We study the growth at the golden rotation number ω = ( √ 5 − 1)/2 of the function sequence Pn(ω) = ∏n r=1 |2 sinπrω|. This sequence has been variously studied elsewhere as a skew product of sines, Birkho sum, q-Pochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence Pn, namely the sub-sequence Qn = ∣∣∣∏Fn r=1 2 sinπ...

We consider a twisted quantum wave guide i.e. a domain of the form Ωθ := rθω × R where ω is a connected open and bounded subset of R2 and rθ = rθ(x3) is a rotation by the angle θ(x3) depending on the longitudinal variable x3. We are interested in the spectral analysis of the Dirichlet Laplacian H acting in Ωθ. We suppose that the derivative θ̇ of the rotation angle can be written as θ̇(x3) = β − ...

We generalize a criterion of Yakubovich for the absolute stability of control processes with periodic coefficients to the case when the coefficients are bounded and uniformly continuous functions. 1. Introduction. In the past two decades, the study of differential equations with time-varying coefficients (nonautonomous differential equations) has benefited from the use of methods of the ergodic...

In previous works we combined feature-based techniques and optical flow methods to obtain depth or motion. The expressions relating the brightness constraint to the 3D localization and motion of a line and its projection were established. In this paper, those expressions have been used to obtain the motion direction of a camera when the rotation velocity is bounded, without assumptions about th...

In this paper, we present a novel method to address the trajectory problem in 2D shape morphing based on the Laplacian coordinates (LCs). Although the LCs capture the geometric details of a shape, they are built in the global coordinate system and thus not rotation invariant [1, 7]. By adding rotation coherence constraints to as-rigid-as-possible transformations applied on the LCs, we make the ...

For a compact spacelike constant mean curvature surface with nonempty boundary in the threedimensional Lorentz–Minkowski space, we introduce a rotation index of the lines of curvature at the boundary umbilical point, which was developed by Choe [‘Sufficient conditions for constant mean curvature surfaces to be round’, Math. Ann. 323(1) (2002), 143–156]. Using the concept of the rotation index a...

We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are un-coupled from updates, their total number is bounded by O(M log(M +N)), where M is the number of updates to an AVL tree of initial size N. Hence, relaxed balancing of AVL trees come...

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift f̃ to the infinite strip à which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set B− ⊂ à such that B− is bounded to the right, the projection of B− to A is dense, ...

The effects of confinement on the dynamics of binary encounters between spherical particles in shear flow are studied for a system bounded by a single planar wall or two parallel planar walls under creeping flow conditions. We show that wall proximity gives rise to a new class of binary trajectories resulting in cross-streamline migration of the particles. In contrast, in unbounded space spheri...

A common approach to the image matching problem is representing images as sets of features in some feature space followed by establishing correspondences among the features. Previous work by Huttenlocher and Ullman [1] shows how a similarity transformation rotation, translation, and scaling between two images may be determined assuming that three corresponding image points are known. While robu...