‘It takes me longer,but I understand better’ – student feedback on structured derivations

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of understanding. Our findings indicate that the main drawbacks experienced by the students are related to time and length. Nevertheless, the overall feedback on the approach was found to be positive, thus encouraging further use of structured derivations in mathematics education.     

Research Article: On Extending Primal-Dual Interior-Point Method for Linear Optimization to Convex Quadratic Symmetric Cone Optimization

Disjoint frames are interesting frames in Hilbert spaces, which were introduced by Han and Larson in [4 D. Han and D. R. Larson ( 2000 ). Frames, Basis and Group Representations . Memoirs of the American Mathematical Society, No. 679. AMS, Providence, RI.  [Google Scholar]]. In this article, we use disjoint frames to construct frames. In particular, we obtain some conditions for the linear combinations of frames to be frames where the coefficients in the combination may be operators. Our results generalize the corresponding results obtained by Han and Larson. Finally, we provide some examples to illustrate our constructions.     

Jordan Superalgebras of Type and the Wedderburn Principal Theorem (WPT)

An analogue of the Wedderburn Principal Theorem (WPT) is considered for finite-dimensional Jordan superalgebras 𝔍 with solvable radical 𝒩, 𝒩 ² = 0, and such that , where 𝔽 is a field of characteristic zero. It is proved that the WPT is valid under some restrictions over the irreducible -bimodules contained in 𝒩, and it is shown with counterexamples that these restrictions cannot be weakened.     

Construction of Nilpotent Jordan Algebras Over any Arbitrary Field

The paper is devoted to the study of annihilator extensions of Jordan algebras and suggests new approach to classify nilpotent Jordan algebras, which is analogous to the Skjelbred–Sund method for classifying nilpotent Lie algebras [2 de Graaf, W. (2007). Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2. J. Algebra 309:640–653.[Crossref], [Web of Science ®] , [Google Scholar], 4 Gong, M.-P. (1998). Clasification of Nilpotent Lie Algebras of Dimension 7 [Ph.D]. Ontario, Canada: University of Waterloo. [Google Scholar], 15 Skjelbred, T., Sund, T. (1978). Sur la classification des algèbres de Lie nilpotentes. C. R. Acad. Sci. Paris Sér. A-B 286:241–242. [Google Scholar]]. Subsequently, we have classified nilpotent Jordan algebras of dimension up to four.