Asymptotic symmetries at future null infinity (I+) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through I+ suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose g...

Asymptotic expansions were first introduced by Henri Poincaré in 1886. This paper describes their application to the semi-classical evaluation of amplitudes in quantum field theory with boundaries. By using zeta-function regularization, the conformal anomaly for a massless spin-12 field in flat Euclidean backgrounds with boundary is obtained on imposing locally supersymmetric boundary condition...

Fixed angle scattering at high energy in a string theory with boundaries satisfying Dirichlet conditions (Dirichlet strings) inD = 4 is shown to have logarithmic dependence on energy, in addition to the power-like behavior known before. High temperature free energy also depends logarithmically on temperature. Such a result could provide a matching mechanism between strings at long distance and ...

In the problem of selecting a linear model to approximate the true unknown regression model, some necessary and/or sufficient conditions are established for the asymptotic validity of various model selection procedures such as Akaike’s AIC, Mallows’ Cp, Shibata’s FPEλ, Schwarz’ BIC, generalized AIC, crossvalidation, and generalized cross-validation. It is found that these selection procedures c...

The widely used textbook by Brassard and Bratley [3] includes a chapter devoted to asymptotic notation (Chapter 3, pp. 79–97). We have attempted to test how suitable the current version of Mizar is for recording this type of material in its entirety. A more detailed report on this experiment will be available separately. This article presents the development of notions and a follow-up article [...

W hat is the probability that two randomly chosen permutations of 1, . . . , n generate the group Sn of all permutations of 1, . . . , n ? How many subgroups of index n can a group with two generators have? What can be said about a group of order 2n which has a nonidentity commutator of length n− 10? These questions all concern different aspects of a field which is very active nowadays and whic...

We argue that any non-gravitational holographic dual to asymptotically flat string theory in d-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a (d − 1)-dimensional timelike hyperboloid (i.e., as a copy of de Sitter space in (d− 1) dimensions), the dual theory is defined on a Lorentz signature spacetime. Conceptual issues regarding such a duality ...

We provide a precise account of some commonly used results from asymptotic theory in probability.

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matc...