This report records a large number of open problems in Affine Algebraic Geometry that were proposed by participants in a Conference on Open Algebraic Varieties at the Centre de Recherches en Mathematiques in Montreal at December 1994....
Historically, investigations on gust encounters have been limited to thin airfoils. In this work, we examine vortex-gust encounters by a family of airfoils at a chord-based Reynolds number Re_c=100, which includes variations in the gust ratio, initia...
Geode is the most popular GD mod loader across all platforms. With an active community of both users and modders, nearly every mod you can imagine has been made or suggested! Geode is open …
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger r...
We show how well known tools of algebraic geometry for the study of finite sets can be fruitfully applied to the study of Waring decompositions of symmetric tensors (forms). We mainly focus on the uniqueness of a given decomposition (the identifiabil...
We present a slowly rotating generalization of a black hole modeled by a Solv horizon geometry, in five dimensional General Relativity. A separable ansatz compatible with Einstein equations is proposed, which is integrated in terms of hypergeometric...
Purpose: Radiotherapy presents unique challenges and clinical requirements for longitudinal tumor and organ-at-risk (OAR) prediction during treatment. The challenges include tumor inflammation/edema and radiation-induced changes in organ geometry, wh...
Extending the usual $\mathbf{C}^{\ast r}$ actions of toric manifolds by allowing asymmetries between the various $\mathbf{C}^{\ast}$ factors, we build a class of non commutative (NC) toric varieties $\mathcal{V}%_{d+1}^{(nc)}$. We construct NC comp...
Using the algebraic geometry method of Berenstein and Leigh (BL), hep-th/0009209 and hep-th/0105229), and considering singular toric varieties ${\cal V}_{d+1}$ with NC irrational torus fibration, we construct NC extensions ${\cal M}_{d}^{(nc)}$ of...
This is one of Petrobras' open repositories on GitHub. It contains the WPRAutoencoders project which encompasses a wellbore pressure response generator, a dataset of 20.000 synthetic pressure responses and an autoencoder neural network capable of clustering this data based on tra…
In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters. However, appr...
This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation theorie...
Code for HodgeNet: Learning Spectral Geometry on Triangle Meshes, in SIGGRAPH 2021. (⭐ 85)
Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we extend FCT by a...
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical
A mistake is pointed out in EGA I, Elements of algebraic geometry, concerning corollary (2.4.4) which is not correct. Quite likely, the hitch has already been noticed, and reported, but we know not who, nor where. New research is recommended to find...
Generating realistic 3D point clouds is a fundamental problem in computer vision with applications in remote sensing, robotics, and digital object modeling. Existing generative approaches primarily capture geometry, and when semantics are considered,...
Based on the compatible pair theory of principal bundle constraint systems, this paper discovers and establishes a complete Spencer differential degeneration theory. We prove that when symmetric tensors satisfy a $λ$-dependent kernel condition $δ_{...
This paper proposes a new theoretical perspective for studying the Hodge conjecture through an analytical framework based on constraint geometry. Our theory begins with a key observation: in compatible pair Spencer theory, a "differential degeneratio...