Background: The shoulder joint internal rotation deficit is inter alia the most important risk factors for throwing athletes. Thus, the present study aims at investigating the effect of eight weeks of rotator cuff muscles’ specific exercises on the range of motion, proprioception and the activation time of the selective shoulder muscles in male volleyball players with shoulder joint inter...

It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the essential numerical range. The latter is described quantitatively, and based on that sufficient conditions are established under which the c-numerical range also is an ellipse. Several examples are considered, including singular integral operators with the Cauchy kernel...

OBJECTIVE In pedestrian traumas, lower limb injuries occur under lateral shearing and bending at the knee joint level. One way to improve injury mechanisms description and consequently knee joint safety is to evaluate the ultimate shearing and bending levels at which ligaments start being injured. METHODS As such data cannot easily and accurately be recorded clinically or during experiments, ...

The numerical range of an n× n matrix polynomial P (λ) = Amλ m + Am−1λ m−1 + . . . + A1λ + A0 is defined by W (P ) = {λ ∈ C : x∗P (λ)x = 0, x ∈ C, x 6= 0}. For the linear pencil P (λ) = Iλ− A, the range W (P ) coincides with the numerical range of matrix A, F (A) = {x∗Ax : x ∈ C, x∗x = 1}. In this paper, we obtain necessary conditions for the origin to be a boundary point of F (A). As a consequ...