Almost every, essentially: Given a Lebesgue measure space (X,B, μ), a property P (x) predicated of elements of X is said to hold for almost every x ∈ X, if the set X \ {x : P (x) holds} has zero measure. Two sets A,B ∈ B are essentially disjoint if μ(A ∩B) = 0. Conservative system: Is an infinite measure preserving system such that for no set A ∈ B with positive measure are A,T−1A,T−2A, . . . p...

Let n ∈ N − {1}, and let A be a Banach algebra. An additive map D : A → A is called n-Jordan derivation if D(a) = D(a)a + aD(a)a + ...+ aD(a)a+ aD(a), for all a ∈ A. Using fixed point methods, we investigate the stability of n–Jordan derivations (n–Jordan ∗−derivations) on Banach algebras (C∗−algebras). Also we show that to each approximate ∗−Jordan derivation f in a C∗− algebra there correspon...

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly differential hyperring $R$ and for any strongly differential hyperideal $I$ of $R,$ the factor hyperring $R/I$ is a strongly differential hyperring. Further we prove that a map $d: R rightarrow R$ is a derivation of a hyperring $R$ if and only if the in...

A new zero-crossing edge detection method is described. Similar to Laplace of a Gaussian (LoG) algorithm, a 7x7 point spread function (PSF) is convolved with the original image to generate a smoothed image. Instead of locating edge position from the smoothed image, as in the case of LoG, we use the smoothed image as a reference to convert the original image into a three-value edge polarity map ...

We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mixing). This is the first such result for an explicitly defined linked-twist map on a manifold other than the two-torus. Our work builds on that of Wojtkowski (1980) who established an ergodic partition for this example using an invariant cone-field...

A comparison in the context of sparse matrices is made between the Product Form of the Inverse PFI (a form of Gauss-Jordan elimination) and the Elimination Form of the Inverse EFI (a form of Gaussian elimination). The precise relation of the elements of these two forms of the inverse is given in terms of the nontrivial elements of the three matrices L, U, U~l associated with the triangular fact...

A comparison in the context of sparse matrices is made between the Product Form of the Inverse PFI (a form of Gauss-Jordan elimination) and the Elimination Form of the Inverse EFI (a form of Gaussian elimination). The precise relation of the elements of these two forms of the inverse is given in terms of the nontrivial elements of the three matrices L, U, U~l associated with the triangular fact...

We numerically reexamine the scaling behavior of period doublings in fourdimensional volume-preserving maps in order to resolve a discrepancy between numerical results on scaling of the coupling parameter and the approximate renormalization results reported by Mao and Greene [Phys. Rev. A 35, 3911 (1987)]. In order to see the fine structure of period doublings, we extend the simple one-term sca...