Related papers: Euclid's Algorithm in quartic CM-fields

Leech's (co)homology groups of finite cyclic monoids are computed.

We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…

Let $K$ be a number field and $\mathfrak{p} \mid (2)$ be a prime ideal. We compute the fourth level of the $\mathfrak{p}$-adic completions of $K$ when the ramification index is $4$ and the inertial degree is trivial for the ideal…

In this paper we develop algorithms of finding homogeneous spaces of semisimple non-compact Lie groups which do not admit compact Clifford-Klein forms. We propose a computer program which checks if the given homogeneous space has a…

We introduce the simplest minimal subtraction method for massive $\lambda \phi^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the…

In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.

Minimal obstructions for embedding 4-regular Eulerian digraphs on the plane are considered in relation to the partial order defined by the cycle removal operation. Their basic properties are provided and all obstructions with parallel arcs…

Let k be an imaginary quadratic number field (with class number 1). We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant…

In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile…

Given a finitely presented Graded Commutative Differential Algebra (GCDA), we present a method to compute its minimal model, together with a map that is a quasi-isomorphism up to a given degree. The method works by adding generators one by…

The complexes of integral forms on the quantum Euclidean group $E_q(2)$ and the quantum plane are defined and their isomorphisms with the corresponding de Rham complexes are established.

We construct an algorithm for the minimal model program in dimension three over the field of algebraic numbers. As auxiliary results, we also construct algorithms for computing bigraded global Hom modules and for computing Stein…

We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory…

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational B\'ezier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using…

In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.

In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal…

This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of…

In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but…

In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from…