Related papers: Numerical computation of H-bases
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface…
The stability of the Standard Model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It…
We study the stable hyperelliptic locus, i.e. the closure, in the Deligne- Mumford moduli space of stable curves, of the locus of smooth hyperelliptic curves. Working on a suitable blowup of the relative Hilbert scheme (of degree 2)…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up…
We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…
We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a hypergeometric…
Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…
This paper examines the robust (strong) H-infinity norm of a linear time-invariant system with discrete delays. The considered system is subject to real-valued, structured, Frobenius norm bounded uncertainties on the coefficient matrices.…
We prove a H\"{o}lder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function $v$ on $\mathbb{R}^d$ from its Fourier transform $\mathcal{F} v$ given on $[-r,r]^d$. This estimate relies…
We show how to adapt the quasi-Newton method to the electronic-structure calculations using systematic basis sets. Our implementation requires less iterations than the conjugate gradient method, while the computational cost per iteration is…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
A_k = {1, a_2, ... a_k} is an h-basis for X if every positive integer not exceeding X can be expressed as the sum of no more than h values a_i; X(h) is called the h-range of the basis. h_0 is the smallest value of h for which X(h) is…
We report on the results of a computer search for primes $p$ which divide an Harmonic number $H_{\lfloor p/N \rfloor}$ with small $N > 1$.
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime $p$ by revisiting the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on…
We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice…
We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.