A new proof of Balinski's theorem on the connectivity of polytopes
- Authors: Pineda-Villavicencio, Guillermo
- Date: 2021
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 344, no. 7 (2021), p.
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- Description: Balinski (1961) proved that the graph of a d-dimensional convex polytope is d-connected. We provide a new proof of this result. Our proof provides details on the nature of a separating set with exactly d vertices; some of which appear to be new. © 2021 Elsevier B.V.
A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressure
- Authors: Gala, Sadek , Ragusa, Maria , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Bolletino dell Unione Matematica Italiana Vol. 14, no. 2 (2021), p. 331-337
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: In this study, we establish a new regularity criterion of weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the pressure field. © 2020, Unione Matematica Italiana.
Alternative representations of the normal cone to the domain of supremum functions and subdifferential calculus
- Authors: Correa, Rafael , Hantoute, Abderrahim , Lopez, Marco
- Date: 2021
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 29, no. 3 (2021), p. 683-699
- Relation: http://purl.org/au-research/grants/arc/DP180100602
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- Description: The first part of the paper provides new characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex functions. These results are applied in the second part to give new formulas for the subdifferential of the supremum function, which use both the active and nonactive functions at the reference point. Only the data functions are involved in these characterizations, the active ones from one side, together with the nonactive functions multiplied by some appropriate parameters. In contrast with previous works in the literature, the main feature of our subdifferential characterization is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of this domain) does not appear. A new type of optimality conditions for convex optimization is established at the end of the paper. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.
An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator
- Authors: Dao, Minh , Phan, Hung
- Date: 2021
- Type: Text , Journal article
- Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (2021), p.
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- Description: Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem. © 2021, The Author(s).
Enlargements of the moreau–rockafellar subdifferential
- Authors: Abbasi, Malek , Kruger, Alexander , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 29, no. 3 (2021), p. 701-719
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: This paper proposes three enlargements of the conventional Moreau–Rockafellar subdifferential: the sup-, sup
On the regularity of weak solutions of the boussinesq equations in besov spaces
- Authors: Barbagallo, Annamaria , Gala, Sadek , Ragusa, Maria , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics Vol. 49, no. 3 (2021), p. 637-649
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space Ḃ
Primal necessary characterizations of transversality properties
- Authors: Cuong, Nguyen , Kruger, Alexander
- Date: 2021
- Type: Text , Journal article
- Relation: Positivity Vol. 25, no. 2 (2021), p. 531-558
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Hölder case is given a special attention. Quantitative relations between the nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings as well as two nonlinear transversality properties of a convex set-valued mapping to a convex set in the range space are discussed. © 2020, Springer Nature Switzerland AG.
Strictly convex banach algebras
- Authors: Yost, David
- Date: 2021
- Type: Text , Journal article
- Relation: Axioms Vol. 10, no. 3 (2021), p.
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- Description: We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C
Strongly regular points of mappings
- Authors: Abbasi, Malek , Théra, Michel
- Date: 2021
- Type: Text , Journal article
- Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (Journal article 2021), p.
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- Description: In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound. © 2021, The Author(s).
The linkedness of cubical polytopes: the cube
- Authors: Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien
- Date: 2021
- Type: Text , Journal article
- Relation: Electronic Journal of Combinatorics Vol. 28, no. 3 (2021), p.
- Relation: http://purl.org/au-research/grants/arc/DP180100602
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- Description: The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. We establish that the d-dimensional cube is [(d + 1)/2]-linked, for every d ≠ 3; this is the maximum possible linkedness of a d-polytope. This result implies that, for every d ≥ 1, a cubical d-polytope is [d/2]-linked, which answers a question of Wotzlaw (Incidence graphs and unneighborly polytopes, Ph.D. thesis, 2009). Finally, we introduce the notion of strong linkedness, which is slightly stronger than that of linkedness. A graph G is strongly k-linked if it has at least 2k + 1 vertices and, for every vertex v of G, the subgraph G − v is k-linked. We show that cubical 4-polytopes are strongly 2-linked and that, for each d ≥ 1, d-dimensional cubes are strongly
Transversality properties : primal sufficient conditions
- Authors: Cuong, Nguyen , Kruger, Alexander
- Date: 2021
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 29, no. 2 (2021), p. 221-256
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: The paper studies ‘good arrangements’ (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties in the nonlinear setting. The Hölder case is given a special attention. Our main objective is not formally extending our earlier results from the Hölder to a more general nonlinear setting, but rather to develop a general framework for quantitative analysis of transversality properties. The nonlinearity is just a simple setting, which allows us to unify the existing results on the topic. Unlike the well-studied subtransversality property, not many characterizations of the other two important properties: semitransversality and transversality have been known even in the linear case. Quantitative relations between nonlinear transversality properties and the corresponding regularity properties of set-valued mappings as well as nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe are also discussed. © 2020, Springer Nature B.V.
Almost simplicial polytopes : the lower and upper bound theorems
- Authors: Nevo, Eran , Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David
- Date: 2020
- Type: Text , Journal article
- Relation: Canadian Journal of Mathematics Vol. 72, no. 2 (2020), p. 537-556. http://purl.org/au-research/grants/arc/DP180100602
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- Description: We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of, and, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where s = 0. We characterize the minimizers and provide examples of maximizers for any. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest. © 2018 Canadian Mathematical Society.
Assessing healthcare providers' performance with and without risk adjustment
- Authors: Morales-Silva, Daniel
- Date: 2020
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 102, no. 1 (AUG 2020), p. 172-173
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Directional metric pseudo subregularity of set-valued mappings: a general model
- Authors: Van Ngai, Huynh , Tron, Nguyen , Van Vu, Nguyen , Théra, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 61-87
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- Description: This paper investigates a new general pseudo subregularity model which unifies some important nonlinear (sub)regularity models studied recently in the literature. Some slope and abstract coderivative characterizations are established. © 2019, Springer Nature B.V.
Dual sufficient characterizations of transversality properties
- Authors: Cuong, Nguyen , Kruger, Alexander
- Date: 2020
- Type: Text , Journal article
- Relation: Positivity Vol. 24, no. 5 (2020), p. 1313-1359
- Relation: https://purl.org/au-research/grants/arc/DP160100854
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- Description: This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to develop a general scheme for quantitative analysis of several transversality properties within the same framework. We consider a general nonlinear setting and establish dual (subdifferential and normal cone) sufficient characterizations of transversality properties of collections of sets in Banach/Asplund spaces. Besides quantitative estimates for the rates/moduli of the corresponding properties, we establish here also estimates for the other parameters involved in the definitions, particularly the size of the neighbourhood where a property holds. Interpretations of the main general nonlinear characterizations for the case of Hölder transversality are provided. Some characterizations are new even in the linear setting. As an application, we provide dual sufficient conditions for nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe. © 2020, Springer Nature Switzerland AG.
- Description: The research was supported by the Australian Research Council, Project DP160100854, and the European Union’s Horizon 2020 research and innovation programme under the Marie Sk
Energy sector development : system dynamics analysis
- Authors: Laimon, Mohamd , Mai, Thanh , Goh, Steven , Yusaf, Talal
- Date: 2020
- Type: Text , Journal article
- Relation: Applied Sciences-Basel Vol. 10, no. 1 (Jan 2020), p. 19
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- Description: The development of a complex and dynamic system such as the energy sector requires a comprehensive understanding of its constituent components and their interactions, and thus requires approaches that can adapt to the dynamic complexity in systems. Previous efforts mainly used reductionist approaches, which examine the components of the system in isolation, neglecting their interdependent nature. Such approaches reduce our ability to understand the system and/or mitigate undesirable outcomes. We adopt a system dynamics approach to construct an integrated model for analysing the behaviour of the energy sector. Although the Australian energy sector is used as a case study, the model can be applied in other context elsewhere around the world The results indicate that the current trajectory of the Australian energy sector is unsustainable and growth is not being controlled. Limits to growth are fast approaching due to excessive fossil fuel extraction, high emissions and high energy dependency. With the current growth, Australia's global CO2 emissions footprint will increase to unprecedented levels reaching 12% by 2030 (9.5% for exports and 2.5% for domestic). Oil dependency will account for 43% and 47% of total consumption by 2030 and 2050. By 2032, coal will be the only fossil fuel resource available in Australia. Expansion of investment in coal and gas production is a large risk.
Orthogonality in locally convex spaces : two nonlinear generalizations of Neumann's lemma
- Authors: Barbagallo, Annamaria , Ernst, Octavian-Emil , Théra, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 484, no. 1 (Apr 2020), p. 18
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- Description: In this note we prove a symmetric version of the Neumann lemma as well as a symmetric version of the Soderlind-Campanato lemma. We establish in this way two partial generalizations of the well-known Casazza-Christenses lemma. This work is related to the Birkhoff-James orthogonality and to the concept of near operators introduced by S. Campanato. (C) 2019 Published by Elsevier Inc.
Polytopes close to being simple
- Authors: Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David
- Date: 2020
- Type: Text , Journal article
- Relation: Discrete and Computational Geometry Vol. 64, no. 1 (2020), p. 200-215
- Relation: http://purl.org/au-research/grants/arc/DP180100602
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- Description: It is known that polytopes with at most two nonsimple vertices are reconstructible from their graphs, and that d-polytopes with at most d- 2 nonsimple vertices are reconstructible from their 2-skeletons. Here we close the gap between 2 and d- 2 , showing that certain polytopes with more than two nonsimple vertices are reconstructible from their graphs. In particular, we prove that reconstructibility from graphs also holds for d-polytopes with d+ k vertices and at most d- k+ 3 nonsimple vertices, provided k
Some new characterizations of intrinsic transversality in hilbert spaces
- Authors: Thao, Nguyen , Bui, Hoa , Cuong, Nguyen , Verhaegen, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 5-39
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- Description: Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties. © 2020, The Author(s).
Spatial modelling of bacterial diversity over the selected regions in Bangladesh by next-generation sequencing : role of water temperature
- Authors: Akter, Nabila , Wahiduzzaman, Md , Yeasmin, Alea , Islam, Kazi , Luo, Jing-Jia
- Date: 2020
- Type: Text , Journal article
- Relation: Applied Sciences (Switzerland) Vol. 10, no. 7 (2020), p.
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- Description: In this study, a spatial model has been developed to investigate the role of water temperature to the distribution of bacteria over the selected regions in the Bay of Bengal, located in the southern region of Bangladesh using next-generation sequencing. Bacterial concentration, quantitative polymerase chain reactions, and sequencing were performed on water samples and identified Acidobacteria, Actinobacteria, Bacteroidetes, Chlorobi, Chloroflexi, Cyanobacteria, Firmicutes, Nitrospirae, Planctomycetes, Proteobacteria, and Verrucomicrobia. The spatial model tessellated the parts of the Bay of Bengal with hexagons and analyzed the relationship between the distribution of bacteria and water temperature. A geographically weighted regression was used to observe whether water temperature contributed strongly or weakly to the distribution of bacteria. The residuals were examined to assess the model's fitness. The spatial model has the potential to predict the bacterial diversity in the selected regions of Bangladesh. © 2020 by the authors.