Related papers: Computing Moment Maps of Hypersurfaces using MAXIM…
We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…
In this paper, we study the asymptotic Plateau problem in hyperbolic space for constant sum Hessian curvature. More precisely, given a asymptotic boundary $\Gamma$, one seeks a complete hypersurface $\Sigma$ in $\mathbb{H}^{n+1}$ satisfying…
A modeling of circular cylindrical metasurfaces using Method of Moments (MoM) based on Generalized Sheet Transition Conditions (GSTCs) is presented. GSTCs are used to link the integral equations for fields on the inner and outer contour of…
In this paper we establish the optimal multilinear restriction estimate for n-1 hypersurfaces with some curvature, where $n$ is the dimension of the underlying space. The result is sharp up to the endpoint and the role of curvature is made…
In this paper we find an algorithm which computes the Hilbert function of schemes $Z$ of "fat points" in $\PP3$ whose support lies on a rational normal cubic curve $C$. The algorithm shows that the maximality of the Hilbert function in…
We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(\log\log n)$.…
We consider homomorphisms of hermitian holomorphic Hilbert bundles. Assuming the homomorphism decreases curvature, we prove that its pointwise norm is plurisubharmonic.
We provide an algebraic setting for cumulants and factorial moments through the classical umbral calculus. Main tools are the compositional inverse of the unity umbra, connected with the logarithmic power series, and a new umbra here…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
In this paper, we study hypersurfaces in Lorentz-Minkowski space $\mathbb{L}^{n+1}$ that are stationary for the moment of inertia with respect to the origin. After giving examples and applications of the maximum principle, we classify, in…
Given a smooth curve $\gamma$ in some $m$-dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat…
We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form $4m^2 5^n-1$. We provide an algorithm capable of proving the primality or compositeness of most…
We compute the minimum number of critical points of a small codimension smooth map between two manifolds. We give as well some partial results for the case of higher codimension when the manifolds are spheres.
We give some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them. We then illustrate these methods by working out several examples in varying degrees of detail. For instance, we…
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose…
The aim of the paper is to show algorithms for geometrical manipulations on NURBS surfaces. These include generating NURBS surfaces that pass through given points, calculating the minimum distance to a point and include line to surface and…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
This paper is a continuation of our earlier work \cite{NRxx} in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave…