We show that there exists a C∞ volume preserving diffeomorphism P of a compact smooth Riemannian manifold M of dimension 4, which is close to the identity map and has nonzero Lyapunov exponents on an open and dense subset G of not full measure and has zero Lyapunov exponent on the complement of G. Moreover, P |G has countably many disjoint open ergodic components.

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

We consider area–preserving diffeomorphisms on tori with zero entropy. We classify ergodic area–preserving diffeomorphisms of the 3–torus for which the sequence {Df}n∈N has polynomial growth. Roughly speaking, the main theorem says that every ergodic area–preserving C2–diffeomorphism with polynomial uniform growth of the derivative is C2–conjugate to a 2–steps skew product of the form T ∋ (x1, ...

We show that any finite system S in a characteristic zero integral domain can be mapped to Z/pZ, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the well-known Freiman isomorphism lemma, which asserts that any finite subset of a torsion-free group can be mapped into Z/pZ, preserving all linear incidences. As applications, we derive...

Using the Perron-Frobenius operator we establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give an extensive specific example using the tent map.

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...

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 ...