Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable po...

Let Ω ⊂ R be a bounded Lipschitz domain and consider the Dirichlet energy functional F[u,Ω] := 1 2 Z

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...

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.

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, show that if B:L?0(G)*x L?0(G)* is asymmetric bi-derivation such [B(m,m),mk] Z(L?0(G)*) for all m (G)*, then B the zero map. Furthermore, characterize generalized biderivations group algebras. We also prove any Jordan 0(G)* a bi-derivation.

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.