Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Zn of arbitrary order n = 2, 3, . . ., but as its symmetry group a larger group — the non-Abelian dihedral group Dn — is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our appr...

The seminal work of Eskin-Masur-Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe the principal boundary for each configuration in terms of twisted differentials over Deligne-Mumford pointed stable curves. We also describe simil...

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by mode-coupling theory. We find that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima, supportin...

The purpose of this study was to investigate the treatment effects on the maxillopalatal mandibular configuration by occipito-mental anchorage (OMA) (maxillary protraction) combined with chin cup appliance (CCA) therapy among growing children. The assessment of geometric morphometric, using Procrustes analysis, thin plate spline analysis, and growth-trended vectors, was applied and integrated t...

A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in...

In this paper, we give the algebraic conditions that a configuration of 5 points in plane must satisfy order to be zeros polynomial isochronous vector field. We use obtained results analyze configurations having some its satisfying particular geometric conditions.

This paper describes a method for qualitatively representing and reasoning about spatial configurations of planar mechanisms. The method has direct relevance to, and implications for, computer-aided mechanism design and robotics. In particular, it can be used to solve spatial configuration problems where exact geometric knowledge is not available, and to provide guidance for the application of ...

The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with specular reflections at the boundaries of the removed cylinders. It is proven here that under a certain geometric condition — slightly stronger than the necessary...

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitat...

The paper proposes a simple method to determine the 3-D location and shape parameters of a right circular cone using structured lights. A vital concept in the proposed method is to convert the complex curved stripe pattern into an equivalent, but simpler, linear stripe pattern. The conic surface patch lying between two visible silhouette edges is replaced by the plane defined by the two silhoue...