The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1, . . . , fn be homogeneous sparse polynomials in the variables y1, . . . , yn and g1, . . . , gn be homogeneous sparse polynomials in the variables x1, . . . , xn. Let fi ◦ (g1, . . . , gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj . Naturally a quest...

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

A very well–covered graph is an unmixed without isolated vertices such that the height of its edge ideal half number vertices. We study these graphs by means Betti splittings and mapping cone constructions. show cover ideals Cohen–Macaulay are splittable. As a consequence, we compute explicitly minimal graded free resolution class prove have homological linear quotients. Finally, conjecture sam...

For an arbitrary curve Z ⊂ P (possibly reducible, non-reduced, unmixed) lying on a normal surface, the general surface S of high degree containing Z is also normal, but often singular. We compute the class groups of the very general such surface, thereby extending the Noether-Lefschetz theorem (the special case when Z is empty). Our method is an adaptation of Griffiths and Harris’ degeneration ...

We discuss whether the NuTeV anomaly can be explained, compatibly with all other data, by QCD effects (maybe, if the strange sea is asymmetric, or there is a tiny violation of isospin), new physics in propagators or couplings of the vector bosons (not really), loops of supersymmetric particles (no), dimension six operators (yes, for one specific SU(2)L-invariant operator), leptoquarks (not in a...

The chemical composition of core-shell nanoparticle clusters have been determined through principal component analysis (PCA) and independent component analysis (ICA) of an energy-dispersive X-ray (EDX) spectrum image (SI) acquired in a scanning transmission electron microscope (STEM). The method blindly decomposes the SI into three components, which are found to accurately represent the isolate...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and im...