For xed matricesM and N , the linear transformation A 7! A MAN is called a displacement of the matrix A. Displacements can simplify matrix equations, as well as matrices themselves. Four principles to solve matrix equations are identi ed: 1) a variety of displacements are needed, 2) we want to recover a matrix from its displacement, 3) changing M and N is natural when A is transposed or inverte...

ABSTRACT There are various useful metrics for finding the distance between two points in Euclidean space. Metrics for finding the distance between two rigid body locations in Euclidean space depend on both the coordinate frame and units used. A metric independent of these choices is desirable. This paper presents a metric for a finite set of rigid body displacements. The methodology uses the pr...

Given a sequence of images taken from a moving camera, they are registered with sub-pixel accuracy in respect to translation and rotation. The sub-pixel registration enables image enhancement in respect to improved resolution and noise cleaning. Both the registration and the enhancement procedures are described. The methods are particulary useful for image sequences taken from an aircraft or sa...

The experiments of Leptos et al. [1] show that the displacements of small particles affected by swimming microorganisms achieve a non-Gaussian distribution, which nevertheless scales diffusively. We use a simple model where the particles undergo repeated ‘kicks’ due to the swimmers to explain the shape of the distribution. Leptos et al. study the microscopic algae Chlamydomonas reinhardthii. Th...

The thermal mean-square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one t...

Results of an experimental investigation of the seismic performance of prefabricated column-footing connections are presented. Tests were conducted on six 1/4-scale prefabricated column specimens inserted into prefabricated footings in two Groups. Group-1 consisted of four specimens, which were tested under constant axial load and cyclic inelastic lateral displacements. The remaining two specim...

The present investigation deals with the propagation of waves in the layer of an anisotropic fibre reinforced thermoelastic solid. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitude of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for Cobalt material...

We propose and demonstrate a displacement control method at the subnanometric scale based on a Michelson interferometer combined with a polarimeter and a phase-locked loop electronic board. Step by step displacements with a step value of 5 nm are presented. A repeatability of 0.47 nm is obtained from back and forth displacements over 1 mum range. We show that a residual ellipticity of less than...

The evolution of the Li-ion displacements in the 3D interstitial pathways of the cubic garnet-type Li(7)La(3)Zr(2)O(12), cubic Li(7)La(3)Zr(2)O(12), was investigated with high-temperature neutron diffraction (HTND) from RT to 600 °C; the maximum-entropy method (MEM) was applied to estimate the Li nuclear-density distribution. Temperature-driven Li displacements were observed; the displacements ...

In formulating the stability problem for an infinite chain of cars, state space is traditionally taken to be the Hilbert space l2, wherein the displacements of cars from their equilibria, or the velocities from their equilibria, are taken to be square summable. But this obliges the displacements or velocity perturbations of cars that are far down the chain to be vanishingly small and leads to a...