Related papers: Fano's inequality is a mistake
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points…
Asymmetric Fano line profiles are frequently encountered, e.g., in the photoionization spectra of atoms and ions. For the fitting of spectral line profiles to experimental spectra the line profiles have to be convolved with the experimental…
We announce a factorization result for equivariant birational morphisms between toric 4-folds whose source is Fano: such a morphism is always a composite of blow-ups along smooth invariant centers. Moreover, we show with a counterexample…
Consider an algebraically closed field k and the Cremona group of all birational transformations of the projective plane over k. We characterize infinite order elements of this group having a non-zero power generating a proper normal…
It is proved that, up to isomorphism, there are only two directed trees that admit a hyponormal weighted shift with nonzero weights whose square has trivial domain. These are precisely those enumerable directed trees, one with root, the…
We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…
Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several known et new results concerning the anti-canonically polar…
We prove that the deformations of a smooth complex Fano threefold X with Picard number 1, index 1, and degree 10, are unobstructed. The differential of the period map has two-dimensional kernel. We construct two two-dimensional components…
The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensional linear space is extended to conditional expectations and…
We construct an analytic norm-increasing $3$-isometric weighted shift on a rootless directed tree, which does not have the wandering subspace property. This answers a question of Shimorin [S2001, p. 185] in the negative. The counterexample…
We prove that a smooth projective variety $X$ of dimension $n$ with strictly nef third, fourth or $(n-1)$-th exterior power of the tangent bundle is a Fano variety. Moreover, in the first two cases, we provide a classification for $X$ under…
Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004)…
In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality.
Weak measurement enables faithful amplification and high precision measurement of small physical parameters and is under intensive investigation as an effective tool in metrology and for addressing foundational questions in quantum…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
We introduce some invariants of Fano varieties and propose a Mukai-type conjecture which characterizes the product of projective spaces. Moreover, we prove that the Ambro--Kawamata effective non-vanishing conjecture implies the Mukai-type…
Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\geq0$, the inequality of Fano type with $q$-entropic functionals…
We model the nonlinear growth of cosmic structure in different dark energy models, using large volume N-body simulations. We consider a range of quintessence models which feature both rapidly and slowly varying dark energy equations of…
We develop technical tools that enable the use of Bellman functions for BMO defined on $\alpha$-trees, which are structures that generalize dyadic lattices. As applications, we prove the integral John--Nirenberg inequality and an inequality…
A reverse H\"older inequality is established on the space of K\"ahler metrics in the first Chern class of a Fano manifold X endowed with Darvas L^{p}-Finsler metrics. The inequality holds under a uniform bound on a twisted Ricci potential…