Petar O. Nikiforov,a Sachin Surade,b Michal Blaszczyk,b Vincent Delorme,c Priscille Brodin,c Alain R. Baulard,c Tom L. Blundell,b Chris Abella* a Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK b Department of Biochemistry, University of Cambridge, 80 Tennis Court Road, Cambridge, CB2 1GA, UK c Inserm U1019 – CNRS UMR 8204, Institut Pasteur de Lille, Uni...

Let H be a graph and t ≥ s ≥ 2 be integers. We prove that if G is an n-vertex graph with no copy of H and no induced copy of Ks,t, then λ(G) = O ( n1−1/s ) where λ(G) is the spectral radius of the adjacency matrix of G. Our results are motivated by results of Babai, Guiduli, and Nikiforov bounding the maximum spectral radius of a graph with no copy (not necessarily induced) of Ks,t.

The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral distribution of eigenvalues of Wigner matrix. In the present paper, we explore the limiting spectral distribution for more general random matrices, and, furthermore, ...

The analytical solution of Dirac equation plays a vital role in relativistic quantum mechanics and solving the Dirac equation to obtain the bound-state energies for with different potential models using various methods for example Nikiforov-Uvarov method, The Laplace transform approach (LTA), factorization method and so on [1-6]. The quantum algebraic structure based to the ordinary CCRs in bot...

Book review: Achkasov V. A., Abalyan A. I., Andreev Nikiforov Ethnopolitical conflicts and mobilization in the modern world: post-soviet context, ed. by Achkasov, I. Abalyan. St Petersburg: Publishing house of RKhGA, 2021. 640 p.

We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and com...

The Nikiforov-Uvarov method is employed to calculate the Schrödinger equation with a rotation Morse potential. The bound state energy eigenvalues and the corresponding eigenfunction are obtained. All of these calculations present an effective and clear method under a Pekeris approximation to solve a rotation Morse model. Meanwhile the results got here are in a good agreement with ones before. P...

Weexplore the effect of the externalmagnetic andAharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the twodimensional (2D) space. We calculate the exact energy eigenvalues and the correspondingun-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field streng...

In 2003 Vladimir Nikiforov [7] began a line of research whose aim was to build an extremal theory of graphs based on spectral theory. We will discuss some of his results and in particular we will focus on a result of Babai and Guiduli [1] that gives a Kövari-Sós-Turán type upper bound on the largest eigenvalue of the adjacency matrix of a Ks,t-free graph. This spectral approach sheds new light ...

The one-dimensional spinless Salpeter equation has been solved for the PT -symmetric generalized Hulthén potential. The Nikiforov-Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive an...