Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by angle. Fix $0 < \alpha 1$. Let $N_\alpha(d)$ denote through origin $\mathbb{R}^d$ with common $\arccos \alpha$. $k$ minimum (if it exists) vertices graph whose adjacency matrix has spectral radius exactly $(1-\a...

BACKGROUND AND PURPOSE The alpha angle is the most used measurement to classify concavity of the femoral head-neck junction. It is not only used for treatment decisions for hip impingement, but also in cohort studies relating hip morphology and osteoarthritis. Alpha angle measurement requires identification of the femoral neck axis, the definition of which may vary between studies. The original...

The normal value of alpha angle is controversial. The aim of this study was to compare the alpha angle in asymptomatic volunteers versus patients who had undergone surgery for symptomatic cam-type femoroacetabular impingement (FAI) and determine a diagnostic cut-off value for symptomatic cam impingement. This is a diagnostic test study. Cases were defined as those patients who had undergone sur...

The use of the alpha angle to help the diagnosis of Femoral Acetabular Impingement (FAI) is common. However, there is currently no standard value available across an asymptomatic pre-arthritic population. We present the first large cohort of Computerised Tomography (CT) based alpha angles in patients with no history of hip pathology, including intra- and interobserver validation. We carried out...

Cam and pincer are two common morphologies responsible for femoroacetabular impingement (FAI). Previous literature has reported that cam deformity is predominantly a male morphology, while being significantly less common in females. Cam morphology is commonly assessed with the alpha angle, measured on radiographs. The purpose of this study is to determine the prevalence of cam morphology utiliz...

Small angle x-ray scattering and viscometric analyses of the alpha-zeins of maize in solution indicated that the molecules were asymmetric. Structure predictions of consensus sequences for the two classes of alpha-zeins, Z19 and Z22, were in good agreement with the alpha-helical contents determined by circular dichroism. Dimensions determined by small angle x-ray scattering and viscometry indic...

AIM To compare the pattern of localised nerve fibre layer (NFL) defects in normal tension glaucoma (NTG) and primary open angle glaucoma (POAG). METHODS 50 NTG eyes and 36 POAG eyes, all with localised NFL defects, were enrolled. On retinal NFL photography, the proximity of the defect to the centre of the fovea (angle alpha) and the sum of the angular width of the defects (angle beta) were de...

UNLABELLED Hybrid PET systems have spatially varying sensitivity profiles. These profiles are dependent on imaging parameters, namely, number of heads, head configuration, spacing between gantry stops, radius of rotation (RoR), and coincident head acceptance angle. METHODS Sensitivity profiles were calculated across a 500-mm field of view (FoV) for a representative set of existing and theoret...

Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...