Calculating Fractional-Parentage Coefficients for Six Body System in Translational Invariant Basis

In this paper we present an independent scheme for constructing fractional parentage coefficients using symmetry group apparatus in translationally invariantmodel space, suitable for the six-particle system composed of three-particle bi-clusters, where the presented subsystems have their own intrinsic clusterization. Simple expressions for corresponding antisymmetrization procedure are presented as well as computational results.

     

On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables

Lithuanian Mathematical Journal - We present upper bounds of the integral $$ {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathrm{P}\left\{{Z}_N0\left({S}_N{X}_1+\dots +{X}_N\right) $$ of...     

Evaluation of diffraction errors in precise pulse-echo measurements of ultrasound velocity in chambers with waveguide

Ultrasound velocity measurements in medicine and biology usually are performed using relatively small measurement chambers. When the pulse-echo method is used, the presence of the reflector close to the transducer can cause essential diffraction errors. These errors may be reduced using an additional buffer rod as a waveguide between the transducer and the measurement chamber. The objective of the presented work was analysis of diffraction errors in measurement chambers with a buffer rod. The work was performed in two steps. In the first stage propagation of transient ultrasonic waves in a buffer rod was analysed using an axisymmetric finite element model. This approach enables all dimensions of the measurement chamber and the waveguide to be taken into account, but is less accurate in the time domain. In the second step the absolute values of diffraction errors were evaluated using a mixed analytic-numeric disk shaped transducer diffraction model. In this case only the dimensions of the waveguide and measurement chamber along the wave propagation direction were taken into account. Diffraction errors were calculated by simulating small changes of ultrasound velocity in the liquid under investigation. The simulation performed allowed optimisation of the dimensions of the measurement chamber and a buffer rod thus minimising measurement errors.     

Ultrasonic fields radiated through matching layers with nonparallel boundaries

In the case of ultrasonic measurements in aggressive media piezoelectric elements of ultrasonic transducers are separated from a medium by thick protective layers, which may posses nonparallel front and back surfaces. This enables to reduce significantly the amplitude of multiple reflections, but the structure of the ultrasonic field radiated through a layer with nonparallel boundaries becomes complicated. The main objective of this paper is to present a method suitable for simulation of ultrasonic fields radiated through a layer with nonparallel boundaries in a transient mode. The proposed simulation method is based on the transformation of a multilayered medium into a virtual one without internal boundaries, equivalent to the actual medium from the point of a view of the relative times of arrival of direct and edge waves. The simulated ultrasonic fields in water are compared with the measurement results and a good correspondence between calculated and measured fields is obtained.