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46Miller, Mirka
20Morris, Sidney
17Kruger, Alexander
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
13Baca, Martin
13Rubinov, Alex
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11Hofmann, Karl
11Pineda-Villavicencio, Guillermo
9Kelarev, Andrei
8Mammadov, Musa
8Outrata, Jiri
6Balbuena, Camino
6Gabriyelyan, Saak
6Yearwood, John
6Yost, David
5Abawajy, Jemal
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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
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40906 Electrical and Electronic Engineering
4Connectivity
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4Lie group
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Classification systems based on combinatorial semigroups

- Abawajy, Jemal, Kelarev, Andrei

**Authors:**Abawajy, Jemal , Kelarev, Andrei**Date:**2013**Type:**Text , Journal article**Relation:**Semigroup Forum Vol. 86, no. 3 (2013), p. 603-612**Full Text:****Reviewed:****Description:**The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theorem gives a complete description of all optimal classification systems defined by one-sided ideals in a construction based on combinatorial Rees matrix semigroups. It strengthens and generalizes previous results, which handled the more narrow case of two-sided ideals. © 2012 Springer Science+Business Media New York.**Description:**2003011021

**Authors:**Abawajy, Jemal , Kelarev, Andrei**Date:**2013**Type:**Text , Journal article**Relation:**Semigroup Forum Vol. 86, no. 3 (2013), p. 603-612**Full Text:****Reviewed:****Description:**The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theorem gives a complete description of all optimal classification systems defined by one-sided ideals in a construction based on combinatorial Rees matrix semigroups. It strengthens and generalizes previous results, which handled the more narrow case of two-sided ideals. © 2012 Springer Science+Business Media New York.**Description:**2003011021

A data mining application of the incidence semirings

- Abawajy, Jemal, Kelarev, Andrei, Yearwood, John, Turville, Christopher

**Authors:**Abawajy, Jemal , Kelarev, Andrei , Yearwood, John , Turville, Christopher**Date:**2013**Type:**Text , Journal article**Relation:**Houston Journal of Mathematics Vol. 39, no. 4 (2013), p. 1083-1093**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Full Text:**false**Reviewed:****Description:**This paper is devoted to a combinatorial problem for incidence semirings, which can be viewed as sets of polynomials over graphs, where the edges are the unknowns and the coefficients are taken from a semiring. The construction of incidence rings is very well known and has many useful applications. The present article is devoted to a novel application of the more general incidence semirings. Recent research on data mining has motivated the investigation of the sets of centroids that have largest weights in semiring constructions. These sets are valuable for the design of centroid-based classification systems, or classifiers, as well as for the design of multiple classifiers combining several individual classifiers. Our article gives a complete description of all sets of centroids with the largest weight in incidence semirings.

Classification systems based on combinatorial semigroups

- Abawajy, Jemal, Kelarev, Andrei

**Authors:**Abawajy, Jemal , Kelarev, Andrei**Date:**2013**Type:**Text , Journal article**Relation:**Semigroup forum Vol. 86, no. 3 (2013), p. 603-612**Full Text:**false**Reviewed:****Description:**The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theorem gives a complete description of all optimal classification systems defined by one-sided ideals in a construction based on combinatorial Rees matrix semigroups. It strengthens and generalizes previous results, which handled the more narrow case of two-sided ideals.

On optimal control of a sweeping process coupled with an ordinary differential equation

**Authors:**Adam, Lukas , Outrata, Jiri**Date:**2014**Type:**Text , Journal article**Relation:**Discrete and Continuous Dynamical Systems - Series B Vol. 19, no. 9 (November 2014 2014), p. 2709-2738**Full Text:**false**Reviewed:****Description:**We study a special case of an optimal control problem governed by a differential equation and a differential rate{independent variational inequality, both with given initial conditions. Under certain conditions, the variational inequality can be reformulated as a differential inclusion with discontinuous right-hand side. This inclusion is known as sweeping process. We perform a discretization scheme and prove the convergence of optimal solutions of the discretized problems to the optimal solution of the original problem. For the discretized problems we study the properties of the solution map and compute its coderivative. Employing an appropriate chain rule, this enables us to compute the subdifferential of the objective function and to apply a suitable optimization technique to solve the discretized problems. The investigated problem is used to model a situation arising in the area of queuing theory.

Qualitative stability of a class of non-monotone variational inclusions. Application in electronics

**Authors:**Adly, Samir , Outrata, Jiri**Date:**2013**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 20, no. 1 (2013), p. 43-66**Full Text:**false**Reviewed:****Description:**The main concern of this paper is to investigate some stability properties (namely Aubin property and isolated cahnness) of a special non-monotone variational inclusion. We provide a characterization of these properties in terms of the problem data and show their importance for the design of electrical circuits involving nonsmooth and non-monotone electronic devices Uke DIAC (Diode Alternating Current). Circuits with other devices like SCR (Silicon Controlled Rectifiers), Zener diodes, thyristors, varactors and transistors can be analyzed in the same way. © Heldermann Verlag.**Description:**2003011029

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

- Adly, Samir, Hantoute, Abderrahim, Théra, Michel

**Authors:**Adly, Samir , Hantoute, Abderrahim , Théra, Michel**Date:**2012**Type:**Text , Journal article**Relation:**Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (February, 2012), p. 985-1008**Full Text:**false**Reviewed:****Description:**The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.

On SPD method for solving canonical dual problem in post buckling of large deformed elastic beam

**Authors:**Ali, Elaf , Gao, David**Date:**2018**Type:**Text , Journal article**Relation:**Communications in Mathematical Sciences Vol. 16, no. 5 (2018), p. 1225-1240**Full Text:****Reviewed:****Description:**This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex potential leads to a stable configuration of the buckled beam, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. However, the local minimum solution leads to an unstable buckled state, which is very sensitive to axial compressive forces, thickness of beam, numerical precision, and the size of finite elements. The method and algorithm proposed in this paper can be used for solving general nonconvex variational problems in engineering and sciences.

**Authors:**Ali, Elaf , Gao, David**Date:**2018**Type:**Text , Journal article**Relation:**Communications in Mathematical Sciences Vol. 16, no. 5 (2018), p. 1225-1240**Full Text:****Reviewed:****Description:**This paper presents a new methodology and algorithm for solving post buckling problems of a large deformed elastic beam. The total potential energy of this beam is a nonconvex functional, which can be used to model both pre- and post-buckling phenomena. By using a canonical dual finite element method, a new primal-dual semi-definite programming (PD-SDP) algorithm is presented, which can be used to obtain all possible post-buckled solutions. Applications are illustrated by several numerical examples with different boundary conditions. We find that the global minimum solution of the nonconvex potential leads to a stable configuration of the buckled beam, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. However, the local minimum solution leads to an unstable buckled state, which is very sensitive to axial compressive forces, thickness of beam, numerical precision, and the size of finite elements. The method and algorithm proposed in this paper can be used for solving general nonconvex variational problems in engineering and sciences.

The core of a sequence of fuzzy numbers

- Aytar, Salih, Pehlivan, Serpil, Mammadov, Musa

**Authors:**Aytar, Salih , Pehlivan, Serpil , Mammadov, Musa**Date:**2008**Type:**Text , Journal article**Relation:**Fuzzy Sets and Systems Vol. 159, no. 24 (2008), p. 3369-3379**Full Text:**false**Reviewed:****Description:**In this paper, based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties. We extend the concept of the core of a sequence of complex numbers, first introduced by Knopp in 1930, to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval [ν, μ] where ν and μ are extreme limit points of the sequence. © 2008 Elsevier B.V. All rights reserved.

Statistical limit inferior and limit superior for sequences of fuzzy numbers

- Aytar, Salih, Mammadov, Musa, Pehlivan, Serpil

**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**Reviewed:****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

- 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

- Baca, Martin, Lin, Yuqing, Miller, Mirka, Youssef, Maged

**Authors:**Baca, Martin , Lin, Yuqing , Miller, Mirka , Youssef, Maged**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1232-1244**Full Text:**false**Reviewed:****Description:**For a graph G = (V, E), a bijection g from V(G) boolean OR E(G) into {1, 2,..., vertical bar V(G)vertical bar + vertical bar E(G)vertical bar} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy E E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if g(V(G)) = {1, 2,..., vertical bar V(G)vertical bar}. We study super (a, d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs. (c) 2006 Elsevier B.V. All rights reserved.**Description:**2003004910

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

Continuous subdifferential approximations and their applications

**Authors:**Bagirov, Adil**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 115, no. 5 (2003), p. 2567-2609**Full Text:**false**Reviewed:****Description:**In this paper, we study continuous approximations to the Clarke subdifferential and the Demyanov– Rubinov quasidifferential. Different methods have been proposed and discussed for the construction of the continuous approximations. Numerical methods for minimization of the locally Lipschitzian functions which are based on the continuous approximations are described and their convergence is studied. To test the proposed methods, numerical experiments have been carried out and discussed in the paper.**Description:**C1**Description:**2003000423

- Baier, Robert, Farkhi, Elza, Roschina, Vera

**Authors:**Baier, Robert , Farkhi, Elza , Roschina, Vera**Date:**2012**Type:**Text , Journal article**Relation:**Nonlinear Analysis: Theory, Methods Applications Vol. 75, no. 3 (2012), p. 1074-1088**Full Text:**false**Reviewed:****Description:**We extend the definition of the directed subdifferential, originally introduced in [R. Baier, E. Farkhi, The directed subdifferential of DC functions, in: A. Leizarowitz, B.S. Mordukhovich, I. Shafrir, A.J. Zaslavski (Eds.), Nonlinear Analysis and Optimization II: Optimization. A Conference in Celebration of Alex Ioffe’s 70th and Simeon Reich’s 60th Birthdays, June 18–24, 2008, Haifa, Israel, in: AMS Contemp. Math., vol. 513, AMS, Bar-Ilan University, 2010, pp. 27–43], for differences of convex functions (DC) to the wider class of quasidifferentiable functions. Such generalization efficiently captures differential properties of a wide class of functions including amenable and lower/upper-View the MathML source functions. While preserving the most important properties of the quasidifferential, such as exact calculus rules, the directed subdifferential lacks the major drawbacks of quasidifferential: non-uniqueness and “inflation in size” of the two convex sets representing the quasidifferential after applying calculus rules. The Rubinov subdifferential is defined as the visualization of the directed subdifferential.

The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus

- Baier, Robert, Farkhi, Elza, Roschina, Vera

**Authors:**Baier, Robert , Farkhi, Elza , Roschina, Vera**Date:**2012**Type:**Text , Journal article**Relation:**Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (2012), p. 1058-1073**Full Text:**false**Reviewed:****Description:**We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, Michel–Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe’s axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.

Diameter-sufficient conditions for a graph to be super-restricted connected

- Balbuena, Camino, Lin, Yuqing, Miller, Mirka

**Authors:**Balbuena, Camino , Lin, Yuqing , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Discrete Applied Mathematics Vol. , no. (2007), p.**Full Text:**false**Reviewed:****Description:**A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G - X must have at least two vertices. The restricted connectivity**Description:**C1

A lower bound on the order of regular graphs with given girth pair

- Balbuena, Camino, Jiang, T., Lin, Yuqing, Marcote, Xavier, Miller, Mirka

**Authors:**Balbuena, Camino , Jiang, T. , Lin, Yuqing , Marcote, Xavier , Miller, Mirka**Date:**2007**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 55, no. 2 (2007), p. 153-163**Full Text:**false**Reviewed:****Description:**The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovács [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209-218]. A (**Description:**C1**Description:**2003004727

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

- Balbuena, Camino, Barker, Ewan, Lin, Yuqing, Miller, Mirka, Sugeng, Kiki Ariyanti

**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**Reviewed:****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

Conical decomposition and vector lattices with respect to several preorders

- Baratov, Rishat, Rubinov, Alex

**Authors:**Baratov, Rishat , Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Taiwanese Journal of Mathematics Vol. 10, no. 2 (2006), p. 265-298**Full Text:****Reviewed:****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

**Authors:**Baratov, Rishat , Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Taiwanese Journal of Mathematics Vol. 10, no. 2 (2006), p. 265-298**Full Text:****Reviewed:****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

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