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We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities,…
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We survey the current state-of-the-art about the dynamical behavior of continuous Lebesgue measure-preserving maps on one-dimensional manifolds.
We investigate topological T-duality in the framework of non-abelian gerbes and higher gauge groups. We show that this framework admits the gluing of locally defined T-duals, in situations where no globally defined ("geometric") T-duals…
This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…
This paper has been superseded by math-ph/0102032, "Bures geometry of the three-level quantum systems. II".
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
We establish the existence of models of quadric surface bundles with prescribed \'etale local forms.
This book contains the material of my research on stereotype duality theories in geometry. It was intended as a continuation of my recently published monograph in De Gruyter on stereotype spaces and algebras.
We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…
Some additional references are included on the last 3 pages.
The proposal of a project aimed on a design of hardware for programming 3D Magnetic Field shapes over sample volume in NMR and MRI is described.
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions. We generalize and extend several existing results in this area.
The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
We study the class field theory of curve defined over two dimensional local field. The approch used here is a combination of the work of Kato-Saito, and Yoshida where the base field is one dimensional
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
In this paper are constructed a series of geometrical objects on the 1-jet fibre bundle $J^1(T,M)$, which is a basic object in the study of classical and quantum field.