This paper presents a new approach to deriving statistically optimal weights for weighted subspace fitting (WSF) algorithms. The approach uses a formula called a “subspace perturbation expansion,” which shows how the subspaces of a matrix change when the matrix elements are perturbed. The perturbation expansion is used to derive an optimal WSF algorithm for estimating directions of arrival in a...

The Rayleigh-Schrr odinger perturbation series for the energy eigenvalue of an anharmonic oscillator deened by the Hamiltonian ^ H (m) () = ^ p 2 + ^ x 2 + ^ x 2m with m = 2; 3; 4;. .. diverges quite strongly for every 6 = 0 and has to summed to produce numerically useful results. However, a divergent weak coupling expansion of that kind cannot be summed eeectively if the coupling constant is l...

A formulation of Einstein gravity, analogous to that for gauge theory arising from the Chalmers-Siegel action, leads to a perturbation theory about an asymmetric weak coupling limit that treats positive and negative helicities differently. We find power counting rules for amplitudes that suggest the theory could find a natural interpretation in terms of a twistor-string theory for gravity with ...

The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on hypersurfaces of constant expansion, constant curvature or constant energy density. The existence of conserved perturbation quantities on scales larger than th...

We study the ground state as well as the first three excited states of the anharmonic oscillator with anharmonicity hx 4 for a range of h = (0, 10) with the first-order logarithmic perturbation iteration method (FOLPIM). This leads to convergent results. The initial choice of the wave function seems only to affect the rate of convergence in the case of the ground state but may critically affect...

We formulate a coupled vibration problem between a structure and an acoustic field by FEM. The problem leads to a non-standard eigenvalue problem. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the non-diagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with ...

1 Time-dependent perturbation theory 1 1.1 Rotating frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Perturbation expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Periodic perturbations . . . . . . . . . . . . . . . . . ....

We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly presented, showing how it implies a kind of duality in perturbation theory, from the start. The approach of renormalization group in perturbation theory is then pr...

We present new results on the summation of nonpower-series expansions in QCD Analytic Perturbation Theory (APT) in the one-loop approximation. We show how to generalize the approach suggested by one of us earlier to the cases of APT and Fractional APT (FAPT) with heavyquark thresholds. Using this approach we analyze the Higgs boson decay H → b̄b. We produce estimations of the higher-order correc...

We investigate the low energy structure of the Kähler potential in SUSY QCD with Nf = Nc + 1 quark flavors. Since this theory’s moduli space is everywhere smooth, a systematic power series expansion of its Kähler potential can be developed in terms of confined meson and baryon fields. Perturbation theory in the supersymmetric sigma model based upon a momentum expansion consistent with naive dim...