Stability of the spine is necessary for preventing pain and enhancing performance (Liebenson, 2006; McGill, 2006). Core muscle endurance is a key quality to train. Many exercises have been developed for the core including traditional ones such as sit-ups which have been recently called into question (McGill, 2006). Training the spine in a neutral posture which reinforces the natural upright cur...

In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic aspects of coverings by planks in the present time as well. The paper is a survey type with a list of open research problems.

[Purpose] This study applied variable plank exercises on a stable surface consisting of a mat, on an unstable surface consisting of a dynamic cushion placed under the upper extremities and lower extremities. [Subjects] Forty-three healthy male and female subjects in their 20s voluntarily consented to participate in this study. [Methods] The subjects performed the plank exercises on the three su...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

The Cauchy problem for the Fokker–Plank–Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker–Plank– Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

Abstract Ball’s complex plank theorem states that if $$v_1,\dots ,v_n$$ v 1 , ⋯ n are unit vectors in $${\mathbb {C}}^d$$ C d , and $$t_1,\...

D. Imperati, M. Cross, K. Kruttwig, P. Galvosas, K. Ulrich, A. Pampel, J. Kärger, M. Hoehn, H. E. Möller, and M. Tittgemeyer Max-Plank Institute for Neurological Research, Cologne, Germany, Department of Computer Science, University of Milan, Milan, Italy, Interdisciplinary Center for Medical Research, Leipzig, Germany, Department of Physics, University of Leipzig, Leipzig, Germany, Max-Plank I...