This paper continues the work [6]. For a Polish group G the notions of G-continuous functions and whirly actions are further exploited to show that: (i) A G-action is whirly iff it admits no nontrivial spatial factors. (ii) Every action of a Polish Lévy group is whirly. (iii) There exists a Polish monothetic group which is not Lévy but admits a whirly action. (iv) In the Polish group Aut (X,X, ...

A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Ban...

We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approxima...

Let A be a Tychonoff space. As is well known, the points of the Stone-Cech compactification ßX "are" the zero-set ultrafilters of X, and the points of the Hewitt real-compactification vX are the zero-set ultrafilters which are closed under countable intersection. It is shown here that a zeroset ultrafilter is a point of the Dieudonné topological completion SX iff the family of complementary coz...

We study several properties of a homotopy solution mapping, based on Zhang and Zhang's homotopy formulation, for continuous nonlinear complementarity problems with such non-monotone maps as quasi-monotone, E 0-, and exceptional regular functions. For these classes of complementarity problems, we establish several suucient conditions to assure the nonemptyness and boundedness of the homotopy sol...

Consider the standard, one dimensional, nonlinear filtering problem for diffusion processes observed in small additive white noise: dXt = b(Xt)dt + dBt , dY ε t = γ(Xt)dt + εdVt , where B·, V· are standard independent Brownian motions. Denote by qε 1(·) the density of the law of Ξ1 conditioned on σ(Y ε t : 0 ≤ t ≤ 1). We provide “quenched” large deviation estimates for the random family of meas...

a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

1. TJ'he first step toward connecting these two basic concepts of topology was taken by L. E. J. Brouwer in 1912 by demonstrating that two continuous mappings of a two-dimensional sphere into itself can be continuously deformed into each other if and only if they have the same degree (that is, if they are equivalent from the point of view of homology theory). After having generalized Brouwer's ...

This paper studies the mapping g → g 2 (mod p) by showing that it inherits its structure from the mapping x → x (mod ordp(g)). We first explore the context in which this mapping is important; specifically, we consider the Diffie-Hellman protocol, Diffie-Hellman problem, and the various problems that have spawned from these including the discrete logarithm and square exponent problems. We then d...