Related papers: Divisors computing the minimal log discrepancy on …

For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.

We present a linear time algorithm for computing a cycle separator in a planar graph that is (arguably) simpler than previously known algorithms. Our algorithm builds on, and is somewhat similar to, previous algorithms for computing…

We deal with a divisorial contraction in dimension 3 which contracts its exceptional divisor to a smooth point. We prove that any such contraction can be obtained by a suitable weighted blow-up.

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

The logarithmic slope of diffractive structure function is a potential observable to separate the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. In this paper we extend our previous analyzes and…

I prove new local inequality for divisors on smooth surfaces, describe its applications, and compare it to a similar local inequality that is already known by experts.

$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling…

We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.

Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…

We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.

We give an explicitly computable lower bound for the arithmetic self-intersection number of the dualizing sheaf on a large class of arithmetic surfaces. If some technical conditions are satisfied, then this lower bound is positive. In…

We make a very detailed analysis of the numerical properties of effective divisors whose support is contained in the exceptional locus of a birational morphism of smooth projective surfaces. As an application we extend Miyaoka's inequality…

We prove that the first gap of $\mathbb R$-complementary thresholds of surfaces is $\frac{1}{13}$. More precisely, the largest $\mathbb R$-complementary threshold for surfaces that is strictly less than $1$ is $\frac{12}{13}$. This result…

An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error…

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…

For a prime number $p>2$, we explain the construction of the difference divisors on the unitary Rapoport-Zink spaces of hyperspecial level and the GSpin Rapoport-Zink spaces of hyperspecial level associated to a minuscule cocharacter $\mu$…

A simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal…

We study the logarithmic vector bundles associated to arrangements of smooth irreducible curves with small degree on the blow-up of the projective plane at one point. We then investigate whether they are Torelli arrangements, that is, they…

We theoretically describe the optical computation of the divergence of a two-dimensional vector field, which is composed by the transverse electric field components of an incident light beam. The divergence is computed in reflection at…

We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…