In this work we study the differential aspects of noncommutative geometry for magnetic $C^*$-algebra which is a 2-cocycle deformation group $\mathbb{R}^2$. This algebra intimately related to Quantum Hall Effect in continuous, and our results aim provide new geometric interpretation Kubo's formula. Taking inspiration from ideas developed by Bellissard during 80's, build an appropriate Fredholm m...

Let n E Z+ and let K be a field. Let ~ be a partial order on {1, 2, ... , n}. Let An(:::;) be the matrix incidence algebra consisting of those n x n matrices A = (ai,j) with entries in K, satisfying ai,j 0 whenever i 1:. j. For a subset £ ~ An (::5), a necessary and sufficient condition that the algebra generated by £ u {I} is An(::5) is that (i) for every 1 :::; i, j :::; n with i =1= j, there...

In this paper, we present an extended relational calculus and algebra for a functional logic deductive database language. The extended relational calculus is based on the relational first-order logic, by adding constraints in the form of equalities and disequalities over complex (partially defined and possibly infinite) values and interpreted functions. In addition, we propose the notion of saf...

In all languages, sentences convey information that allows people to locate situations in time. Languages vary: some have tense and tense-like forms, others do not. I will suggest general pragmatic principles to account for how temporal location works in language. The principles have different realizations according to the forms that are syntactically obligatory in a given language. I will begi...

a) A parser which assigns a tree structure to sentences. The fragment which the parser can analyse corresponds roughly to the fragment of English described by R. Montague in 'The proper treatment of quantification in ordinary English'. Our fragment contains however more tense forms, temporal adverbs, and temporal conjunctions. In particular we treat the notoriously difficult pair of tense forms...

We study the action of the symmetric group Σn on a tensor product of n − 1 copies of a commutative Hopf algebra A, defined by the second author [8]. We show that for ‘nice’ Hopf algebras, the cohomology algebra H∗(Σn;A⊗n−1) is independent of the coproduct if n.(n − 2)! is invertible in the ground ring. Let A be a graded, connected, unital, counital, associative, coassociative Hopf algebra. In s...

This paper proposes a new look at the so-called ‘present-perfect puzzle’. It suggests that it is in fact part of a bigger problem, concerning all tenses in a language situating an event one step before the moment of utterance. I argue that present perfects compete with simple past tenses, and that the distribution of these tenses shows signs of the impact of this competition. The outcome of the...