Related papers: Artin approximation property and the General Neron…

The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.

We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the…

We derive expressions required in generalizing the Gutzwiller approximation to models comprising arbitrarily degenerate localized orbitals.

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…

Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a…

We use surface adapted ellipsoidal coordinates to obtain a first order post-Newtonian (PN) approximation to Dedekind ellipsoids with the intention of proceeding to higher orders.

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…

The paper proposes an artificial neural network (ANN) being a global approximator for a special class of functions, which are known as generalized homogeneous. The homogeneity means a symmetry of a function with respect to a group of…

The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given…

We will present the benefits of using methods of non-standard analysis in dynamic projective geometry. One major application will be the desingulariazation of geometric constructions.

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…

These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.

This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs…

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…

This paper focuses on establishing $L^2$ approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based on a decomposition theorem for convolutional kernels with a large spatial…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…