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For the quantum quartic anharmonic oscillator with the Hamiltonian H = (p²+x²)/2+λx4, which is one of the traditional quantum-mechanical and quantum-field-theory models, we study summation of its factorially divergent perturbation series by the proposed method of averaging of the corresponding Padé approximants. Thus, for the first time, we are able to construct the Padé-type approximations that possess correct asymptotic behaviour at infinity with a rise of the coupling constant λ. The approach gives very essential theoretical and applicatory-computational advantages in applications of the given method. We also study convergence of the applied approximations and calculate by the proposed method the ground state energy E0(λ) of the anharmonic oscillator for a wide range of variation of the coupling constant λ. [ABSTRACT FROM AUTHOR]

Simple relations connecting the strange quark mass to the splittings of the light hyperon masses were obtained on the basis of the phenomenological quark model compatible with the present-day theory of strong interactions, i.e. with quantum chromodynamics (QCD). Strange quark mass ms 89.5 ± 19.5 MeV, calculated in the proposed approach, is in good agreement with the modern evaluations and calculations of this quantity, mainly obtained by the lattice QCD methods. [ABSTRACT FROM AUTHOR]