Related papers: A comprehensive Cartesian to geodetic coordinate t…
Spatial grounding, the process of associating natural language expressions with corresponding image regions, has rapidly advanced due to the introduction of transformer-based models, significantly enhancing multimodal representation and…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
This short survey reviews some aspects of spaces of positive-definite self-adjoint linear transformations on R^n and on C^n, including the standard Riemannian metric and the relation with the exponential mapping acting on self-adjoint…
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting…
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…
We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.
We provide an alternative, constructive proof that the collection $\mathcal{M}$ of isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance is a geodesic space. The core of our proof is a construction of explicit…
This is a topical review on the generalization of the Jordan-Wigner transformations to any spin and spatial dimensions.
A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed.
In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact and cocontact geometry, the canonoid…
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
Since their introduction by Thurston, geodesic laminations on hyperbolic surfaces occur in many contexts. In this paper, we propose a generalization of geodesic laminations on locally CAT(0), complete, geodesic metric spaces, whose boundary…
In a first course of general relativity it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it 'looks' curved. In these situations it is very useful to have…
A general introduction to lattice QCD suitable for graduate students in experimental and theoretical particle physics. Aimed at those who want to know how lattice calculations are done, and what the pitfalls are, without having to do the…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…