A new way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given in the present paper. Firstly, the proof of nonexistence of real algebras without zero divisors in all dimensions except 1,2,4 and 8 was given in [1]. It was based on the simplicial cohomology operation technique. Later on the methods of K-theory cohomology operations gave one a possibi...

I introduce a way of constructing fiber bundle whose fibers are given by hypercomplex algebras and woven appropriate structure group, present that novel gauge theory can be built on the bundle. In this work, aim to answer question about how nature selects one preferred vacuum among degenerate physical vacua, called {\it selection problem}. end, found presence impenetrable domain wall prohibits ...

Let Σg (respectively Σ/J be a closed oriented surface of genus g (respectively h), where g (respectively h) is a non-negative integer. Let Diff+Σh be the group of all orientation-preserving difϊeomorphisms of Σ/j with C°°-topology. A Σ^bundle over Σg (also called a surface bundle over a surface) is fiber bundle ξ = (£", Σg,p, Σ/^Diff+Σfr) over Σ^ with total space E, fiber Σ&, projection p : E —...

In this review we present evidence from many experimental studies which challenge the concept of predestination of His bundle fibers. Using both intra- and extracellular His bundle pacing in the context of atrio-ventricular block and the development of bundle branch blocks these experimental studies provide the underlying mechanisms for the recent clinical findings showing the benefits of perma...