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Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin$^c$…
We prove that only finitely many Shimura curves can have gonality bounded by a given number, and we study the computability of this finite set. Motivated by the relation between hyperellipticity (that is, gonality 2) and the vanishing of…
Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive. The cost increases even more if multiple simulations are needed to account for the randomness in…
The Bounded Negativity Conjecture predicts that for every complex projective surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have been…
Sharp features such as edges and corners play an important role in the perception of 3D models. In order to capture them better, we propose quadric loss, a point-surface loss function, which minimizes the quadric error between the…
We establish an arithmetic intersection theory in the framework of Arakelov geometry over adelic curves. To each projective scheme over an adelic curve, we associate a multi-homogenous form on the group of adelic Cartier divisors, which can…
To each local field (including the real or complex numbers) we associate a quantum dilogarithm and show that it satisfies a pentagon identity and some symmetries. Using an angled version of these quantum dilogarithms, we construct three…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
For cubic pencils we define the notion of an involution curve. This is a curve which intersects each curve of the pencil in exactly one non-base point of the pencil. Involution curves can be used to construct integrable maps of the plane…
Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree $d\ge 2$, we provide lower bounds for the following four numerical invariants:…
The influence of atmospheric turbulence on acquired imagery makes image interpretation and scene analysis extremely difficult and reduces the effectiveness of conventional approaches for classifying and tracking objects of interest in the…
We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…
We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…
In the context of numerical simulations of the vascular system, local geometric uncertainties have not yet been examined in sufficient detail due to model complexity and the associated large numerical effort. Such uncertainties are related…
In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.