A universal lower bound for the first positive eigenvalue of the Dirac operator on a compact quaternionic Kähler manifold M of positive scalar curvature is calculated. It is shown that it is equal to the first positive eigenvalue on the quaternionic projective space. For this, the horizontal tangent bundle on the canonical SO(3)-bundle over M is equipped with a hyperkählerian structure and the ...

We address the problem of feature correspondences in images of coplanar ellipses with objective to benefit of robust ellipse fitting algorithm. The main difficulty is the lack of projective invariant points immediately available. Therefore, our key idea is to construct virtual line and point features using the property of tangent invariance under perspective projection. The proposed method requ...

We studied the eye movements of a racing driver during high-speed practice to see whether he took in visual information in a different way from a normal driver on a winding road [1, 2]. We found that, when cornering, he spent most of the time looking close to, but not exactly at, the tangent points on the inside edges of the bends. Each bend was treated slightly differently, and there was a hig...

In this paper we study the problem of shape analysis and its application in locating facial feature points on frontal faces. We propose a Bayesian inference solution based on tangent shape approximation called Bayesian Tangent Shape Model (BTSM). Similarity transform coefficients and the shape parameters in BTSM are determined through MAP estimation. Tangent shape vector is treated as the hidde...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...

Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational discretizations is often the set of configuration pairs, analogously corresponding to initial and terminal points of a tangent vector. We develop alternative discrete an...

Abstract. Continuing our work on the fundamental groups of conic-line arrangements [3], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common p...