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15Kruger, Alexander
8Pineda-Villavicencio, Guillermo
7Yost, David
5Miller, Mirka
5Morris, Sidney
5Outrata, Jiri
3Kelarev, Andrei
3Mammadov, Musa
3Pierce, Robyn
3Rubinov, Alex
3Ugon, Julien
2Abawajy, Jemal
2Baca, Martin
2Burachik, Regina
2Gabriyelyan, Saak
2Gao, David
2Henrion, René
2Hofmann, Karl
2Ivanov, Anatoli
2Nevo, Eran

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120102 Applied Mathematics
5Mathematics
5Metric regularity
4Normal cone
4Slope
4Variational analysis
30802 Computation Theory and Mathematics
3Banach space
3Error bounds
3Metric subregularity
20906 Electrical and Electronic Engineering
2Alternating projections
2CAS
2Calmness
2Constraint qualification
2Graph labeling
2Intrinsic transversality
2Linear convergence
2Nonconvex optimization

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Teaching with CAS in a time of transition

- Kendal, Margaret, Stacey, Kaye, Pierce, Robyn

**Authors:**Kendal, Margaret , Stacey, Kaye , Pierce, Robyn**Date:**2002**Type:**Text , Journal article**Relation:**International Journal of Computer Algebra in Mathematics Education Vol. 9, no. 2 (2002), p. 113-128**Full Text:****Reviewed:****Description:**Integrating a powerful instrument such as CAS into teaching and learning mathematics requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use CAS. One teacher used CAS with the primary goal of increasing understanding but restricted students’ use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasising timesaving routines by hand and with CAS. Through these case studies we comment on the following issues related to teaching with CAS: different ways of organising the classroom, variety in approaches to teaching the use of CAS, the increased range of methods for solving problems and for teaching, the contrast between using of graphics calculators and CAS, the challenge of finding the place of by-hand skills and CAS use, and the curriculum and assessment changes required in schools.**Description:**C1**Description:**2003000120

**Authors:**Kendal, Margaret , Stacey, Kaye , Pierce, Robyn**Date:**2002**Type:**Text , Journal article**Relation:**International Journal of Computer Algebra in Mathematics Education Vol. 9, no. 2 (2002), p. 113-128**Full Text:****Reviewed:****Description:**Integrating a powerful instrument such as CAS into teaching and learning mathematics requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use CAS. One teacher used CAS with the primary goal of increasing understanding but restricted students’ use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasising timesaving routines by hand and with CAS. Through these case studies we comment on the following issues related to teaching with CAS: different ways of organising the classroom, variety in approaches to teaching the use of CAS, the increased range of methods for solving problems and for teaching, the contrast between using of graphics calculators and CAS, the challenge of finding the place of by-hand skills and CAS use, and the curriculum and assessment changes required in schools.**Description:**C1**Description:**2003000120

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

Twisted sums with C(K) spaces

- Cabello Sanchez, Felix, Castillo, Jesus, Kalton, Nigel, Yost, David

**Authors:**Cabello Sanchez, Felix , Castillo, Jesus , Kalton, Nigel , Yost, David**Date:**2003**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 355, no. (2003), p. 4523-4541**Full Text:****Reviewed:****Description:**If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 -->**Description:**C1**Description:**2003002201

**Authors:**Cabello Sanchez, Felix , Castillo, Jesus , Kalton, Nigel , Yost, David**Date:**2003**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 355, no. (2003), p. 4523-4541**Full Text:****Reviewed:****Description:**If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 -->**Description:**C1**Description:**2003002201

Algebraic insight underpins the use of CAS for modelling

**Authors:**Pierce, Robyn**Date:**2005**Type:**Text , Journal article**Relation:**The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117**Full Text:****Reviewed:****Description:**Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.**Description:**C1**Description:**2003001447

**Authors:**Pierce, Robyn**Date:**2005**Type:**Text , Journal article**Relation:**The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117**Full Text:****Reviewed:****Description:**Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.**Description:**C1**Description:**2003001447

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

- Rubinov, Alex, Mohebi, Hossein

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

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

Colocality and twisted sums of Banach spaces

- Jebreen, H. M., Jamjoom, F. B. H., Yost, David

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

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

- 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

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

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

Necessary and sufficient conditions for stable conjugate duality

- Burachik, Regina, Jeyakumar, Vaithilingam, Wu, Zhiyou

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

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

- Pineda-Villavicencio, Guillermo, Gomez, Jose, Miller, Mirka, Pérez-Rosés, Hebert

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

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

Sum graph based access structure in a secret sharing scheme

- Miller, Mirka, Slamet, Surjadi, Sugeng, Kiki Ariyanti

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

**Authors:**Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119**Full Text:****Reviewed:****Description:**Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.**Description:**C1**Description:**2003001595

Vertex-magic total labeling of generalized Petersen graphs and convex polytopes

- Miller, Mirka, Baca, Martin, MacDougall, James

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

**Authors:**Miller, Mirka , Baca, Martin , MacDougall, James**Date:**2006**Type:**Text , Journal article**Relation:**JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99**Full Text:****Reviewed:****Description:**To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.**Description:**C1**Description:**2003001602

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

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

Iwasawa's local splitting theorem for pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****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

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****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

- Dmitruk, Andrei, Kruger, Alexander

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

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

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.

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