We call these geometries bi-affine geometries. They are of two types, according to whether the point and the hyperplane chosen are incident or not. We also prove that there are just three types of flag-transitive simply connected examples for the rank 4 case of the above diagram, namely ...
Full abstract relation extraction from biological texts with bi-affine relation attention networks - patverga/bran
In particular, all Lie bialgebra structures on $\\widetilde{sl_2(\\mathbb{C}_q)}$ are shown to be triangular coboundary. This result is obtained by employing some techniques, which may also work for more general extended affine Lie algebras, to prove the triviality of the first ...
We show that the affine quantum group \\({ext{U}}_q (\\widehat{{ext{sl}}}_{ext{2}} )\\) is isomorphic to a bicross-product central extension \\(\\mathbb{C}\\mathbb{Z}_\\chi \\blacktriangleright riangleleft {ext{U}}_q (L{ext{sl}}_2 )\\) of the quantum loop group...
The topological invariants of spaces of bipolynomials without multiple roots are connected with characteristic classes of rational functions with two poles and generalized braid groups associated to extended affine Weyl groups of the serie A. We prove that the cohomology rings of the spaces of bi...
2) affine linearity 仿射线性3) affine nonlinear 仿射非线性 1. The nonlinear state-feedback decoupling control law for affine nonlinear systems is discussed. 讨论了仿射非线性系统的非线性状态反馈解耦控制律的更一般形式,提出并证明了当系统的相对阶次之和小于系统维数时,非线性闭环解耦系统实现线性化并...
Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps DOI: 10.1016/j.aim.2015.02.008 Jonas Azzam,Matthew Badger,Tatiana Toro Full-Text Cite this paper Add to My Lib Abstract: A quasiplane $f(V)$ is the image of an $n$-dimensional Euclidean subspace $V$ of...
The paper concerns fractal homeomorphism between the attractors of two bi-affine iterated function systems. After a general discussion of bi-affine functions, conditions are provided under which a bi-affine iterated function system is contractive, thus guaranteeing an attractor. After a general ...
After a general discussion of bi-affine\nfunctions, conditions are provided under which a bi-affine iterated function\nsystem is contractive, thus guaranteeing an attractor. After a general\ndiscussion of fractal homeomorphism, fractal homeomorphisms are constructed for\na specific type of bi-affine ...
Bi-affine modelArray perturbationsSparse source localizationNon-uniform spatial sampling geometries, such as nested and coprime arrays, are provably capable of localizing O (M-2) sources using only M sensors. However, such guarantees require the physical locations of the sensors to satisfy certain ...