| 1. |
- Sorooshian, Shahryar, 1980, et al.
(author)
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Expedited analytical hierarchical process for multicriteria decision making
- 2022
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In: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
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Journal article (peer-reviewed)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 2. |
- Armakan, Abdoreza, et al.
(author)
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Enveloping algebras of certain types of color hom-Lie algebras
- 2020
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In: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 - 9783030418502 ; , s. 257-284
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Book chapter (peer-reviewed)abstract
- In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free hom-associative color algebra on a hom-module is described for a certain type of color hom-Lie algebras and is applied to obtain the universal enveloping algebra of those hom-Lie color algebras. Finally, this construction is applied to obtain the extension of the well-known Poincaré–Birkhoff–Witt theorem for Lie algebras to the enveloping algebra of the certain types of color hom-Lie algebra such that some power of the twisting map is the identity map.
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| 3. |
- Skalski, Adam, et al.
(author)
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Coupling capacity in C∗-algebras
- 2023
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In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. - 1473-7124 .- 0308-2105. ; In Press
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Journal article (peer-reviewed)abstract
- Given two unital C∗-algebras equipped with states and a positive operator in the enveloping von Neumann algebra of their minimal tensor product, we define three parameters that measure the capacity of the operator to align with a coupling of the two given states. Further, we establish a duality formula that shows the equality of two of the parameters for operators in the minimal tensor product of the relevant C∗-algebras. In the context of abelian C∗-algebras, our parameters are related to quantitative versions of Arveson's null set theorem and to dualities considered in the theory of optimal transport. On the other hand, restricting to matrix algebras we recover and generalize quantum versions of Strassen's theorem. We show that in the latter case our parameters can detect maximal entanglement and separability.
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| 4. |
- Lundberg, Anna L.V. 1967
(author)
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Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis
- 2022
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In: International Electronic Journal of Mathematics Education. - Eastbourne, United Kingdom : Modestum Publishing Ltd. - 1306-3030. ; 17:1
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Journal article (peer-reviewed)abstract
- This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.
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| 5. |
- Ghandehari, M., et al.
(author)
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Beurling-Fourier algebras on Lie groups and their spectra
- 2021
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In: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 391
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Journal article (peer-reviewed)abstract
- We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU(n), the Heisenberg group H-r, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover (E) over tilde (2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate that "polynomially growing" weights do not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. (C) 2021 Elsevier Inc. All rights reserved.
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| 6. |
- Musonda, John, 1981-, et al.
(author)
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Reordering in noncommutative algebras associated with iterated function systems
- 2020
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In: Springer Proceedings in Mathematics and Statistics. - Cham : Springer. - 9783030418496 ; , s. 509-552
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Conference paper (peer-reviewed)abstract
- A general class of multi-parametric families of unital associative complex algebras, defined by commutation relations associated with group or semigroup actions of dynamical systems and iterated function systems, is considered. A generalization of these commutation relations in three generators is also considered, modifying Lie algebra type commutation relations, typical for usual differential or difference operators, to relations satisfied by more general twisted difference operators associated with general twisting maps. General reordering and nested commutator formulas for arbitrary elements in these algebras are presented, and some special cases are considered, generalizing some well-known results in mathematics and physics. © Springer Nature Switzerland AG 2020.
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| 7. |
- Ardila, Federico, et al.
(author)
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The equivariant Ehrhart theory of the permutahedron
- 2020
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In: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 148:12, s. 5091-5107
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Journal article (peer-reviewed)abstract
- Equivariant Ehrhart theory enumerates the lattice points in a polytope with respect to a group action. Answering a question of Stapledon, we describe the equivariant Ehrhart theory of the permutahedron, and we prove his Effectiveness Conjecture in this special case.
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| 8. |
- Eur, Christopher, et al.
(author)
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The universal valuation of Coxeter matroids
- 2021
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In: Bulletin of the London Mathematical Society. - : Wiley. - 0024-6093 .- 1469-2120. ; 53:3, s. 798-819
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Journal article (peer-reviewed)abstract
- Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the universal valuative invariant of Coxeter matroids. A key ingredient is the family of Coxeter Schubert matroids, which correspond to the Bruhat cells of flag varieties. In the process, we compute the universal valuation of generalized Coxeter permutohedra, a larger family of polyhedra that model Coxeter analogues of combinatorial objects such as matroids, clusters, and posets.
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| 9. |
- Casarino, V., et al.
(author)
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On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one
- 2024
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In: Annali Di Matematica Pura Ed Applicata. - 0373-3114 .- 1618-1891. ; 203:1, s. 205-219
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Journal article (peer-reviewed)abstract
- Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1, 1) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p < 8 were already known.
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| 10. |
- Muhumuza, Asaph Keikara, et al.
(author)
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The Wishart Distribution on Symmetric Cones
- 2023
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In: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 661-684
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Conference paper (peer-reviewed)abstract
- In this paper we discuss the extension of the Wishart probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions in the field of Herm(m,C), Herm(m,H), Herm(3,O) that denotes respectively the Jordan algebra of all Hermitian matrices of size m× m with complex entries, the skew field H of quaternions, and the algebra O of octonions. This density is characterised by the Vandermonde determinant structure and the exponential weight that is dependent on the trace of the given matrix.
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