in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

We use this theorem to derive the same corollaries for the theories covered by the theorem as were derived for the strongly minimal case in [2]. We also note that the theorem is in some senses optimal. Specifically we can easily construct trivial Morley Rank 1 theories which are not categorical and for which the conclusion of the theorem fails. Also Marker in [3] constructs trivial totally cate...

Let M be a matroid defined by an independence oracle on ground set S, and let A ⊆ S. We present an incremental polynomial-time algorithm for enumerating all minimal (maximal) subsets of S which span (do not span) A. Special cases of these problems include the generation of bases, circuits, hyperplanes, flats of given rank, circuits through a given element, generalized Steiner trees and multiway...

Multiclass gene selection and classification of cancer are rapidly gaining attention in recent years, while conventional rank-based gene selection methods depend on predefined ideal marker genes that basically devised for binary classification. In this paper, we propose a novel gene selection method based on a gene’s local class discriminability, which does not require any ideal marker genes fo...

Let k be a local field of characteristic not 2, and let G be the group of k-rational points of a connected reductive linear algebraic group defined over k with a simple derived group of k-rank at least 2. We construct new uniform pointwise bounds for the matrix coefficients of all infinite-dimensional irreducible unitary representations of G. These bounds turn out to be optimal for SLn(k), n ≥ ...

In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of subsets {At | t ∈ N} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements ft of G under which #{t ∈ N | ftx ∈ At} is infinite for a.e. x ∈ G/Γ. The main tool is exponential decay of correlation coefficients of smooth fu...

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single “hierarchy”; these are enumerated by the ordered Bell numbers. In this note we determine the number of “hierarchical orderings” or “societies”, where the n elements are first partitioned into m ≤ n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the o...

We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce’s self-dual metrics on the 4-manifold H 2 × T 2 that extend smoothly to nCP, the connected sum of complex projective planes. Indeed, we explicitly realize projective models of the twistor spaces of arbitrary Joyce metrics on nCP in a CP-bundle over CP, and show that they contain the twistor spaces of H 2 × T 2 a...

We determine analytically the modulus of the second eigenvalue for the web hyperlink matrix used by Google for computing PageRank. Specifically, we prove the following statement: “For any matrix , where is an row-stochastic matrix, is a nonnegative rank-one row-stochastic matrix, and ! " , the second eigenvalue of has modulus # $&%'#( ) . Furthermore, if has at least two irreducible closed subs...

An automatic classification scheme of on-line handwritten signatures is presented. A Multilayer Perceptron (MLP) with a hidden layer is used as classifier, and two different signature classes are considered, namely: legible and non-legible name. Signatures are represented considering different feature subsets obtained from global information. Mahalanobis distance is used to rank the parameters ...