Related papers: Automated Proofs in Geometry : Computing Upper Bou…
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a…
We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…
We proposed an algorithm that covers some cases of Hamilton Circuit Problem.
We describe an algorithm for listing all elements of bounded height in a given number field.
This paper explores the application of Hurlbert's Linear Optimization Technique to determine bounds on pebbling numbers. By applying Hurlbert's weight functions and optimization methods, we derive upper bounds for specific graph families.…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to…
We investigate an overdetermined Torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problems, we prove existence and…
We develop a method for proving sup-norm and H\"older estimates for $\overline{\partial}$ on wide class of finite type pseudoconvex domains in $\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of…
We study the problem of finding maximum-area triangles that can be inscribed in a polygon in the plane. We consider eight versions of the problem: we use either convex polygons or simple polygons as the container; we require the triangles…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In…
We show that any two geometric triangulations of a closed hyperbolic, spherical or Euclidean manifold are related by a sequence of Pachner moves and barycentric subdivisions of bounded length. This bound is in terms of the dimension of the…