Ground reaction forces (GRF) reflect the force history of human body contact with the ground. The purpose of this study was to explore human gait abnormalities due to planovalgus by comparing vertical GRF data between individuals with planovalgus and those with neutrally aligned feet. Second we estimated associations between various measurements and vertical GRF parameters in a pediatric popula...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

The implementation of the Debye, narrowband Lorentzian, and wideband Lorentzian dielectric and magnetic media in the numerical tool EZ-FDTD developed at the University of Missouri-Rolla (UMR is described. This tool allows efficient and robust full-wave finite-difference time-domain modeling of different complex electromagnetic structures. Algorithms for dispersive media use the linear recursive...

By using variational methods, we study the existence and multiplicity of trajec-tories under a vectorial potential on (standard) stationary Lorentzian manifolds possibly with boundary. 1. Introduction and statement of the results. The pair (ᏸ,g) is called Lorentzian manifold if ᏸ is a connected finite-dimensional smooth manifold with dim ᏸ ≥ 2 and g is a Lorentzian metric on ᏸ, that is, g is a ...

A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a non-total imprisoning spacetime is globally hyperbolic if and only if for every metric choice in the conformal class the Lorentzian distance is continuous. Moreove...

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

An atomic force microscopy (AFM) based technique is demonstrated for measuring the elastic modulus of individual nanowires/nanotubes aligned on a solid substrate without destructing or manipulating the sample. By simultaneously acquiring the topography and lateral force image of the aligned nanowires in the AFM contacting mode, the elastic modulus of the individual nanowires in the image has be...

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. Our results imply that the Singer index for four-dimensional Lorentzian manifolds is greater or equal to 2. PACS numbers: 04.20, 02.40 AMS classificat...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k