 29, no. (2004), p. 183-191**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000905

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:**

Characterization of eccentric digraphs

- Gimbert, Joan, Lopez, Nacho, Miller, Mirka, Ryan, Joe

**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**Reviewed:****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

Undergraduate mathematics curricula - A new approach

- Giri, Jason, Pierce, Robyn, Turville, Christopher

**Authors:**Giri, Jason , Pierce, Robyn , Turville, Christopher**Date:**2003**Type:**Text , Journal article**Relation:**New Zealand Journal of Mathematics Vol. 32 , no. Supplementary Issue (2003), p. 155-162**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000363

- 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 irregular total labellings

- Baca, Martin, Jendrol, Stanislav, Miller, Mirka, Ryan, Joe

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

**Authors:**Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388**Full Text:****Reviewed:****Description:**Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.**Description:**C1**Description:**2003004909

Sophus Lie's third fundamental theorem and the adjoint functor theorem

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 8, no. 1 (2005), p. 115-133**Full Text:**false**Reviewed:****Description:**The essential attributes of a Lie group G are the associated Lie algebra LðGÞ and the exponential function exp : LðGÞ ! G. The prescription L operates not only on Lie groups but also on morphisms between them: it is a functor. Many features of Lie theory are shared by classes of topological groups which are much larger than that of Lie groups; these classes include the classes of compact groups, locally compact groups, and pro-Lie groups, that is, complete topological groups having arbitrarily small normal subgroups N such that G=N is a (finitedimensional) Lie group. Considering the functor L it is therefore appropriate to contemplate more general classes of topological groups. Certain functorial properties of the assignment of a Lie algebra to a topological group (where possible) will be essential. What is new here is that we will introduce a functorial assignment from Lie algebras to groups and investigate to what extent it is inverse to the Lie algebra functor L. While the Lie algebra functor is well known and is cited regularly, the existence of a Lie group functor available to be cited and applied appears less well known. Sophus Lie’s Third Fundamental Theorem says that for each finite-dimensional real Lie algebra there is a Lie group whose Lie algebra is (isomorphic to) the given one; but even in classical circumstances it is not commonly known that this happens in a functorial fashion and what the precise relationship between the Lie algebra functor and the Lie group functor is.**Description:**C1**Description:**2003001415

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