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The spectral-angular and angular distributions of parametric X-radiation for case of backward diffraction (particular case of Bragg geometry scheme) is discussed. It is shown that in case of Bragg geometry it is necessary to use dynamical…
In this paper, we investigate certain graded-commutative rings which are related to the reciprocal plane compactification of the coordinate ring of a complement of a hyperplane arrangement. We give a presentation of these rings by…
This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical…
We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…
We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective…
We propose an application of the Angular X-ray Cross-Correlation Analysis (AXCCA) to the scattered intensity distribution measured in three-dimensional (3D) reciprocal space from a single crystalline sample. Contrary to the conventional…
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…
On the base of the distinction between covariant and contravariant metric tensor components, a new (multivariable) cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian has been derived and parametrized…
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of…
We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and…
The Laplace equation in the two-dimensional Euclidean plane is considered in the context of the inverse stereographic projection. The Lie algebra of the conformal group as the symmetry group of the Laplace equation can be represented solely…
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…
A class of Cantor-type spaces and related geometric structures are discussed.
We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel.…
In this paper we embed $m$-dimensional Euclidean space in the geometric algebra $Cl_m $ to extend the operators of incidence in ${R^m}$ to operators of incidence in the geometric algebra to generalize the notion of separator to a decision…
We extend the notion of triangle to "imaginary triangles" with complex valued sides and angles, and parametrize families of such triangles by plane algebraic curves. We study in detail families of triangles with two commensurable angles,…
These notes combine results from two papers by the present authors viz., Part I (arXiv:2205.10299) and Part II (arXiv:2212.13028) into one streamlined version for better readability, along with a review on theory of complex multiplication…
The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…
We investigate the distributional extension of the $k$-plane transform in $\mathbb{R}^d$ and of related operators. We parameterize the $k$-plane domain as the Cartesian product of the Stiefel manifold of orthonormal $k$-frames in…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…