相关论文: Computing multi-point Seshadri constants on P2
Let $L$ be a nef line bundle on a smooth complex projective variety $X$ of dimension $n$. Demailly has introduced a very interesting invariant --- the Seshadri constant $\epsilon(L,x)$ --- which in effect measures how positive $L$ is…
Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in…
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase…
The main result provides an algorithm for determining the minimal free resolution of ideals of fat point subschemes of ${\bf P}^2$ involving up to 8 general points with arbitrary multiplicities; the results hold over algebraically closed…
We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor computing the minimal log discrepancy computes no log…
A method for extracting the Levy stability index $\mu$ from the multi-fractal spectrum $f(\alpha)$ in high energy multiparticle production is proposed. This index is an important parameter, characterizing the non-linear behaviour of…
We define Seshadri constants for Higgs bundles on smooth projective varieties over algebraically closed fields of characteristic zero. This definition is inspired by and analogous to the notion of Seshadri constants for ordinary vector…
We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained…
We will show that for any $n\ge N$ points on the $N$-dimensional sphere $S^N$ there is a closed hemisphere which contains at least $\lfloor\frac{n+N+1}{2}\rfloor$ of these points. This bound is sharp and we will calculate the amount of sets…
A characterization of nef and good divisors is given: a divisor D on a smooth complex projective variety is nef and good if and only if the asymptotic multiplier ideals of sufficiently high multiples of e(D) D$ are trivial, where e(D)…
We study stable blow-up dynamics in the $L^2$-supercritical nonlinear Schr\"{o}dinger equation in various dimensions. We first investigate the profile equation and extend the result of X.-P. Wang [38] and Budd et al. [4] on the existence…
We analyze the point decomposition problem (PDP) in binary elliptic curves. It is known that PDP in an elliptic curve group can be reduced to solving a particular system of multivariate non-linear system of equations derived from the so…
We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of $\mathbb{P}^3$ outside certain planes using universal torsors.
We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross-Pitaevskii theory. Our primary focus is on a two-dimensional system with a non-local soft-core interaction, where the…
Let $E$ be a vector bundle of rank $n$ on $\mathbb{P}^1$. Fix a positive integer $d$. Let $\mathcal{Q}(E,d)$ denote the Quot scheme of torsion quotients of $E$ of degree $d$ and let $Gr(E,d)$ denote the Grassmann bundle that parametrizes…
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for…
We complete the explicit study of a three-fold divisorial contraction whose exceptional divisor contracts to a point, by treating the case where the point downstairs is a singularity of index $n \ge 2$. We prove that if this singularity is…