A new family of distance-regular graphs is constructed. They are antipodal 2 -fold covers of the complete graph on 2 vertices. The automorphism groups are determined, and the extended Preparata codes are reconstructed using walks on these graphs. There are connections to other interesting structures: the graphs are equivalent to certain generalized Hadamard matrices; and their underlying 3-clas...

A new family of distance-regular graphs is constructed. They are antipodal 22t−1-fold covers of the complete graph on 22t vertices. The automorphism groups are determined, and the extended Preparata codes are reconstructed using walks on these graphs. There are connections to other interesting structures: the graphs are equivalent to certain generalized Hadamard matrices; and their underlying 3...

We search for an abelian description of the Yang-Mills instantons on certain eight dimensioanl manifolds with the special holonomies Spin(7) and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of monopole-like equations governing the 8-dimensional U(1) connections and spinors, which are supposed to be the dual theory of the nonabelian instantons. We also give a...

Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint a...

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold giv...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

Measures of residual risk are developed as extension of measures of risk. They view a random variable of interest in concert with an auxiliary random vector that helps to manage, predict, and mitigate the risk in the original variable. Residual risk can be exemplified as a quantification of the improved situation faced by a hedging investor compared to that of a single-asset investor, but the n...