The standard Lichnerowicz comparison theorem states that if the Ricci curvature of a closed, Riemannian n-manifold M satisfies Ric (X,X) ≥ a (n − 1) |X| for every X ∈ TM for some fixed a > 0, then the smallest positive eigenvalue λ of the Laplacian satisfies λ ≥ an. The Obata theorem states that equality occurs if and only if M is isometric to the standard n-sphere of constant sectional curvatu...

LARS ANDERSSON, MATTIAS DAHL, AND RALPH HOWARD Abstract. Let g be a Lorentzian metric on the plane R2 that agrees with the standard metric g0 = −dx + dy outside a compact set and so that there are no conjugate points along any time-like geodesic of (R2 , g). Then (R2 , g) and (R2 , g0) are isometric. Further, if (M, g) and (M∗, g∗) are two dimensional compact time oriented Lorentzian manifolds ...

Purpose: This study aimed to evaluate the symmetry of the isometric strength of the shoulder and scapulothoracic muscles in volleyball and futsal athletes. Methods: In this case-control study, the strength of the scapulothoracic muscles and rotation of the shoulders in 20 adult volleyball athletes and 20 futsal adult athletes, who were randomly selected from sports clubs around Tehran, were me...

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

Both isometric exercise and cold stress have been suggested as alternatives to dynamic exercise for the detection of obstructive coronary artery disease. A non-imaging nuclear probe was used to measure left ventricular ejection fraction and relative left ventricular volumes continuously during both of these stress tests in 24 normal subjects. There was a significant fall in left ventricular eje...

Eight moderately active male subjects where tested for peak force in an isometric knee extension test and peak force and rate of force development in an isometric squat test. Both tests where performed at a 100 degrees knee angle and average integrated electromyography (IEMG) was measured from the vastus medialis (VM), vastus lateralis (VL) and biceps femoris (BF) muscles. Subjects performed th...