In this paper, a novel training method is proposed to increase the classification efficiency of support vector machine (SVM). The efficiency of the SVM is determined by the number of support vectors, which is usually large for representing a highly convoluted separation hypersurface. We noted that the separation hypersurface is made unnecessarily over-convoluted around extreme outliers, which d...

Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface, and also define a functor to the stable module category of maximal Cohen-Macaulay modules on the hypersurface. We introduce a new functorial concept of matrix factorizations for complete intersections that allows us to describe the asymptotic structure of mi...

D.E . BARRETT AND J . E . FORNAESS We study the regularity of the induced foliation of a Levi-flat hypersurface in C'° , showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question .

When n satisfies an inequality which is almost best possible, we prove that the k-plane sections of every smooth, degree d, complex hypersurface in Pn dominate the moduli space of degree d hypersurfaces in Pk. As a corollary we prove that, for n sufficiently large, every smooth, degree d hypersurface in Pn satisfies a version of “rational simple connectedness”. 1. Statement of results In their ...

This note is an extension of the paper [HMP]. The main theorem of [HMP] states that a relatively smooth hypersurface (i.e. a hypersurface whose singular locus has sufficient large codimension with respect to its degree) is unirational. A mild modification can generalize this to complete intersections. As an application, we will show the Fano variety of a relatively smooth hypersurface is also u...

In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse; in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semiRiemannian Banach space is an essen...

Viro method plays an important role in the study of topology of real algebraic hypersurfaces. The T -primitive hypersurfaces we study here appear as the result of Viro’s combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We use th...

A real algebraic variety is maximal (with respect to the SmithThom inequality) if the sum of the Betti numbers (with Z2 coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We prove that there exist polytopes that are not Newton polytopes of any maximal hypersurface in the corresponding toric variety. On the other hand we show that for any poly...

A hypersurface of order (n+ 1)(ph − 1) in projective space of dimension n of prime characteristic p has an invariant monomial. This implies that a hypersurface of order (n+1)(ph−1)−1 determines an invariant point. A hypersurface of order d < n+ 1 in a projective space of dimension n of characteristic two has an invariant set of subspaces of dimension d− 1 determined by one linear condition on t...