Cross fields are auxiliary in the generation of quadrangular meshes. A method to generate cross fields on surface manifolds is presented in this paper. Algebraic topology constraints on quadrangular meshes are first discussed. The duality between quadrangular meshes and cross fields is then outlined, and a generalization to cross fields of the Poincaré-Hopf theorem is proposed, which highlights...

From the first shoulder arthroscopy performed on a cadaver in 1931, shoulder arthroscopy has grown tremendously in its ability to diagnose and treat pathologic conditions about the shoulder. Despite improvements in arthroscopic techniques and instrumentation, it is only recently that arthroscopists have begun to explore precise anatomical structures within the subdeltoid space. By way of a thor...

One of the best-known and most beautiful parts of mathematics is the classification of the simple Lie groups over the complex numbers. This was achieved in the late 1880s by Wilhelm Killing, whose work was remodelled by Élie Cartan in 1894, and it is now referred to as the Killing-Cartan classification. A Lie group is called simple if it has no non-trivial, connected, normal subgroups, and the ...

According to the special requirements of Sheet Molding Compound (SMC) a set of quadrangular leveling system is designed, whose leveling precision is controlled by electro-hydraulic proportional technology. Based on analyzing the components and working principle of the quadrangular leveling system, the mathematical model of this system is established. The dynamic characteristics of stability and...

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If the adjacency matrix of a directed graph forms a pattern of a combinatorially orthogonal matrix, ...

Quadrangular resection is the gold standard technique for correction of the posterior leaflet prolapse in mitral valve disease. Prompted by the idea that the anterior leaflet of the tricuspid valve corresponds to the posterior leaflet of the mitral valve in its structure and function, we conducted a quadrangular resection of the anterior leaflet of the tricuspid valve in a case of tricuspid end...

Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of quadrangular discrete surfaces. The construction makes use of asymptotic coordi...