Search results for "rete"
showing 10 items of 3470 documents
An integral representation for decomposable measures of measurable functions
1994
We start with a measurem on a measurable space (Ω,A), decomposable with respect to an Archimedeant-conorm ⊥ on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.
On Rough Sets in Topological Boolean Algebras
1994
We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.
Sobriety and spatiality in categories of lattice-valued algebras
2012
The paper provides an analogue of the famous equivalence between the categories of sober topological spaces and spatial locales for the framework of (L,M)-fuzzy topology of Kubiak and Sostak (and partly to that of Guido). To be more general, we replace locales with localic lattice-valued algebras in the sense of Di Nola and Gerla and use the respective generalized topological setting. As a result, it appears that the shift from crisp algebras to lattice-valued algebras weakens (resp. strengthens) considerably the classical (including the point-set lattice-theoretic setting of Rodabaugh) notion of sobriety (resp. spatiality).
Collection Principles in Dependent Type Theory
2002
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.
Intersection subgroups of complex hyperplane arrangements
2000
Abstract Let A be a central arrangement of hyperplanes in C n , let M( A ) be the complement of A , and let L ( A ) be the intersection lattice of A . For X in L ( A ) we set A X ={H∈ A : H⫆X} , and A /X={H/X: H∈ A X } , and A X ={H∩X: H∈ A \ A X } . We exhibit natural embeddings of M( A X ) in M( A ) that give rise to monomorphisms from π 1 (M( A X )) to π 1 (M( A )) . We call the images of these monomorphisms intersection subgroups of type X and prove that they form a conjugacy class of subgroups of π 1 (M( A )) . Recall that X in L ( A ) is modular if X+Y is an element of L ( A ) for all Y in L ( A ) . We call X in L ( A ) supersolvable if there exists a chain 0⫅X 1 ⫅⋯⫅X d =X in L ( A ) …
Graded Involutions on Upper-triangular Matrix Algebras
2009
Let UTn be the algebra of n × n upper-triangular matrices over an algebraically closed field of characteristic zero. We describe all G-gradings on UTn by a finite abelian group G commuting with an involution (involution gradings).
Involution Codimensions of Finite Dimensional Algebras and Exponential Growth
1999
Abstract Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution ∗ over F . We study the asymptotic behavior of the sequence of ∗ -codimensions c n ( A , ∗ ) of A and we show that Exp(A, ∗ ) = lim n → ∞ c n ( A , ∗ ) exists and is an integer. We give an explicit way for computing Exp( A , ∗ ) and as a consequence we obtain the following characterization of ∗ -simple algebras: A is ∗ -simple if and only if Exp( A , ∗ ) = dim F A .
Polynomial identities with involution, superinvolutions and the Grassmann envelope
2017
Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.
Polynomial growth and identities of superalgebras and star-algebras
2009
Abstract We study associative algebras with 1 endowed with an automorphism or antiautomorphism φ of order 2, i.e., superalgebras and algebras with involution. For any fixed k ≥ 1 , we construct associative φ -algebras whose φ -codimension sequence is given asymptotically by a polynomial of degree k whose leading coefficient is the largest or smallest possible.
Law of the Iterated Logarithm
2020
For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.