نتایج جستجو برای: concave ellipsoid
تعداد نتایج: 12465 فیلتر نتایج به سال:
Corresponding to each origin-symmetric convex (or more general) subset of Euclidean n-space R, there is a unique ellipsoid with the following property: The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace ofR. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid and its polar (the ...
The present study aimed at clarifying the cell kinetics of the mouse ureteral epithelium by focusing on vesicle maturation in the cells and labeling with bromodeoxyuridine (BrdU). Electron microscopically, superficial cells were characterized by concave plaques in the apical plasma membrane and numerous fusiform vesicles in the cytoplasm. Intermediate cells were laden with ellipsoid vesicles, a...
BACKGROUND Prostate volume can affect whether patients qualify for brachytherapy (desired size ≥20 mL and ≤60 mL) and/or active surveillance (desired PSA density ≤0.15 for very low risk disease). This study examines variability in prostate volume measurements depending on imaging modality used (ultrasound versus MRI) and volume calculation technique (contouring versus ellipsoid) and quantifies ...
Structure model index (SMI) is widely used to measure rods and plates in trabecular bone. It exploits the change in surface curvature that occurs as a structure varies from spherical (SMI = 4), to cylindrical (SMI = 3) to planar (SMI = 0). The most important assumption underlying SMI is that the entire bone surface is convex and that the curvature differential is positive at all points on the s...
The MVE estimator is an important estimator in robust statistics and characterized by an ellipsoid which contains inside 100β percent of given points in IR n and attains the minimal volume, where β ∈ [0.5, 1.0) is of usual interest. The associated minimal ellipsoid can be considered as a generalization of the minimum volume covering ellipsoid which covers all the given points since the latter e...
BACKGROUND Kidney volume (KV) becomes clinically relevant in autosomal dominant polycystic kidney disease (ADPKD) management. KV can be conveniently estimated (ceKV) using ellipsoid volume equations with three axes measurements; however, the accuracy and reliability are unknown. METHODS KVs of 347 kidneys in 177 consecutive ADPKD patients were determined with a volumetric method (standard-KV)...
Associated with each body K in Euclidean n-space Rn is an ellipsoid 02K called the Legendre ellipsoid of K . It can be defined as the unique ellipsoid centered at the body’s center of mass such that the ellipsoid’s moment of inertia about any axis passing through the center of mass is the same as that of the body. In an earlier paper the authors showed that corresponding to each convex body K ⊂...
We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...
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