| 1. |
- Grevholm, Barbro
(författare)
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Recent Nordic research in mathematics education illustrated by examples from NORMA17
- 2021
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Ingår i: Mathematics. - 2227-7390. ; 9:8, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed.
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| 2. |
- Ait-Mlouk, Addi, et al.
(författare)
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WINFRA : A Web-Based Platform for Semantic Data Retrieval and Data Analytics
- 2020
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Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 8:11
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Tidskriftsartikel (refereegranskat)abstract
- Given the huge amount of heterogeneous data stored in different locations, it needs to be federated and semantically interconnected for further use. This paper introduces WINFRA, a comprehensive open-access platform for semantic web data and advanced analytics based on natural language processing (NLP) and data mining techniques (e.g., association rules, clustering, classification based on associations). The system is designed to facilitate federated data analysis, knowledge discovery, information retrieval, and new techniques to deal with semantic web and knowledge graph representation. The processing step integrates data from multiple sources virtually by creating virtual databases. Afterwards, the developed RDF Generator is built to generate RDF files for different data sources, together with SPARQL queries, to support semantic data search and knowledge graph representation. Furthermore, some application cases are provided to demonstrate how it facilitates advanced data analytics over semantic data and showcase our proposed approach toward semantic association rules.
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| 3. |
- Amo-Navarro, Jesus, et al.
(författare)
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Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives
- 2021
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:19
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Tidskriftsartikel (refereegranskat)abstract
- In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.
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| 4. |
- Anderson, Johan, 1973
(författare)
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Information Geometric Investigation of Solutions to the Fractional Fokker-Planck Equation
- 2020
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:5
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Tidskriftsartikel (refereegranskat)abstract
- A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker-Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality (alpha) of the stable Levy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index alpha is computed.
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| 5. |
- Anjum, Asad Ur Rehman, et al.
(författare)
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Sensitivity Analysis of Mathematical Model to Study the Effect of T Cells Infusion in Treatment of CLL
- 2020
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naive, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters' behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia.
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| 6. |
- Brändas, Erkki J., 1940-
(författare)
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There Are Quantum Jumps
- 2015
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Ingår i: Mathematics. - : Published by MDPI AG, Basel, Switzerland. - 2227-7390. ; 3:2, s. 319-328
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Tidskriftsartikel (refereegranskat)abstract
- In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order.
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| 7. |
- Dai, Deliang, et al.
(författare)
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High-Dimensional Mahalanobis Distances of Complex Random Vectors
- 2021
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Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:16
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c = p/n -> infinity. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F = S2-1S1-the product of a sample covariance matrix S-1 (from the independent variable array (be(Z(i))(1xn)) with the inverse of another covariance matrix S-2 (from the independent variable array (Z(j not equal i))(pxn))-are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S-1 and S-2 of the F-matrix is not required.
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| 8. |
- Enayat, Ali, 1959, et al.
(författare)
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On Effectively Indiscernible Projective Sets and the Leibniz-Mycielski Axiom
- 2021
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:14
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Tidskriftsartikel (refereegranskat)abstract
- Examples of effectively indiscernible projective sets of real numbers in various models of set theory are presented. We prove that it is true, in Miller and Laver generic extensions of the constructible universe, that there exists a lightface Π21 equivalence relation on the set of all nonconstructible reals, having exactly two equivalence classes, neither one of which is ordinal definable, and therefore the classes are OD-indiscernible. A similar but somewhat weaker result is obtained for Silver extensions. The other main result is that for any n, starting with 2, the existence of a pair of countable disjoint OD-indiscernible sets, whose associated equivalence relation belongs to lightface Πn1, does not imply the existence of such a pair with the associated relation in Σn1 or in a lower class.
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| 9. |
- Ghandour, Elsa, et al.
(författare)
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Almost complex surfaces in the nearly Kähler SL(2, R) × SL(2, R)
- 2020
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:7
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Tidskriftsartikel (refereegranskat)abstract
- The space SL(2, R) × SL(2, R) admits a natural homogeneous pseudo-Riemannian nearly Kahler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.
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| 10. |
- Grevholm, Barbro
(författare)
-
Recent Nordic research in mathematics education illustrated by examples from NORMA17
- 2021
-
Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:8, s. 1-26
-
Tidskriftsartikel (refereegranskat)abstract
- A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers,teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed.
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