Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

┴N as an Abstract Elementary Class

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COMUNICAEMAT: comunicant objectius matemàtics unint nombres, càlcul, algebra, espai, mesura anglès i tecnologia

S' ha realitzat una anàlisi de processos comunicatius i didàctics en un treball de matemàtiques a Primària en llengua anglesa, emmarcat dins un projecte escolar plurilingüe. El treball s' organitza en forma de recerca-acció que analitza dos objectius principals: (a) elaboració de propostes d' activitat matemàtica i de formació de professorat, i (b) anàlisi del treball realitzat en una experiència escolar. Els resultats mostren que: (1) Les dificultats generals observades, es centren més sobre el contingut de la llengua matemàtica (anomenat L4), pel damunt de les pròpies de l’ús de la llengua anglesa L3. (2) Les decisions del professorat privilegiant l’ús de L1 i L2 (català i castellà) per a treballar L4 s’han mostrat positives i adients. La proposta elaborada, que segueix el model CLIL (Content Language Integrated Learning) ha estat positiva i reproduïble (3) Ha estat possible constatar un bon treball amb els estudiants de formació inicial de mestres de llengua estrangera futurs docents dins l'assignatura de Matemàtiques i la seva Didàctica.a la Formació de professorat. Tanmateix es reconeixen dificultats degudes al poc coneixement previ dels estudiants en L3 i L4 i el fet de ser la primera experiència d’aquest tipus que realitzen. (4) L’alumnat de l’escola és capaç de tenir una bona conversa oral en anglès al final de Primària, que creix en qualitat fins dominar estructures causals pròpies del raonament deductiu. (5) L’alumnat guanya en confiança en l’ús de les quatre llengües ,(6) el professorat incorpora relativament elements didàctics nous en la seva acció pedagògica.

A conjecture of Bavula on homomorphisms of Weyl algebra

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Abstract splines in Krein spaces

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When is the second local multiplier algebra of a C*-algebra equal to the first?

We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C*-algebra to agree with the first.

On absoluteness of categoricity in abstract elementary classes

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Graded algebra automorphisms

We consider the Clifford algebra C(q) of a regular quadratic space (V, q) over a field K with its structure of Z/2Z-graded K-algebra. We give a characterization of the group of graded automorphisms of C(q). In the last section we introduce the Z/nZ-graded algebras and we study as well as the group of graded automorphisms for some of them.

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.

Functional neuroanatomy of contextual acquisition of concrete and abstract words

The meaning of a novel word can be acquired by extracting it from linguistic context. Here we simulated word learning of new words associated to concrete and abstract concepts in a variant of the human simulation paradigm that provided linguistic context information in order to characterize the brain systems involved. Native speakers of Spanish read pairs of sentences in order to derive the meaning of a new word that appeared in the terminal position of the sentences. fMRI revealed that learning the meaning associated to concrete and abstract new words was qualitatively different and recruited similar brain regions as the processing of real concrete and abstract words. In particular, learning of new concrete words selectively boosted the activation of the ventral anterior fusiform gyrus, a region driven by imageability, which has previously been implicated in the processing of concrete words.