Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used develop the quantitative structure-activity relationship (QSAR), structure-property (QSPR) corresponding chemical compound. Various techniques have been developed calculate TI graph. Recently technique calculating degree-based from M-polynomial has introdu...

Abstract. Recently, M. Abért and T. Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Abért and Hubai proved that for a Benjamini-Schramm convergent sequence of finite graphs, the chromatic measures converge in holomorphic moments. They also showed that the normalized log of the chromatic polynom...

Schrödinger bound-state problem in D dimensions is considered for a set of central polynomial potentials containing 2q arbitrary coupling constants. Its polynomial (harmonicoscillator-like, quasi-exact, terminating) bound-state solutions of degree N are sought at an (q + 1)-plet of exceptional couplings/energies, the values of which comply with (the same number of) termination conditions. We re...

We give, using an explicit expression obtained in [V. Jones, Ann. of Math. 126, 335 (1987)], a basic hypergeometric representation of the HOMFLY polynomial of (n,m) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result the (m,n) ↔ (n,m) symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilso...

In this paper, we introduce and analyze the behavior of a nonlinear subdivision operator called PPH, which comes from its associated PPH reconstruction on nonuniform grids. The acronym stands for Piecewise Polynomial Harmonic, since is built by using piecewise polynomials defined means an adaption based use weighted Harmonic mean. novelty work lies in generalization already existing scheme to c...

The subject began in 1975, when Yau [Y1] proved that there are no nonconstant, positive harmonic functions on a complete manifold with nonnegative Ricci curvature. A few years later, Cheng [C] pointed out that using a local version of Yau’s gradient estimate, developed in his joint work with Yau [CY], one can show that there are no nonconstant harmonic functions of sublinear growth on a manifol...

Harmonic navigation of multiple low-cost robotic wheelchairs in a topology of wireless sensor nodes that are deployed in a dynamic and crowded indoor environment is a Non-deterministic Polynomial-time hard (NP-hard) problem. To address this problem, we propose a distributed multi-wheelchair global harmonic navigation algorithm. The distinguishing features of the proposed navigation algorithm ar...

A program able to use hybrid free rotor plus harmonic oscillator basis functions for the variational study of large and small amplitude vibrations is developed. The Hamiltonian matrix elements between harmonic oscillator eigenfunctions and polynomial terms are calculated using a recursive algorithm. This technique permits use of only one basic algorithm to compute the kinetic and potential part...