Passive Source Localization Using Acoustic Intensity in Multipath-Dominant Shallow-Water Waveguide

The array invariant technique has been recently proposed for passive source localization in the ocean. It has successfully estimated the source–receiver horizontal range in multipath-dominant shallow-water waveguides. However, it requires a relatively large-scale hydrophone array. This study proposes an array invariant method that uses acoustic intensity, which is a vector quantity that has the same direction as the sound wave propagating through a water medium. This method can be used to estimate not only the source–receiver horizontal range, but also the azimuth to an acoustic source. The feasibility of using a vector quantity for the array invariant method is examined through a simulation and an acoustic experiment in which particle velocity signals are obtained using a finite difference approximation of the pressure signals at two adjacent points. The source localization results estimated using acoustic intensity are compared with those obtained from beamforming of the acoustic signals acquired by the vertical line array.

Uncertainty and the ranking of economics journals

Journal rankings often show significant changes compared to previous rankings. This gives rise to the question of how well estimated the rank of a journal is. In this contribution, we consider uncertainty in a ranking of economics journals. We use the invariant method of Pinski and Narin to rank the journals. We propose an uncertainty measure, which is based on a bootstrap approach. The measure is the average absolute change in rank, which we see as a reasonable uncertainty measure regarding rankings. We further calculate, based on the bootstrap method, 95% confidence interval for the observed values of the invariant method. We show that ranks of the highest, as well as the lowest, ranked journals are well estimated, while there is a high degree of uncertainty regarding the rank of many mid-ranked journals. The distribution of the underlying measure is useful for identifying groups of journals that are more or less of the same quality (from the point of view of the invariant measure). The journal with the highest observed value of the invariant measure, Journal of Political Economy, has the best performance and constitutes a singleton, whereas Quarterly Journal of Economics and Econometrica form the next group (there is a slight overlap between the two with respect to confidence intervals). The journals ranked between about 190–230 form another group in which there are no major quality differences between the journals, as the confidence intervals are overlapping.

ANALYTICAL SOLUTION OF (2+1) DIMENSIONAL DIRAC EQUATION IN TIME-DEPENDENT NONCOMMUTATIVE PHASE-SPACE

In this article, we studied the system of a (2+1) dimensional Dirac equation in a time-dependent noncommutative phase-space. More specifically, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method based on the construction of the Lewis-Riesenfeld invariant. Knowing that we obtained the time-dependent Dirac Hamiltonian of the problem in question from a time-dependent Bopp-Shift translation, then used it to set the Lewis- Riesenfeld invariant operators. Thereafter, the obtained results were used to express the eigenfunctions that lead to determining the general solution of the system.

Estimation of the Stage of Search Process for the Simplex Invariant Method

The article describes the synthesis of rules used for estimating the stage of searching for the simplex invariant method. Computational experiments were carried out on a non-stationary static model. Characteristics of the optimum search and tracking process were obtained. The characteristics were analyzed. Based on the obtained patterns rules were developed that allow evaluating the stage of the search process: movement towards the optimum or its tracking. In conclusion, a summary of the research is given