This paper addresses the numerical solution of nonlinear eigenvector problems such as Gross–Pitaevskii and Kohn–Sham equation arising in computational physics chemistry. These characterize critical points energy minimization on infinite-dimensional Stiefel manifold. To efficiently compute minimizers, we propose a novel Riemannian gradient descent method induced by an energy-adaptive metric. Qua...

Planetary protection in trajectory design aims to assess the impact probability of space-mission-disposed objects based on their initial uncertain conditions, avoid contaminating other planetary environments. High-precision dynamic models and propagation methods are required reach high confidence levels small estimated probabilities. These requirements have so far confined analyses robust Monte...

Two-dimensional (2D) Stiefel-Whitney insulator (SWI), which is characterized by the second class, a new class of topological phases with zero Berry curvature. As novel state, it has been well studied in theory but seldom realized realistic materials. Here we propose that large liganded Xenes, i.e., hydrogenated and halogenated 2D group-IV honeycomb lattices, are SWIs. The nontrivial topology Xe...

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology....

Suppose that (Φ,Mn) is a smooth (Z2)-action on a closed smooth n-dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set F vanish in positive dimension. This paper shows that if dimMn > 2k dimF and each pdimensional part F p possesses the linear independence property, then (Φ,Mn) bounds equivariantly, and in particular,...

Paper published in the proceedings of the workshop " Leprobì eme de factorisation de Hur-ABSTRACT A bibliography on the Hurwitz transformations is given. We deal here, with some details, with two particular Hurwitz transformations, viz, the R 4 → R 3 Kustaanheimo-Stiefel transformation and its R 8 → R 5 compact extension. These transformations are derived in the context of Fock-Bargmann-Schwing...

The quantum algebra su q (2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of q-bosons. In connection with the quantum algebra su q (2), we discuss the q-analogues of the harmonic oscillator and the angular momentum. We also introduce q-analogues of the hydrogen atom by means of a q-deformation of the Pauli equations and of the ...

The exploitation of symmetry is a very important principle in mathematics, physics and engineering sciences. The aim of the SYMMETRY package is to give an easy access to the underlying theory of linear representations for small groups. For example the dihedral groups D3, D4, D5, D6 are included. For an introduction to the theory see Serre [3] or Stiefel and Fässler [4]. For a given orthogonal (...

Given a manifold M , Milnor and Stasheff studied in [1] the diagonal cohomology class u′′ ∈ Hm(M ×M ;Z/2) that describes the orientation of the tangent bundle, and is related to its Stiefel-Whitney Classes. We generalize this concept to fiber bundles M → E → N where the fiber and base are manifolds, relate it to the diagonal homology class, study the naturality of the construction, give further...