This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions transitivity, point pairwise iterated compactness, weakly etc. are introduced. Later, it is shown that under homeomorphism, transitivity implies transitivity. Moreover, homeomorphism; compactness and found to be equivalent. we apply our results in the development process a human embryo from zygote until bi...

We find upper bounds for the spherical cap discrepancy of set minimizers Riesz s-energy on sphere $$\mathbb S^d.$$ Our results are based a Sobolev introduced by Thomas Wolff in an unpublished manuscript where estimates logarithmic energy S^2$$ were obtained. result improves previously known $$0\le s<2$$ and $$s\ne 1$$ S^2,$$ $$s=0$$ is Wolff’s result, $$d-t_0<s<d$$ with $$t_0\approx 2.5$$ when ...

The aim of this paper is to introduce a new class of sets called (i,j) r^g closed sets and a new class of maps called D^(i,j) continuous maps and D^(i,j)irresolute maps in bitopological spaces. Also we introduce some new spaces called (i,j) – T^1/2 , (i,j) ^T 1/2 ,*T^1/2, ^T*1/2 and ^Trg and obtain their basic properties. Mathematics Subject Classification: 54A10

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density toplologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on in…nitary combinatorics due to Kestelman and to Borwein and Ditor. As a by-product we give a uni…ed proof of the measure and category cases of Unif...

We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of ”quantum differential forms” as a projective module in the spirit of the Serre-Swan approach. Also, we use ”braided tangent vector fields” which are q-analogs of Poisson vector fields asso...