Related papers: Images of circles, lines, balls and half-planes un…
Multi-plane light conversion allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the…
This is a version of a part of the book ``Transformations of Grassman Spaces'' (in progress). We study transformations of Grassman spaces preserving certain geometrical constructions related to buildings. The next part will be devoted to…
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.
We analyze the creation of particles in two dimensions under the action of conformal transformations. We focus our attention on Mobius transformations and compare the usual approach, based on the Bogolubov coefficients, with an alternative…
We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks,…
A vexing problem involving nonassociativity is resolved, allowing a generalization of the usual complex Mobius transformations to the octonions. This is accomplished by relating the octonionic Mobius transformations to the Lorentz group in…
We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
The study of electronic transitions within a molecule connected to the absorption or emission of light is a common task in the process of the design of new materials. The transitions are complex quantum mechanical processes and a detailed…
The study of the number of photons leads to a new way of characterizing curves and to a novel integral invariant over curves.
We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
The paper investigates random fields in the ball. It studies three types of such fields: restrictions of scalar random fields in the ball to the sphere, spin, and vector random fields. The review of the existing results and new spectral…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
Context. Small bodies change their brightness due to different motives: Rotation along their axis or axes, combined with irregular shapes and/or changing surface properties, or changes in the geometry of observations. In this work, we…
Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…
We present a full geometric characterization of the $1$-dimensional (semialgebraic) images $S$ of either $n$-dimensional closed balls $\overline{\mathcal B}_n\subset{\mathbb R}^n$ or $n$-dimensional spheres ${\mathbb S}^n\subset{\mathbb…
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.