Wiener–Hosoya Matrix of Connected Graphs

Let G be a connected (molecular) graph with the vertex set V(G)={v1,⋯,vn}, and let di and σi denote, respectively, the vertex degree and the transmission of vi, for 1≤i≤n. In this paper, we aim to provide a new matrix description of the celebrated Wiener index. In fact, we introduce the Wiener–Hosoya matrix of G, which is defined as the n×n matrix whose (i,j)-entry is equal to σi2di+σj2dj if vi and vj are adjacent and 0 otherwise. Some properties, including upper and lower bounds for the eigenvalues of the Wiener–Hosoya matrix are obtained and the extremal cases are described. Further, we introduce the energy of this matrix.

THE USE OF STRUCTURAL COMPACT MATRIX METHOD FOR CALCULATING THE COM-PACTNESS COEFFICIENT

The method of compact matrix description of regular three-dimensional spatial configurations and numerical techniques developed on its basis for calculating some structural and energy parameters of cubic lattices have proved to be more effective in comparison with other numerical methods. The suc-cessful application of the compact matrix method for the description of the simplest hexagonal lattice allows us to develop more efficient numerical methods for calculating the structural and energy pa-rameters of lattices of this type.

Quantum Web of Gravity

The recently proposed and logically developed paradigm of deep genetical affinity of scientific terms "energy-entropy-information" harmonizes classical and quantum physics with general and special theories of relativity. For the first time in engineering practice, a complex vector-tensor-matrix description of gravitational, thermal and electromagnetic fields in ideal solid, liquid and gaseous media was performed analytically and without preliminary measurements. The basic set of fundamental quantum constants of the standard physical model has been computed with an extreme precision of 1/10^64, which is a natural limit arising due to elementary recursive arithmetic and elementary functional analysis in digital notation.

Airy minima in 4He +28Si elastic and inelastic scattering

We present the results of the [Formula: see text]-matrix description of the [Formula: see text] elastic and inelastic scattering differential cross-sections between 40 and 240 MeV with allocation of Airy minima of various orders. The first-order Airy minima have been unambiguously identified in the differential cross-sections for elastic scattering and inelastic scattering to the first [Formula: see text] state of [Formula: see text] at energies [Formula: see text] MeV, and the second-order Airy minima — at [Formula: see text] MeV. The angular positions of these minima obey an inverse dependence on energy. The intensities of nuclear refraction and absorption also obey the same energy dependence.