Related papers: Necessary Conditions for Schur-Positivity
The author's extensions of Brockett's and Coron's necessary conditions for stabilizability are shown to be independent in the fiber bundle picture of control, but the latter is shown to be stronger in the vector bundle picture if the state…
We provide new sufficient conditions under which Ryser's conjecture holds.
We will prove an analogue of Landau's necessary conditions [Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967).] for spaces of functions whose Hankel transform is supported in a…
In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism from Y to X where the geometry of Y is "nicer" than that of X. One version of this problem, first studied by Faltings,…
Necessary and sufficient conditions are given for the existence of extended Schmidt decompositions, with more than two subspaces.
We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…
Given a rational homogeneous manifold $S=G/P$ of Picard number one and a Schubert variety $S_0 $ of $S$, the pair $(S,S_0)$ is said to be homologically rigid if any subvariety of $S$ having the same homology class as $S_0$ must be a…
Given an element in a finite-dimensional real vector space, $V$, that is a nonnegative linear combination of basis vectors for some basis $B$, we compute the probability that it is furthermore a nonnegative linear combination of basis…
We begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s. We prove that this…
A Banach space is {\it polynomially Schur} if sequential convergence against analytic polynomials implies norm convergence. Carne, Cole and Gamelin show that a space has this property and the Dunford-Pettis property if and only if it is…
We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
In this short article we obtain some necessary conditions for a so-called fractional Hardy-Sobolev's inequalities in multidimensional case. We also give some examples to show the sharpness of these inequalities.
This work provides two sufficient conditions in terms of sections or projections for a convex body to be a polytope. These conditions are necessary as well.
We continue the study of real polynomials acting entrywise on matrices of fixed dimension to preserve positive semidefiniteness, together with the related analysis of order properties of Schur polynomials. Previous work has shown that,…
Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…
In the study of properties within one dimensional dynamics, the assumption of a negative Schwarzian derivative has been shown to be very useful. However, this condition may seem somewhat arbitrary, as it is not inherently a dynamical…
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
This article has two parts. In the first part we introduce two positivity conditions for the modified $\chi_y$-genus on almost-complex manifolds and show that each of them implies a family of optimal Chern number inequalities. It turns out…
We describe a sufficient condition for actions constructed in projective superspace to possess an SU(2) R-symmetry. We check directly that this condition implies that the corresponding hyperkahler varieties, constructed by means of the…