Polynomial Approximation of Functions: Historical Perspective and New Tools

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the thinking process of the creators of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Geodesic Between the Hilbert Basis Theorem and Gordan''''s Lemma

Gordan's Lemma and Hilbert Basis theorem, both merging from establishing thefinite generation of invariants, are proved in one combinatorial set up, namely, thesemigroup N~n     

格值命题逻辑LP(X)中不可分极简式的性质

基于格值命题逻辑LP(X)的α-归结原理及α-归结自动推理方法，能够较好地刻画具有可比较性和不可比较性的不确定性信息。LP(X)中的不可分极简式是一个非常重要的概念，本文对蕴涵运算个数小于3的不可分极简式的性质和判定方法进行了讨论，得到了一些重要结论。     

N-半单代数与蕴涵代数

研究了有限结合代数与各种蕴涵代数的联系,得到了一些有趣的结果:N-半单代数的中心幂等元集G(R)按照“→”或者“*”等运算分别构成与蕴涵代数(F I代数、BCK代-数、BC I代-数、BCC代-数、W a jsberg代数等)等价的代数系统。     

Elementary Operators on Standard Operator Algebras

We present a new simple proof of the structural result for elementary operators on standard operator algebras. Using the idea of this short proof we can characterize surjective maps between standard operator algebras having a certain multiplicativity-like property appearing in the abstract definition of elementary operators of length one. In particular, we show that such maps are automatically additive.     

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014–2015 at the ‘ETSEIB'of Universitat Politècnica de Catalunya (UPC).     

Summands of Stable Equivalences of Morita Type

A stable equivalence of Morita type between two finite dimensional algebras with no separable summand will be shown to restrict to stable equivalences of Morita type between their summands. We will apply this to prove that stable equivalence of Morita type preserves self-injectivity of algebras and the property of being symmetric.     

Algebra Structures Arising from Yang–Baxter Systems

Yang–Baxter operators from algebra structures appeared for the first time in [11 D?sc?lescu , S. , Nichita , F. ( 1999 ). Yang–Baxter operators arising from (co)algebra structures . Comm. Algebra 27 : 5833 – 5845 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 22 Nichita , F. ( 1999 ). Self-inverse Yang–Baxter operators from (co)algebra structures . J. Algebra 218 : 738 – 759 .[Crossref], [Web of Science ®] , [Google Scholar], 23 Nuss , P. ( 1997 ). Noncommutative descent and non-abelian cohomology . K-Theory 12 ( 1 ): 23 – 74 .[Crossref] , [Google Scholar]]. Later, Yang–Baxter systems from entwining structures were constructed in [8 Brzeziński , T. , Nichita , F. F. ( 2005 ). Yang–Baxter systems and Entwining Structures . Comm. Algebra 33 : 1083 – 1093 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. In fact, Yang–Baxter systems are equivalent with braid systems. In this paper we show that braidings and entwinings of various algebraic structures—in particular, algebra factorisations—can be constructed from a braid system, whence from a Yang–Baxter system as well.     

De Morgan (2, n)-Semigroups of n-Place Functions

An abstract characterization of sets of some partial functions from Aⁿ to A closed with respect to the Menger's and Mann's superpositions and a quasicomplementation is presented.