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Appendix A - Algebra
Greg Friedman, Texas Christian University
Book:

Singular Intersection Homology

Published online:

18 September 2020

Print publication:

24 September 2020, pp 713-738
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Summary

We review some algebraic topics that are useful throughout the text, including the Koszul sign convention, chain homotopies, algebraic mapping cones, projective modules, Dedekind domains, and signatures of bilinear forms.

Bilinear forms on potential spaces in the unit circle
Part of
Carme Cascante, Joaquín M. Ortega
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 4 / August 2020

Published online by Cambridge University Press:

19 March 2019, pp. 2117-2154

Print publication:

August 2020
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In this paper we characterize the boundedness on the product of Sobolev spaces Hs(𝕋) × Hs(𝕋) on the unit circle 𝕋, of the bilinear form Λb with symbol b ∈ Hs(𝕋) given by
$${{\Lambda}_b} (\varphi, \psi): = \int_{\open T} {\left( {{{( - {\Delta })}^s} + I} \right)(\varphi \psi )(\eta )b(\eta ) {\rm d}\sigma (\eta ).}$$

A note on multiplicative functions on progressions to large moduli
Part of
- Multiplicative number theory
Ben Green
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 1 / February 2018

Published online by Cambridge University Press:

04 December 2017, pp. 63-77

Print publication:

February 2018
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Let f : ℕ → ℂ be a bounded multiplicative function. Let a be a fixed non-zero integer (say a = 1). Then f is well distributed on the progression n ≡ a (mod q) ⊂ {1,…, X}, for almost all primes q ∈ [Q, 2Q], for Q as large as X1/2+1/78−o(1).

Bell Polynomials to the Kadomtsev-Petviashivili Equation with Self-Consistent Sources
Shufang Deng
Journal:

Advances in Applied Mathematics and Mechanics / Volume 8 / Issue 2 / April 2016

Published online by Cambridge University Press:

27 January 2016, pp. 271-278

Print publication:

April 2016
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Bell Polynomials play an important role in the characterization of bilinear equation. Bell Polynomials are extended to construct the bilinear form, bilinear Bäckhand transformation and Lax pairs for the Kadomtsev-Petviashvili equation with self-consistent sources.

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