In our previous work, we have generalized the notion of dually flat or Hessian manifold to quasi-Hessian manifold; it admits metric be degenerate but possesses a particular symmetric cubic tensor (generalized Amari-Centsov tensor). Indeed, naturally appears as singular model in information geometry and related fields. A is locally accompanied with possibly multi-valued potential its dual, whose...

Using the idea of a generalized Kähler structure, we construct bihermitian metrics on CP2 and CP1×CP1, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M . We highlight the role of holomorphic Poisson structures in all these constructions.

Recent study suggests that there are natural connections between quantum information theory and the Yang–Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the generalized Bell matrix to yield all the GHZ states from the product base, prove it to form a unitary braid representation and present a new type of solution o...

The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, since they are not dual. This paper offers them attention, comming to the following conclusions: some kind of hardly describable ”local preduality” still makes pos...

In this paper, the generalized -centroidal mean and its dual form in 2 variables are introduced. Also, studied some properties and prove their monotonicity. Further, shown that various means are partic- ular cases of generalized $bf{alpha}$-centroidal mean.

In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a φ-function, the same function that is used in the definition of non-parametric φ-families. The properties of φ-functions proved to be crucial in the generalization of Rényi divergence. Assuming appropriate conditions, we verify that the general...

This paper gives max characterizations for the sum of the largest eigen-values of a symmetric matrix. The elements which achieve the maximum provide a concise characterization of the generalized gradient of the eigenvalue sum in terms of a dual matrix. The dual matrix provides the information required to either verify rst-order optimality conditions at a point or to generate a descent direction...