The fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simul...

This work deals with the computation of power spectrum large-scale structure using dynamical system approach for a multi-fluid universe in scalar-tensor theory gravity. We use $1+3$ covariant to obtain evolution equations and study behavior matter perturbation equations. The is based on equivalence between $f(R)$ gravity find that, power-law $(R^{n})$ models, $1<n<1.3$, we have evolving above g...

In this paper, a single discriminating indicator to assess the deterioration of power quality (Deviation Factor of Power Quality) is proposed using tensor analysis and wavelet packet transform (WPT). This factor can be used in the presence of stationary and non-stationary power quality disturbances. In addition, practical examples are included to validate the deviation factor of power quality.

Let V be the 7-dimensional irreducible representations of G2. We decompose the tensor power V ⊗n into irreducible representations of G2 and obtain all irreducible representations of G2 in the decomposition. This generalizes Weyl’s work on the construction of irreducible representations and decomposition of tensor products for classical groups to the exceptional group G2.

Consider the following consistent Sylvester tensor equation[mathscr{X}times_1 A +mathscr{X}times_2 B+mathscr{X}times_3 C=mathscr{D},]where the matrices $A,B, C$ and the tensor $mathscr{D}$ are given and $mathscr{X}$ is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...