The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup. We prove that this quas...

The problem of maximal hyperplane section of Bp(C) with p≥ 1 is considered, which is the complex version of central hyperplane section problem of Bp(R). The relation between the complex slicing problem and the complex isotropic constant of a body is established, an upper bound estimate for the volume of complex central hyperplane sections of normalized complex p(C)-balls that does not depend on...

The generalized intersection cut (GIC) paradigm is a recent framework for generating cutting planes in mixed integer programming with attractive theoretical properties. We investigate this computationally unexplored paradigm and observe that a key hyperplane activation procedure embedded in it is not computationally viable. To overcome this issue, we develop a novel replacement to this procedur...

Hyperplane fitting factor rotations perform better than conventional rotations in attaining simple structure for complex configurations. Hyperplane rotations are reviewed and then compared using familiar examples from the literature selected to vary in complexity. Included is a new method for fitting hyperplanes, hypermax, which updates the work of Horst (1941) and Derflinger and Kaiser (1989)....

Suppose ∆ is a dual polar space of rank n and H is a hyperplane of ∆. Cardinali, De Bruyn and Pasini have already shown that if n ≥ 4 and the line size is greater than or equal to four then the hyperplane complement ∆ −H is simply connected. This paper is a follow-up, where we investigate the remaining cases. We prove that the hyperplane complements are simply connected in all cases except thre...

The conventional optimal hyperplane classi er is de ned on Euclidean space where the norm is given a priori. In this paper, we propose a new optimal hyperplane classi er in which the norm also adapts for learning. For practical implementation, the norm is restricted to a weighted Euclidean norm and the weights are controlled in learning. The statistical properties of this classi er is analyzed ...

In this article we exhibit certain projective degenerations of smoothK surfaces of degree g in P whose Picard group is generated by the hyperplane class to a union of two rational normal scrolls and also to a union of planes As a consequence we prove that the general hyperplane section of such K surfaces has a corank one Gaussian map if g or g We also prove that the general such hyperplane sect...

Suppose ∆ is a dual polar space of rank n and H is a hyperplane of ∆. Cardinali, De Bruyn and Pasini have already shown that if n ≥ 4 and the line size is greater than or equal to four then the hyperplane complement ∆ − H is simply connected. Shpectorov proved a similar result for n ≥ 3 and line size five and above. We will prove a similar result for n ≥ 5 and line size three and above. We also...