Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...

The concepts of (∈,∈ ∨ q)-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, (∈,∈∨q)-fuzzy (implicative, positiv...

A general linear theory is presented which describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed (time-frequency) domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier tra...

In this paper we will introduce a certain collection of fuzzy subsets of a nonempty set X. This certain collection gives raise to a useful new fuzzy partition. This new fuzzy partition gives us a way of generating a fuzzy equivalence relation as in the ordinary case; any partition generates an equivalence relation. Mathematics Subject Classification: 03E72, 46S40, 26E50

We use natural gradient (NG) learning neural networks (NNs) for modeling and identifying nonlinear systems with memory. The nonlinear system is comprised of a discrete-time linear filter H followed by a zero-memory nonlinearity g(·). The NN model is composed of a linear adaptive filter Q followed by a two-layer memoryless nonlinear NN. A Kalman filter-based technique and a search-and-converge m...

This work propose a new Kalman filter-based method for integrity monitoring, following the solution separation approach of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm. This method evaluates the separation of state correction using different subsets of measurement to detect abnormalities as well as potential faulty satellites for exclusion. This approach differs from ...

We study principles of the form: if a name σ is forced to have certain property φ, then there ground model filter g such that σg satisfies φ. prove general correspondence connecting these forcing axioms. Special cases main theorem are: Any axiom can be expressed as principle. For instance, PFA equivalent to: A principle for rank 1 names (equivalently, nice names) subsets ω1. 2 sets reals. λ-bou...

It is proved that any countable topological group in which the filter of neighborhoods identity element not rapid contains a discrete set with precisely one nonisolated point. This gives negative answer to Protasov's question on existence ZFC nondiscrete all subsets are closed. also extremally disconnected implies ultrafilter and, hence, cannot be constructed ZFC.