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Books by Pat Muldowney
Theory of Integration, 1962
Ralph Henstock published four books on integration theory. The first was "Theory of Integration",... more Ralph Henstock published four books on integration theory. The first was "Theory of Integration", first published in 1962 and reprinted in 1963. It includes the signature property of the gauge (or generalized Riemann) integral, that every derivative function is integrable. It provides theorems for taking limits (including differentiation) under the integral sign, Fubini's theorem, and a theory of variation. The other books are "Linear Analysis" (1967), "Lectures on the Theory of Integration" (1988), and "The General Theory of Integration" (1991).
To read them, here are links to Henstock's four books:
Lectures on the Theory of Integration, by Ralph Henstock, 1988
This book is an update by Henstock of his 1962 book "Theory of Integration" (reprinted 1963). It ... more This book is an update by Henstock of his 1962 book "Theory of Integration" (reprinted 1963). It includes necessary and sufficient conditions for the integrability of the limit of integrable functions. Notation and proofs are improved. The book was scanned and uploaded by P. Muldowney in 2023.
Henstock's four books on the theory of integration can be read in archive.org
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics, 2021
GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley & Sons,... more GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley & Sons, 2021
A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus
Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics.
Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author’s previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable.
Redmondism is a persistent element throughout Irish politics. The picture presented to us is of a... more Redmondism is a persistent element throughout Irish politics. The picture presented to us is of a thorough-going democrat, a man of peace, almost like Gandhi. Gandhi supported Britain's Great War, didn't he?
But there is a great big black hole in the centre of this picture. The elephant in the room is the mob violence used by Redmond to capture and hold his leading position in Irish politics.
This is a Supplement to the book "A Modern Theory of Random Variation" (Wiley, 2012). It contains... more This is a Supplement to the book "A Modern Theory of Random Variation" (Wiley, 2012). It contains corrections and clarification of topics covered in the text. The most significant error is Theorem 63 (page 174 of the book) which is false; and this Supplement deals with the issues arising from the error. The Supplement also contains a listing of typographical errors in the book.
Proceedings of the XII Summer Symposium in Real Analysis (1988). Co-edited with P. Bullen, P.-Y... more Proceedings of the XII Summer Symposium in Real Analysis (1988).
Co-edited with P. Bullen, P.-Y. Lee, J.L. Mawhin, W.F. Pfeffer.
Authors: P.S. Bullen, Chew T.-S., S.F.L. de Foglio, C. Pierson-Gorez, R. Henstock, J. Kurzweil & J. Jarnik, S. Leader, Lee P.-Y., P. Maritz, P. Muldowney, P. Mikusinski & K. Ostaszewski, W.F. Pfeffer, V.A. Skvortsov, J.D. Stegman.
Published 1990 by Springer-Verlag.
American Mathematical Society Special Session on Non-absolute Integration University of Toronto... more American Mathematical Society
Special Session on Non-absolute Integration
University of Toronto, Canada,
September 23-24, 2000
Editors: M. Federson, P. Muldowney, E. Talvila
http://www.emis.de/proceedings/Toronto2000/
This material consists of four chapters of a manuscript by Ralph Henstock, which remained unpubli... more This material consists of four chapters of a manuscript by Ralph Henstock, which remained unpublished in the Henstock Archive at the University of Ulster. Edited and typed up by Pat Muldowney in 2016.
These are the notes of lectures given by Ralph Henstock at the New University of Ulster in 1970-7... more These are the notes of lectures given by Ralph Henstock at the New University of Ulster in 1970-71.
Whole number 247 of Scientiae Mathematicae Japonicae, Vo. 67, No. 1, Special issue in memory of R... more Whole number 247 of Scientiae Mathematicae Japonicae, Vo. 67, No. 1, Special issue in memory of Ralph Henstock, published January 2008.
Poems of seventeenth century author and soldier Piaras Feiritéar (Pierce Ferriter). Includes an a... more Poems of seventeenth century author and soldier Piaras Feiritéar (Pierce Ferriter). Includes an account of the so-called rebellion of 1641 and its Cromwellian outcome, written by Brendan Clifford.
Published in 1999 by Aubane Historical Society, using traditional Gaelic script.
http://aubanehistoricalsociety.org/
Vision poems of Eoghan Rua Ó Súilleabháin (Owen Roe O'Sullivan) c. 1748 - 1784, with English tran... more Vision poems of Eoghan Rua Ó Súilleabháin (Owen Roe O'Sullivan) c. 1748 - 1784, with English translations.
(Volume 1 of Works of ERÓS)
Includes "Ireland in the 18th Century: revisionist history under the spotlight", by Brendan Clifford.
Published 2002 by Aubane Historical Society
http://aubanehistoricalsociety.org/
Volume 2 of the works of Eoghan Rua Ó Súilleabháin. Published in 2009 by Aubane Historical Socie... more Volume 2 of the works of Eoghan Rua Ó Súilleabháin.
Published in 2009 by Aubane Historical Society
http://aubanehistoricalsociety.org/
Re-print of the 1795 United Irish publication by the Belfast Northern Star, with a profile of Pat... more Re-print of the 1795 United Irish publication by the Belfast Northern Star, with a profile of Patrick Lynch and Charlotte Brooke.
Published by Athol Books, 1999.
http://www.atholbooks.org/
Re-print, with English translation of Mícheál Ó Siochfhradha's Stair-sheanchas Éireann - a narrat... more Re-print, with English translation of Mícheál Ó Siochfhradha's Stair-sheanchas Éireann - a narrative history of Ireland from prehistoric times until the present. It gives a lucid, concise account of all the major events over two millennia. It is the perfect introduction to the course of Irish history, and for many years it was a standard school textbook, in Irish, at Secondary level.
Published by Aubane Historical Society, 2005.
http://aubanehistoricalsociety.org/
At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County Offaly... more At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County Offaly, and their house was burned. The people who were shot were not Irish "rebels" or uninvolved civilians. They were loyalist Protestants who had chosen to take up arms against the democratically elected Irish government.
In 2007 the Irish broadcasting agency RTÉ produced a television documentary ("The Killings at Coolacrease") which portrayed the executions of the two Pearson brothers as a sectarian anti-Protestant atrocity in furtherance of a land-grab, as part of an ethnic cleansing drive by the Irish independence movement against an ethnic minority. RTÉ claimed that their film was based on documentary evidence.
This book shows that the film-makers could not substantiate their case, that they did not possess the documentary evidence they claimed, and that their film was spurious propaganda.
Published in 2008 by Aubane Historical Society.
http://aubanehistoricalsociety.org/
Papers by Pat Muldowney
Political Freedom and the Siege of Derry, 1997
Was the Closing of the Gates the starting point of Constitutional Government and Religious Liberty?
Theory of Integration, 1962
Ralph Henstock published four books on integration theory. The first was "Theory of Integration",... more Ralph Henstock published four books on integration theory. The first was "Theory of Integration", first published in 1962 and reprinted in 1963. It includes the signature property of the gauge (or generalized Riemann) integral, that every derivative function is integrable. It provides theorems for taking limits (including differentiation) under the integral sign, Fubini's theorem, and a theory of variation. The other books are "Linear Analysis" (1967), "Lectures on the Theory of Integration" (1988), and "The General Theory of Integration" (1991).
To read them, here are links to Henstock's four books:
Lectures on the Theory of Integration, by Ralph Henstock, 1988
This book is an update by Henstock of his 1962 book "Theory of Integration" (reprinted 1963). It ... more This book is an update by Henstock of his 1962 book "Theory of Integration" (reprinted 1963). It includes necessary and sufficient conditions for the integrability of the limit of integrable functions. Notation and proofs are improved. The book was scanned and uploaded by P. Muldowney in 2023.
Henstock's four books on the theory of integration can be read in archive.org
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics, 2021
GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley & Sons,... more GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley & Sons, 2021
A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus
Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics.
Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author’s previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable.
Redmondism is a persistent element throughout Irish politics. The picture presented to us is of a... more Redmondism is a persistent element throughout Irish politics. The picture presented to us is of a thorough-going democrat, a man of peace, almost like Gandhi. Gandhi supported Britain's Great War, didn't he?
But there is a great big black hole in the centre of this picture. The elephant in the room is the mob violence used by Redmond to capture and hold his leading position in Irish politics.
This is a Supplement to the book "A Modern Theory of Random Variation" (Wiley, 2012). It contains... more This is a Supplement to the book "A Modern Theory of Random Variation" (Wiley, 2012). It contains corrections and clarification of topics covered in the text. The most significant error is Theorem 63 (page 174 of the book) which is false; and this Supplement deals with the issues arising from the error. The Supplement also contains a listing of typographical errors in the book.
Proceedings of the XII Summer Symposium in Real Analysis (1988). Co-edited with P. Bullen, P.-Y... more Proceedings of the XII Summer Symposium in Real Analysis (1988).
Co-edited with P. Bullen, P.-Y. Lee, J.L. Mawhin, W.F. Pfeffer.
Authors: P.S. Bullen, Chew T.-S., S.F.L. de Foglio, C. Pierson-Gorez, R. Henstock, J. Kurzweil & J. Jarnik, S. Leader, Lee P.-Y., P. Maritz, P. Muldowney, P. Mikusinski & K. Ostaszewski, W.F. Pfeffer, V.A. Skvortsov, J.D. Stegman.
Published 1990 by Springer-Verlag.
American Mathematical Society Special Session on Non-absolute Integration University of Toronto... more American Mathematical Society
Special Session on Non-absolute Integration
University of Toronto, Canada,
September 23-24, 2000
Editors: M. Federson, P. Muldowney, E. Talvila
http://www.emis.de/proceedings/Toronto2000/
This material consists of four chapters of a manuscript by Ralph Henstock, which remained unpubli... more This material consists of four chapters of a manuscript by Ralph Henstock, which remained unpublished in the Henstock Archive at the University of Ulster. Edited and typed up by Pat Muldowney in 2016.
These are the notes of lectures given by Ralph Henstock at the New University of Ulster in 1970-7... more These are the notes of lectures given by Ralph Henstock at the New University of Ulster in 1970-71.
Whole number 247 of Scientiae Mathematicae Japonicae, Vo. 67, No. 1, Special issue in memory of R... more Whole number 247 of Scientiae Mathematicae Japonicae, Vo. 67, No. 1, Special issue in memory of Ralph Henstock, published January 2008.
Poems of seventeenth century author and soldier Piaras Feiritéar (Pierce Ferriter). Includes an a... more Poems of seventeenth century author and soldier Piaras Feiritéar (Pierce Ferriter). Includes an account of the so-called rebellion of 1641 and its Cromwellian outcome, written by Brendan Clifford.
Published in 1999 by Aubane Historical Society, using traditional Gaelic script.
http://aubanehistoricalsociety.org/
Vision poems of Eoghan Rua Ó Súilleabháin (Owen Roe O'Sullivan) c. 1748 - 1784, with English tran... more Vision poems of Eoghan Rua Ó Súilleabháin (Owen Roe O'Sullivan) c. 1748 - 1784, with English translations.
(Volume 1 of Works of ERÓS)
Includes "Ireland in the 18th Century: revisionist history under the spotlight", by Brendan Clifford.
Published 2002 by Aubane Historical Society
http://aubanehistoricalsociety.org/
Volume 2 of the works of Eoghan Rua Ó Súilleabháin. Published in 2009 by Aubane Historical Socie... more Volume 2 of the works of Eoghan Rua Ó Súilleabháin.
Published in 2009 by Aubane Historical Society
http://aubanehistoricalsociety.org/
Re-print of the 1795 United Irish publication by the Belfast Northern Star, with a profile of Pat... more Re-print of the 1795 United Irish publication by the Belfast Northern Star, with a profile of Patrick Lynch and Charlotte Brooke.
Published by Athol Books, 1999.
http://www.atholbooks.org/
Re-print, with English translation of Mícheál Ó Siochfhradha's Stair-sheanchas Éireann - a narrat... more Re-print, with English translation of Mícheál Ó Siochfhradha's Stair-sheanchas Éireann - a narrative history of Ireland from prehistoric times until the present. It gives a lucid, concise account of all the major events over two millennia. It is the perfect introduction to the course of Irish history, and for many years it was a standard school textbook, in Irish, at Secondary level.
Published by Aubane Historical Society, 2005.
http://aubanehistoricalsociety.org/
At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County Offaly... more At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County Offaly, and their house was burned. The people who were shot were not Irish "rebels" or uninvolved civilians. They were loyalist Protestants who had chosen to take up arms against the democratically elected Irish government.
In 2007 the Irish broadcasting agency RTÉ produced a television documentary ("The Killings at Coolacrease") which portrayed the executions of the two Pearson brothers as a sectarian anti-Protestant atrocity in furtherance of a land-grab, as part of an ethnic cleansing drive by the Irish independence movement against an ethnic minority. RTÉ claimed that their film was based on documentary evidence.
This book shows that the film-makers could not substantiate their case, that they did not possess the documentary evidence they claimed, and that their film was spurious propaganda.
Published in 2008 by Aubane Historical Society.
http://aubanehistoricalsociety.org/
Political Freedom and the Siege of Derry, 1997
Was the Closing of the Gates the starting point of Constitutional Government and Religious Liberty?
arXiv: Classical Analysis and ODEs, 2017
In generalized Riemann integration (or Henstock-Kurzweil integration), the formation of the parti... more In generalized Riemann integration (or Henstock-Kurzweil integration), the formation of the partitions used in Riemann sum construction is regulated by rules known as gauges. This article examines gauges for multi-dimensional Cartesian product domains.
The theory of integration (including measure) is the basis for the study of probability and rando... more The theory of integration (including measure) is the basis for the study of probability and random variation. Thus Henstock’s Riemann-type integration theory has relevance to our understanding of random variation. Henstock addressed this issue in many of his published works, in which he gave interpretations of probability, of the statistical analysis of data, and of random processes. His analysis of Feynman’s nonabsolute integrals in quantum mechanics brings this subject properly into the domain of random variation. http://www.jams.or.jp/scm/contents/e-2007-6/2007-59.pdf
arXiv: Pricing of Securities, 2015
An analytic method for pricing American call options is provided; followed by an empirical method... more An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in "A Modern Theory of Random Variation", by Patrick Muldowney, 2012.
arXiv: Classical Analysis and ODEs, 2016
Ralph Henstock (1923 - 2007), with (independently) Jaroslav Kurzweil, was the originator of the R... more Ralph Henstock (1923 - 2007), with (independently) Jaroslav Kurzweil, was the originator of the Riemann-complete or generalized Riemann integral. This material consists of four chapters of a book proposal to Cambridge University Press, which remained unpublished in the Henstock Archive at the University of Ulster. Section 5 presents a novel approach to taking limits under the integral sign, and goes on to place the traditional monotone and dominated convergence theorems of Lebesgue in this new context.
Irish Mathematical Society Bulletin, 2017
Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are ce... more Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are certain areas of the subject where this theorem is deficient. Deeper criteria for convergence of integrals are described in this article.
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics, 2021
GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley &am... more GAUGE INTEGRAL STRUCTURES FOR STOCHASTIC CALCULUS AND QUANTUM ELECTRODYNAMICS, John Wiley & Sons, 2021 A stand-alone introduction to specific integration problems in the probabilistic theory of stochastic calculus Picking up where his previous book, A Modern Theory of Random Variation, left off, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics introduces readers to particular problems of integration in the probability-like theory of quantum mechanics. Written as a motivational explanation of the key points of the underlying mathematical theory, and including ample illustrations of the calculus, this book relies heavily on the mathematical theory set out in the author’s previous work. That said, this work stands alone and does not require a reading of A Modern Theory of Random Variation in order to be understandable.
Mathematica Bohemica, 2006
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Real Analysis Exchange, 2000
The classical Black-Scholes-Merton method for pricing European call options uses the Itô calculus... more The classical Black-Scholes-Merton method for pricing European call options uses the Itô calculus to model the processes involved. We show how to model stochastic process using Henstock integrands instead of Itô differentials (or stochastic integrals), and we show how to derive the Black-Scholes partial differential equation and pricing formulae using elementary methods. 2 2σ 2 (t j − t j−1) (t j − t j−1) dx j ,
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best ef... more Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representation or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.
Lecture Notes in Mathematics, 1990
We show how to define a gauge, and hence an integral, in function space. Applying the theory to F... more We show how to define a gauge, and hence an integral, in function space. Applying the theory to Feynman integration, we show that the Feynman integrals are path integrals.
The theory of integration (including measure) is the basis for the study of probability and rando... more The theory of integration (including measure) is the basis for the study of probability and random variation. Thus Henstock's Riemann-type integration theory has relevance to our understanding of random variation. Henstock addressed this issue in many of his published works, in which he gave interpretations of probability, of the statistical analysis of data, and of random processes. His analysis of Feynman's nonabsolute integrals in quantum mechanics brings this subject properly into the domain of random variation.
"At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County ... more "At the end of the Irish War of Independence, two brothers were shot in Coolacrease, County Offaly, and their house was burned. The people who were shot were not Irish "rebels" or uninvolved civilians. They were loyalist Protestants who had chosen to take up arms against the democratically elected Irish government. In 2007 the Irish broadcasting agency RTÉ produced a television documentary ("The Killings at Coolacrease") which portrayed the executions of the two Pearson brothers as a sectarian anti-Protestant atrocity in furtherance of a land-grab, as part of an ethnic cleansing drive by the Irish independence movement against an ethnic minority. RTÉ claimed that their film was based on documentary evidence. This book shows that the film-makers could not substantiate their case, that they did not possess the documentary evidence they claimed, and that their film was spurious propaganda. Published in 2008 by Aubane Historical Society. http://aubanehistoricalsociety.org/"
nancial asset or security is a claim to some payment. It may take the physical form of a piece of... more nancial asset or security is a claim to some payment. It may take the physical form of a piece of paper on which a legal contract specifying the claim is written. Assets are frequently traded | bought and sold. We are concerned with establishing the monetary value, here and now, of such entities. Because if their correct monetary value is unknown, they cannot be traded fairly. A forward contract is a simple kind of derivative asset. It is an agreement to trade a security at a future time T for a price K called the delivery price. The party who is going to buy is said to hold the long position in the forward contract, and the party who is going to sell holds the short position. At the time of writing the forward contract, no money changes hands between the two parties, so the initial value of the forward is zero. But at some time t between the time of writing the contract and its time of expiry, the underlying security value may increase or decrease. So the value of the long position...
Journal of Applied Analysis, 2002
Using arguments which apply equally well to the study of Brownian motion and Feynman path integra... more Using arguments which apply equally well to the study of Brownian motion and Feynman path integrals, the relationship between two expressions which arise in derivative asset pricing theory is examined. Detailed explanations are given for some of the key points in the theory of Henstock integrals in function spaces.
Bulletin of the London Mathematical Society, 2006
Bulletin of the London Mathematical Society, 2010
Ralph Henstock 〈1〉 was born in the coal-mining village of Newstead, near Nottingham, UK, on 2 Jun... more Ralph Henstock 〈1〉 was born in the coal-mining village of Newstead, near Nottingham, UK, on 2 June 1923; the only child of mineworker and former coalminer William Henstock and Mary Ellen Henstock (née Bancroft). On the Henstock side, he was descended from ...
Guns for Democracy's Table: A Review of the Physical Force Unionism of the Ulster Unionist P... more Guns for Democracy's Table: A Review of the Physical Force Unionism of the Ulster Unionist Party. Pat Muldowney North West Labour Publications, 1998.
https://sites.google.com/site/nicclabour/campaign-for-labour-representation?authuser=0
The idea is to try to demonstrate how to use the mathematical techniques of A Modern Theory of Ra... more The idea is to try to demonstrate how to use the mathematical techniques of A Modern Theory of Random Variation in exposition of the quantum mechanics described in Feynman-Hibbs, especially where the mathematical formulations of the latter are problematic. A new edition of Feynman-Hibbs, emended by D.F. Styer, was published by Dover in 2010.
To read, go to:
https://sites.google.com/site/stieltjescomplete/home/notes-on-feynman-hibbs
These are Ralph Henstock's lectures in integration theory, from notes taken by Pat Muldowney in 1... more These are Ralph Henstock's lectures in integration theory, from notes taken by Pat Muldowney in 1970-71. Notes edited by Pat Muldowney in 2015.