Search results for Abstract analysis

14 - The Hypergeometric Function
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 293-315
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Computing the fundamental group of a higher-rank graph
Part of
- Categories with structure
- (Co)homology theory
Sooran Kang, David Pask, Samuel B.G. Webster
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 3 / August 2021

Published online by Cambridge University Press:

26 August 2021, pp. 650-661
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about higher-rank graphs when we show that the abelianization of the fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.

3 - Continuous Functions and Uniform Convergence
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 40-57
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

7 - The Expansion of Functions in Infinite Series
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 125-152
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

13 - The Zeta-Function of Riemann
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 276-292
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

15 - Legendre Functions
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 316-354
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

23 - Ellipsoidal Harmonics and Lamé’s Equation
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 567-610
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

21 - The Theta-Functions
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 486-516
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Contents
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp v-xvi
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Preface to the First Edition
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp xxvi-xxvi
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation
Part of
Lihua Deng, Haifeng Shang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 5 / October 2022

Published online by Cambridge University Press:

26 August 2021, pp. 1109-1138

Print publication:

October 2022
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in $\mathbb {R}^{d}$ with $d=2\ or\ 3$. By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in $\mathbb {R}^{2}$. Moreover, we obtain the global regularity for fractional hyperviscosity case in $\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.

Part II - The Transcendental Functions
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 241-242
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

16 - The Confluent Hypergeometric Function
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 355-372
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

18 - The Equations of Mathematical Physics
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 407-425
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

4 - The Theory of Riemann Integration
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 58-80
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

5 - The Fundamental Properties of Analytic Functions; Taylor’s, Laurent’s and Liouville’s Theorems
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 81-109
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Author index
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 648-651
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Subject index
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp 652-668
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Frontmatter
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp i-iv
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Preface to the Fifth Edition
E. T. Whittaker, G. N. Watson
Edited by Victor H. Moll, Tulane University, Louisiana
Book:

A Course of Modern Analysis

Published online:

07 August 2021

Print publication:

26 August 2021, pp xxi-xxii
- Chapter
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Abstract analysis

Refine search

Refine search

Actions for selected content:

25994 results in Abstract analysis

14 - The Hypergeometric Function

Computing the fundamental group of a higher-rank graph

3 - Continuous Functions and Uniform Convergence

7 - The Expansion of Functions in Infinite Series

13 - The Zeta-Function of Riemann

15 - Legendre Functions

23 - Ellipsoidal Harmonics and Lamé’s Equation

21 - The Theta-Functions

Contents

Preface to the First Edition

Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation

Part II - The Transcendental Functions

16 - The Confluent Hypergeometric Function

18 - The Equations of Mathematical Physics

4 - The Theory of Riemann Integration

5 - The Fundamental Properties of Analytic Functions; Taylor’s, Laurent’s and Liouville’s Theorems

Author index

Subject index

Frontmatter

Preface to the Fifth Edition

Abstract analysis

Refine search

Refine search

Actions for selected content:

Save Search

25994 results in Abstract analysis