In 1970, E. M. Andreev published a classification of all three dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles [3]. Given a combinatorial description of a polyhedron, C, Andreev’s Theorem provides five classes of linear inequalities, depending on C, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron real...

This paper presents a fault classification method for transmission lines based on voltage phasors using classification and regression trees (CART). The proposed method is intended to aid system operators in understanding the outputs of a PMU only state estimator. Faults are classified into four categories when the estimator is positive sequence and into ten categories when the estimator is thre...

This paper deals with two new methods, based on k-NN algorithm, for fault detection and classification in distance protection. In these methods, by finding the distance between each sample and its fifth nearest neighbor in a predefault window, the fault occurrence time and the faulty phases are determined. The maximum value of the distances in case of detection and classification procedures is ...

We study spherical quadrilaterals whose angles are odd multiples of π/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are finitely many one-dimensional continuous families which we enumerate. In each family the conformal modulus is either bounded from above or bounded from below, ...

Materials and methods The formetric measurement system reconstructs human back surfaces in semi-real time. From the acquiesced 3D data a set of objective parameters can be calculated in an automatic way: We present some of the newest parameters for detection and classification of scoliosis and other severe back deformities: Symmetry and torsion of pelvis, waist, scapula and shoulders in relatio...

Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were...

Background Static radiographic angles and other clinical qualitative observations are used traditionally for classifying flatfeet. Correlation of foot shape measurements, taken from pressure footprints under dynamic conditions, with radiographic angles was preliminarily investigated in young flatfeet [1]. The aim of this study is to assess the sensitivity and specificity of existing or purposel...

Both collinear factorization theorem 1 and kT factorization theorem 2,3 are the fundamental tools of perturbative QCD (PQCD), where kT denotes parton transverse momenta. In these theorems the amplitude for an exclusive process can be calculated as an expansion of αs(Q) and Λ/Q with Q being a large momentum transfer and Λ a small hadronic scale. Similarly, in the heavy quark limit mb → ∞, mb bei...