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We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $…
This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we…
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. I also cover some important classes of applications: electron-positron…
Perturbation theory is applied to one-dimensional scattering systems consisting of a general class of inhomogeneous and isotropic slabs having size $L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha \chi(z)$, where…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
The perturbation of the dromion of the Davey-Stewartson-1 equation is studied over the large time.
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…
Perturbation theory is developed to analyze the impact of noise on data and has been an essential part of numerical analysis. Recently, it has played an important role in designing and analyzing matrix algorithms. One of the most useful…
This survey revolves around the question how the roots of a monic polynomial (resp. the spectral decomposition of a linear operator), whose coefficients depend in a smooth way on parameters, depend on those parameters. The parameter…
Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our…
Structured perturbation results for invariant subspaces of $\Delta$-Hermitian and Hamiltonian matrices are provided. The invariant subspaces under consideration are associated with the eigenvalues perturbed from a single defective…
This paper is the first in a series of three which attempt to resolve the difficulties that have plagued the $NN-\pi NN$ problem for the past ten years. Various theoretical inconsistencies in the current formulation have been pointed out…
S-matrices for integrable perturbations of $N=2$ superconformal field theories are studied. The models we consider correspond to perturbations of the coset theory $G_k \times H_{g-h} /H_{k+g-h} $. The perturbed models are closely related to…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
A remarkable extension of Rayleigh-Schroedinger perturbation method is found. Its (N+q) x (N+1) - dimensional Hamiltonians (as emerging, e.g., during quasi-exact constructions of bound states) are non-square matrices at q > 1. The role of…
This survey focuses on two main types of finite-rank perturbations: self-adjoint and unitary. We describe both classical and more recent spectral results. We pay special attention to singular self-adjoint perturbations and model…
Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
We extend twisted inner fluctuations to twisted spectral triples that do not meet the twisted first-order condition, following what has been done in [6] for the non-twisted case. We find a similar non-linear term in the fluctuation, and…
We investigate the initial condition which are simultaneously consistent with perturbation equations in both the radiation-dominated and the mater-dominated epochs. The exact formula for the spectrum transfer-function is derived.