Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD

Jet exhaust noise suppressor

Noise suppression for a jet engine exhaust is provided by an annular divergent body attached to an exhaust nozzle. The smallest diameter of the divergent body is larger than the diameter of the exhaust nozzle exit to form an annular step which produces a shock wave in the exhaust as it passes the step. An annular shroud is disposed around the divergent body and causes outside air to pass through voids in the divergent body to mix with the jet exhaust gas. The divergent body includes a plurality of channels with separators between the channels

Divergent Platforms

A robust feature of models of electoral competition between two opportunistic, purely office-motivated parties is that both parties become indistinguishable in equilibrium. I this short note, I show that this strong connection between the office motivation of parties and their equilibrium choice of identical platforms depends on the following two - possibly counterfactual - assumptions: 1. Issue spaces are uni-dimensional and 2. Parties are unitary actors whose preferences can be represented by expected utility functions. The main goal here is to provide an example of a two-party model in which parties offer substantially different platforms in equilibrium even though no exogenous asymmetries are assumed. In this example, some voters’ preferences over the 2-dimensional issue space are assumed to exhibit non-convexities and parties evaluate their actions with respect to a set of beliefs on the electorate.Downs model, Games with Incomplete Preferences, Knightian Uncertainty, Uncertainty Aversion, Platform Divergence

A Study on Flouting Maxims in Divergent Novel

This research focuses on flouting maxim in Divergent novel which aim is to find the types and the function of flouting maxim. The researchers used descriptive qualitative research because the researchers strived to analyze and discusses the sentences of utterances which performs flouting maxim in Divergent novel. This research uses pragmatic approach which uses Grice's theory of maxim. The result of this study shows that 21 data which are appropriated with the characteristic of flouting maxim. They consist of 12 flouting maxim of quantity, 2 flouting maxim of quality and 7 flouting maxim of relevance. Based on the data analysis the researchers concluded: the functions for flouting maxim of quantity are to explain more about topic, to stress something and unwillingness to cooperate; the functions for flouting maxim of quality are to show panic, to convince the addressee and to hide something; the functions for flouting maxim of relevance are to change the topic of conversation and to avoid talking about something