Asymptotic expansions for ordinary differential equations , Asymptotic expansions for ordinary differential equations , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Asymptotic expansions for ordinary differential equations

Stability of Plane-Parallel Couette Flow.

This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 (the last such overviews were provided by [231, 371]). Due to the limitations on space, this is in way intended to be an exhaustive survey on the topic.

background or methods

Singular perturbations and time scales in control theory and applications: An overview

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE.

https://iopscience.iop.org/article/10.1088/1751-8113/48/15/153001/pdf

Lectures on differential equations for Feynman integrals

Sequence transformations and their applications

We find a relation between the spectrum of solitons of massive $N=2$ quantum field theories in $d=2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric $N=2$ conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A--D--E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.

/pdf/on-classification-of-n-2-supersymmetric-theories-e-mail-2qtjj8kis0.pdf

Asymptotic expansions for ordinary differential equations

Citations

Stability of Plane-Parallel Couette Flow.

Singular perturbations and time scales in control theory and applications: An overview

Lectures on differential equations for Feynman integrals

Sequence transformations and their applications

On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)

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