<span>This paper defined a new type of topology known as Interior topology. This work falls among the types (such general topology, supra generalized and filter) that are motivated by real-world concepts such orbits planets around sun, electron nucleus, so on. form is self-contained. The primary objective this study to respond question “Is capable producing topology?”. Finally, we define ...

This paper proposes Principal Component Analysis (PCA) to find adaptive bases for multiresolution. An input image is decomposed into components (compressed images) which are uncorrelated and have maximum l2 energy. With only minor modification, a single layer linear network using the Generalized Hebbian Algorithm (GHA) is used for multiresolution PCA. The decomposition has been successfully app...

This paper applies the newly developed methodology of Bai and Ng (2002, 2003), providing the decomposition of large panel data into systematic and idiosyncratic components, to both returns and turnover. When combined with a GLS-based principal components approach, we demonstrate their procedure works well for both returns and turnover, despite the presence of severe heteroscedasticity and non-s...

Individuals with generalized anxiety disorder (GAD) display poor emotional conflict adaptation, a cognitive control process requiring the adjustment of performance based on previous-trial conflict. It is unclear whether GAD-related conflict adaptation difficulties are present during tasks without emotionally-salient stimuli. We examined conflict adaptation using the N2 component of the event-re...

Based on the theory of Fermat reals we introduce new topologies on spaces of Colombeau generalized points and derive some of their fundamental properties. In particular, we obtain metric topologies on the space of near-standard generalized points that induce the standard Euclidean topology on the reals. We also give a new description of the sharp topology in terms of the natural extension of th...

Abstract In this paper, interesting properties of the generalized topological spaces, generated by monotonic maps $$\sigma = (cl_{\delta }\circ int_{\delta }),$$ σ = ( c l δ ∘ i<...

Let (X, d) a metric space and BX = X × R denote the partially ordered set of (generalized) formal balls in X. We investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X, d) is a totally bounded metric space, and show examples of spaces for which the ...