In this paper, we establish Desch-Schappacher type multiplicative and additive perturbation theorems for existence families for arbitrary order abstract Cauchy problems in a Banach space: u(n)(t) = Au(t) (t ≥ 0); u(j)(0) = xj (0 ≤ j ≤ n− 1). As a consequence, we obtain such perturbation results for regularized semigroups and regularized cosine operator functions. An example is also given to ill...

Two toy Hamiltonians of anharmonic oscillators are considered. Both of them are found exactly solvable not only in the limit of infinite spatial dimension D but also in the next D ≫ 1 approximation. This makes all their bound states tractable via perturbation series in 1/ √ D ≪ 1.

Two approaches to the combination of robust variational deconvolution with positivity constraints are considered. The first approach modifies a standard robust variational deconvolution method by carrying out a gradient descent with respect to a multiplicative perturbation, which can also be considered as gradient descent in a hyperbolic metric. The second approach is based on the representatio...

Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain.The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.

This paper studies the Schatten-q error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on via projection bound. Then, we lower bounds to justify tightness upper error. further develop user-friendly sin? for subspace based Finally, demonstrate advantage our results over ones in literature simulation.

We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of J. von zur Gathen and I. E. Shparlinski.