Related papers: The generalized e-bundle
We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\cite{Zh}: every diffeomorphism with nontrivial global generalized…
Given a principal fibre bundle with structure group $S$, and a fibre transitive Lie group $G$ of automorphisms thereon, Wang's theorem identifies the invariant connections with certain linear maps $\psi\colon \mathfrak{g}\rightarrow…
Despite all its well-known flaws and calls for its dismissal, the notorious $h$-index is still used in many instances when awarding grants, or promoting and hiring scientists. To address this, I set out to devise a better index, with the…
The definition of the g-index is as arbitrary as that of the h-index, because the threshold number g^2 of citations to the g most cited papers can be modified by a prefactor at one's discretion, thus taking into account more or less of the…
An attempt is made to construct composable composite entropy with different $q$ indices of subsystems and address the H-theorem problem of the composite system. Though the H-theorem does not hold in general situations, it is shown that some…
Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…
We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any…
We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…
In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the…
A new definition for the notion of a (general) $\infty$-category is given.
We prove that the gcd of certain infinite number of integers associated to generalised arithmetic progressions remains bounded independent of the progression. Using this we also get bounds on the indices of certain congruence subgroups of…
We consider integrable deformations of the XXZ spin chain for periodic and open boundary conditions. In particular, we classify all long-range deformations and study their impact on the spectrum. As compared to the XXX case, we have the…
When evaluating the lengthy inclusion-exclusion expansion many of its terms may turn out to be zero, and hence should be discarded beforehand. Often this can be done. The main idea is that the index sets of nonzero terms constitute a set…
For a category with subobjects and factorization, here we describe a new category which we call category of chain bundles and it is shown that this new category is also a category with subobjects and admits factorization under certain…
We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished…
To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we assign algebras called braided non-commutative spheres. For any such algebra, we introduce and compute a q-analog of the Chern-Connes index. Unlike the standard…
If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…
The main goal of this article is to introduce the concept of $EM-G-$graded rings. This concept is an extension of the notion of $EM-$rings. Let $G$ be a group and $R$ be a $G-$graded commutative ring. The $G-$gradation of $R$ can be…
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative…