A Generalized Integral Manifold Theorem

Generalized Integral Siding Mode Manifold Design: A Sum of Squares Approach

—this paper presents a new forum an integral sliding mode manifold named as a general forum, and then proposes an algorithmic approach based on sum of squares (SOS) programming, to design a generalized integral sliding mode manifold and controller for nonlinear systems with both matched and unmatched uncertainty. The method gives sufficient conditions to obtain a solution for designing the cont...

A Fixed Point Theorem in Generalized D-metric Spaces

Generalized Unsupervised Manifold Alignment

In this paper, we propose a Generalized Unsupervised Manifold Alignment (GUMA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserv...

A Generalized Cantor Theorem

A well known theorem of Cantor asserts that the cardinal of the power-set of a given set always exceeds the cardinal of the original set. An analogous result for sets having additional structure is the well known theorem that the set of initial segments of a well ordered set always has order type greater than the original set. These two theorems suggest that there should be a similar result for...

A Generalized Winternitz Theorem

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ∈ P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P . We also give a family of examples showing that this result is the best possible. Mathematics Subject Classification (2010). 51E99.