INTrODUCTION Recurrent neural networks whose neurons are fully interconnected have been utilized to implement associative memories and solve optimization problems. These networks are regarded as nonlinear dynamical feedback systems. Stability properties of this class of dynamical networks are an important issue from applications point of view. ABSTrACT Global stability analysis for complex-valu...

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

Belief propagation methods are powerful tools for various problems in computer vision. While most methods assume a discrete set of labels for each node in the graphical model, there has recently been an increased interest in using real-valued labels and continuous probability density functions for such problems. We propose using channel representations (soft histograms) as a new way of moving f...

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...

For a zero-dimensional topological space X and totally ordered field F with interval topology, Cc(X, F) denotes the ring consisting of field-valued continuous functions countable range on X. This article aims to study investigate rings quotients Cc(X,F). Qc(X,F) (resp. qc(X,F)), maximal classical) Cc(X,F) as modified analogue Q(X) q(X)), C(X) are characterized. It is proved that Qc(S), subring ...

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

Let C(L) be the ring of real-valued continuous functions on a frame L. In this paper, strongly fixed ideals and characterization of maximal ideals of C(L) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C(L), is st...

<p>For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on C ∗ (X, its subring bounded functions, and Σ(X, denote collection all rings that lie between C). We show there is natural correlation absolutely convex ideals/ prime ideals/maximal ideals/z-ideals/z ◦ -ideals in P(X, their real-valued counterparts ∩ C(X). These corr...