Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ‘classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets F ⊆ R...

The manifold of a planar array in a direction finding system may be considered as two families of azimuth and elevation curves, where the-parameter curves are as well as while the-parameter curves hyperhelical geodesic are. Since the-curves are not hyperhelical, their curvatures depend on and neither so analytical evaluation of curvatures of order greater than two can become exceedingly laborio...

The Perceptual Organization of Visual Flows Ohad Ben-Shahar 2003 Locally parallel dense patterns visual flows define a perceptually coherent structure of particular significance to perceptual organization. Geometrically, it is argued that a proper way to investigate these structures requires the frame field approach from differential geometry, a study that leads to the notion of visual flow cur...

Although considerable biomechanical investigations have been conducted to understand the response of the cervical spine under whiplash (rear impact-induced postero-anterior loading to the thorax), studies delineating the effects of initial spinal curvature are limited. This study advanced the hypothesis that abnormal curvatures (straight or kyphotic) of the cervical column affect spinal kinemat...

OBJECTIVE To investigate the relationship between excursion of the diaphragm muscle and spinal curvatures in mouth breathing children. METHODS A total of 52 children of both sexes, aged from 5 to 12 years, were studied. After otorhinolaryngological assessment, the children were divided into two groups: mouth breathers and nose breathers. All of the children underwent videofluoroscopic examina...

We discuss recursive formulas for Branson’s Q-curvatures. These formulas present Q-curvatures of any order on manifolds of even dimension in terms of lower order Q-curvatures and lower order GJMS-operators. They are universal in the sense that their formulation does not depend on the dimension of the underlying space. We introduce two algorithms of different nature for the computation of the co...

Objective: To determine the difference in mean corneal curvatures before and after pterygium excision, by using automated refraction and keratometry. Methodology: This quasi-experimental study was conducted at Eye Unit-I, Bahawal Victoria Hospital, Bahawalpur, from March 2010 to August 2010. Thirty patients with primary pterygium were analyzed before and after pterygium surgery for corneal curv...

The aim of this study was to compare the thoracic and lumbar curvatures and pelvic tilt in relaxed standing and maximal trunk flexion among highlytrained young athletes from three different sports disciplines. Thirty-two male canoeists, 30 male kayakers and 24 male tennis players were recruited for the study. The Spinal Mouse® system was used to measure the thoracic and lumbar sagittal spinal c...

In this paper, we calculate the Gaussian curvatures of dual spherical indicatrix curves formed on unit sphere by Blaschke vectors and instantaneous Pfaff parallel equidistant ruled surfaces (DPERS) give relationships between these curvatures. addition to—in cases where base DPERS are closed—computing integral invariants curves. Additionally, show them. Finally, provide an example for each

The notion of general weighted Ricci curvatures appears naturally in many problems. N-Ricci curvature and the projective are just two special ones with totally different geometric meanings. In this paper, we study curvatures. We find that Randers metrics certain isotropic must have S-curvature. Then classify them via their navigation expressions. also equations characterize almost curvature.