Approximate determination of the plasma potential spatial distribution in the isolated dust particle vicinity

In this paper, results of two numerical models are compared. The main purpose of these models is to determine the self-consistent spatial distributions of plasma (electric potential and space charge) near isolated spherical dust particles. In the first model, the spatial distribution of the self-consistent plasma potential is determined by expanding the plasma space charge spatial distribution in Legendre polynomials; in the second model, it is determined by direct numerical integration of the Poisson equation solution. The results show that the dependences of the system main parameters (wake magnitude and position, dipole moment of the ion cloud) coincide for small values of the external electrostatic field. With an increase in the external field strength, the dependences for two models cease to coincide, which is due to the inapplicability of Legendre polynomial decomposition in the case of strong anisotropy.

On Normalized Laplacians, Degree-Kirchhoff Index and Spanning Tree of Generalized Phenylene

The normalized Laplacian is extremely important for analyzing the structural properties of non-regular graphs. The molecular graph of generalized phenylene consists of n hexagons and 2n squares, denoted by Ln6,4,4. In this paper, by using the normalized Laplacian polynomial decomposition theorem, we have investigated the normalized Laplacian spectrum of Ln6,4,4 consisting of the eigenvalues of symmetric tri-diagonal matrices LA and LS of order 4n+1. As an application, the significant formula is obtained to calculate the multiplicative degree-Kirchhoff index and the number of spanning trees of generalized phenylene network based on the relationships between the coefficients and roots.

The Three Hundred Project: quest of clusters of galaxies morphology and dynamical state through Zernike polynomials

The knowledge of the dynamical state of galaxy clusters allows to alleviate systematics when observational data from these objects are applied in cosmological studies. Evidence of correlation between the state and the morphology of the clusters is well studied. The morphology can be inferred by images of the surface brightness in the X-ray band and of the thermal component of the Sunyaev-Zel’dovich (tSZ) effect in the millimetre range. For this purpose, we apply, for the first time, the Zernike polynomial decomposition, a common analytic approach mostly used in adaptive optics to recover aberrated radiation wavefronts at the telescopes pupil plane. With this novel way we expect to correctly infer the morphology of clusters and so possibly, their dynamical state. To verify the reliability of this new approach we use more than 300 synthetic clusters selected in THE THREE HUNDRED project at different redshifts ranging from 0 up to 1.03. Mock maps of the tSZ, quantified with the Compton parameter, y-maps, are modelled with Zernike polynomials inside R500, the cluster reference radius. We verify that it is possible to discriminate the morphology of each cluster by estimating the contribution of the different polynomials to the fit of the map. The results of this new method are correlated with those of a previous analysis made on the same catalogue, using two parameters that combine either morphological or dynamical-state probes. We underline that instrumental angular resolution of the maps has an impact mainly when we extend this approach to high-redshift clusters.

Oil Price Forecasting Using a Time-Varying Approach

The international crude oil market plays an important role in the global economy. This paper uses a variable time window and the polynomial decomposition method to define the trend term of time series and proposes a crude oil price forecasting method based on time-varying trend decomposition to describe the changes in trends over time and forecast crude oil prices. First, to characterize the time-varying characteristics of crude oil price trends, the basic concepts of post-position intervals, pre-position intervals and time-varying windows are defined. Second, a crude oil price series is decomposed with a time-varying window to determine the best fitting results. The parameter vector is used as a time-varying trend. Then, to quantitatively describe the continuation of the time-varying trend, the concept of the trend threshold is defined, and a corresponding algorithm for selecting the trend threshold is given. Finally, through the predicted trend thresholds, the historical reference data are selected, and the time-varying trend is combined to complete the crude oil price forecast. Through empirical research, it is found that the time-varying trend prediction model proposed in this paper achieves a better prediction than several common models. These results can provide suggestions and references for investors in the international crude oil market to understand the trends of oil prices and improve their investment decisions.

Public Key Cryptosystem Based on Polynomial Composition

The public key cryptosystem is an extension of an asymmetric key cryptosystem. The public key cryptosystems have been developed based on the concepts of matrix, polynomial and polynomial decomposition. In this study, we will introduce the public key cryptosystem over polynomial composition. This research is a literature study. The results show that the polynomial composition can be used in public-key cryptosystems by modifying special functions to apply commutative properties<em>.</em>