In this article, we construct the scalar–diquark–axialvector–diquark–antiquark-type interpolating currents, and study the masses and pole res-idues of the \(J^{P}=\frac {3}{2}^{\pm }\) hidden-charmed pentaquark states with the QCD sum rules. In calculations, we use the formula \(\mu =\sqrt {M^2_{P}-(2{\mathbb {M}}_c)^2}\) to determine the energy scales of the QCD spectral densities. We obtain the masses of the hidden-charm pentaquark states with the strangeness \(S=-1\) and \(S=-2\), which can be confronted with the experimental data in the future.

In this paper, the Lie point symmetry analysis method is used to investigate the (2+1)-dimensional Burgers equations. We have obtained the optimal system of Lie subalgebras. Some new exact solutions for the (2+1)-dimensional Burgers equations are obtained.

In this work, a solution of the Einstein equations for axially symmetric closed null string has been found. At each moment of time, the direction of its motion is orthogonal to the plane in which null string is located. An absence of limit transition between the found solution and a solution for a closed null string of constant radius has been shown. This may indicate a stability of configuration of a closed null string in shape of a circle during motion in an external gravitational field. An influence of this field for such a null string may be reduced to a change of its motion as a whole (without change of its shape and size) or to a change of its radius. It has been noted that a part of characteristics of null string gas, such as an ability to form a domain structure and an existence of polarized states (multi-string systems), does not depend on a shape of a null string. However, a dynamics of a test null string in a field of such a multi-string system will have peculiarities.

Taking the velocity dispersion term into account in the Jeans equation describing the disk model, counterintuitively allows to reduce the local mass-to-light ratio at the outskirts of flattened galaxies, and stop the unbound growth of mass function. This is possible thanks to a more intertwined relation between the gravitational potential and the rotation curve than for spheroidal systems. This effect is illustrated on the example of galaxy UGC 6446 by finding iteratively the column mass density from the rotation curve supplemented with an isotropic velocity dispersion profile in the disk plane. Along with galactic magnetic fields, this effect would allow to reduce the local mass-to-light ratio at the galactic outskirts.

Gold plays a significant role in the investment market. The analysis of influence factors of the gold price is a research hotspot for the portfolio managers, investors and regulatory authorities. There are a lot of articles which investigate the gold price using different methods. However, there is a scarce literatures on the research of the gold price from the perspective of internal structure of the temporal sequence. In this paper, we generate a novel approach which combines variational mode decomposition (VMD), principal component analysis (PCA) and independent component analysis (ICA) (VMD-PCA-ICA). Specifically, three steps are contained: firstly, the gold price is decomposed into the sum of intrinsic mode functions (IMFs) via VMD method and the recombination of IMFs (RIMFs) is obtained in light of the contribution coefficients between IMF and gold price data. Secondly, PCA is applied to RIMFs and the principal components (PCs) are acquired. Finally, ICA method is utilized to separate the gold price and independent components (ICs) are obtained. The proposed approach demonstrates that the gold price sequence is a linear combination of ICs. Meanwhile, the influence factors of the gold price are analysed from the viewpoint of the correspondence between ICs and economic factors. Compared with the EMD-ICA, EEMD-ICA and VMD-ICA, the approach in this paper has the fastest convergence speed.