We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold is such a stratified vector bundle. 1 Families of vector spaces Let R be the field of real numbers and R = R ⊕ · · · ⊕ R be the standard n-dimensional R-vec...

Definition 1.1. A symplectic vector space is a pair (V, ω) where V is a finite dimensional vector space (over R) and ω is a bilinear form which satisfies • Skew-symmetry: for any u, v ∈ V , ω(u, v) = −ω(v, u). • Nondegeneracy: for any u ∈ V , ω(u, v) = 0 ∀v ∈ V implies u = 0. A linear symplectomorphism of a symplectic vector space (V, ω) is a vector space isomorphism ψ : V → V such that ω(ψu, ψ...

The present article demonstrates a way of formulating a neuro-fuzzy approach for feature extraction under unsupervised training. A fuzzy feature evaluation index for a set of features is newly de8ned in terms of degree of similarity between two patterns in both the original and transformed feature spaces. A concept of 9exible membership function incorporating weighted distance is introduced for...

Vagueness and high dimensional space data are usual features of current data. The paper is an approach to identify conceptual structures among fuzzy three dimensional data sets in order to get conceptual hierarchy. We propose a fuzzy extension of the Galois connections that allows to demonstrate an isomorphism theorem between fuzzy sets closures which is the basis for generating lattices ordere...

A high-speed multiprocessor architecture for brain-like analyzing information represented in analytic, graphand table forms of associative relations to search, recognize and make a decision in n-dimensional vector discrete space is offered. Vector-logical process models of actual applications, where the quality of solution is estimated by the proposed integral non-arithmetical metric of the int...

Operads are a specific tool for encoding type of algebras. For instance there are operads encoding associative algebras, commutative and associative algebras, Lie algebras, pre-Lie algebras, dendriform algebras, Poisson algebras and so on. A usual way of describing a type of algebras is by giving the generating operations and the relations among them. For instance a Lie algebra L is a vector sp...

Structural pattern recognition approaches offer the most expressive, convenient, powerful but computational expensive representations of underlying relational information. To benefit from mature, less expensive and efficient state-of-the-art machine learning models of statistical pattern recognition they must be mapped to a low-dimensional vector space. Our method of explicit graph embedding br...

We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...

An additive quaternary [n,k,d]-code (length n, dimension k, minimum distance d) is a 2k-dimensional \mathbb F 2 -vector space of n-tuples with entries in ⊕\mathbb (the 2-dimensional vector over ) Hamming d. We determine the optimal parameters codes k ≤ 3. The most challenging case k=2.5. prove t...