This paper presents an approach to build a soft sensor based on computational intelligence techniques. The goal is to identify fuzzy models from numerical data. First of all, the fuzzy model input variables are selected from the secondary variables set by applying Kohonen maps. Then, the Lipschitz quotients are used to select the lag structure of the fuzzy model. A fuzzy clustering algorithm is...

Let p be a prime. It is a fundamental problem to classify the absolute Galois groups GF of fields F containing a primitive pth root of unity. In this paper we present several constraints on such GF , using restrictions on the cohomology of index p normal subgroups from [LMS]. In section 1 we classify all maximal p-elementary abelian-by-order p quotients of these GF . In the case p > 2, each suc...

We investigate the k-error linear complexity of pseudorandom binary sequences of period pr derived from the Euler quotients modulo pr−1, a power of an odd prime p for r ≥ 2. When r = 2, this is just the case of polynomial quotients (including Fermat quotients) modulo p, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the k-error ...

Let p be a prime. It is a fundamental problem to classify the absolute Galois groups GF of fields F containing a primitive pth root of unity ξp. In this paper we present several constraints on such GF , using restrictions on the cohomology of index p normal subgroups from [LMS]. In section 1 we classify all maximal p-elementary abelian-by-order p quotients of these GF . In the case p > 2, each ...

We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverings (with covering indices equals 2) and our second family is given as Cayley graphs of finite groups with very short presentations with only 2 generators and 4 relations. Both families are based on particular finite q...

We relate two measures of complexity of regular languages. The first is syntactic complexity, that is, the cardinality of the syntactic semigroup of the language. That semigroup is isomorphic to the semigroup of transformations of states induced by non-empty words in the minimal deterministic finite automaton accepting the language. If the language has n left quotients (its minimal automaton ha...

Geometric invariant theory (GIT) was developed in the 1960s by Mumford in order to construct quotients of reductive group actions on algebraic varieties and hence to construct and study a number of moduli spaces, including, for example, moduli spaces of bundles over a nonsingular projective curve [26, 28]. Moduli spaces often arise naturally as quotients of varieties by algebraic group actions,...

It has been observed many times, both in the Monthly and elsewhere, that the set of all quotients of prime numbers is dense in the positive real numbers. In this short note we answer the related question: “Is the set of all quotients of Gaussian primes dense in the complex plane?” Quotient sets {s/t : s, t ∈ S} corresponding to subsets S of the natural numbers have been intensely studied in the...

An elementary, self-contained proof of a result of Pouzet and Rosenberg and of Harper is given. This result states that the quotient of certain posets (called unitary Peck) by a finite group of automorphisms retains some nice properties, including the Sperner property. Examples of unitary Peck posets are given, and the techniques developed here are used to prove a result of Lovhz on the edge-re...

For (b), let Θ be any subset of Γ, x in its complement, U as in (a). The neighbourhood xU of x contains at most one element of Γ. There exists a neighbourhood of x contained in xU and not containing any element of Θ. For (c), let V = U ·U, which is compact. The intersection of Γ with V is compact, and covered by disjoint neighbourhoods of each of its points. This intersection must therefore be ...