相关论文: The minimal log discrepancy

We introduce an approach of Riemann--Roch theorem to the boundedness problem of minimal log discrepancies in fixed dimension. After reducing it to the case of a Gorenstein terminal singularity, firstly we prove that its minimal log…

In this article left invariant measures and functionals on locally compact nonassociative fan loops are investigated. For this purpose necessary properties of topological fan loops, estimates and approximations of functions on them are…

This paper characterizes singularities with Mather minimal log discrepancies in the highest unit interval, i.e., the interval between $d-1$ and $d$, where $d$ is the dimension of the scheme. The class of these singularities coincides with…

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.

We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the…

We prove the existence of pl-flips.

In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…

Some properties of the multiway discrepanc of rectangular matrices of nonnegative entries are discussed. We are able to prove the continuity of this discrepancy, as well as some statements about the multiway discrepancy of some special…

We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.

We prove some variational analysis of regularity and weak convergence of nonlocal variational principle.

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

In this note, we will show that delta invariant of a log Fano pair can be approximated by lc places of complements of plt type if it is no greater than one. Give a log Fano pair with delta invariant no greater than one, under the assumption…

Higher-dimensional analogs of the predictable degree property and column reducedness are defined, and it is proved that the two properties are equivalent. It is shown that every multidimensional convolutional code has, what is called, a…

In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…

We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree $n$, with not necessarily independent coefficients, decays like $\sqrt{\log n/n}$. Our proofs rely on…

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…

The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal…

The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-theoretic properties, but also have numerous connections to geometry and topology. We discuss basic properties of these integer-valued invariants, as…

In topological data analysis persistence modules are used to distinguish the legitimate topological features of a finite data set from noise. Interleavings between persistence modules feature prominantly in the analysis. One can show that…

A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…