transform from A J Kohn

Posted on Apr 28, 2020

Below is a long blog post about 50 years of work on the theory and computation of the inverse scattering transform, from A. J. Kohn in 1963 through to my work with H. Dautray in 2014-15 (and others too). It’s not intended as an introduction – see instead “A Short History Of The Inverse Scattering Transform” by L. R. Taylor which appeared in the SIAM Review (SIAM) vol 18 no 3 pp 527–535 September 1976 or downloadable here http://www.math.ucdavis.edu/~taylor/paper_files/PDFs/Taylor76a.pdf . Instead it is meant more for those who are already familiar with this topic but want to learn more detail than they can get out of Wikipedia! I started working on the theory of IST in August 1963 at Imperial College under Professor David Tuckerman after graduating from Oxford University that July having completed Part II Mathematics & Physics there. As part of the coursework requirement for this degree we had studied diffraction problems: in particular, reflection off two plane parallel mirrors with different refractive indices. From his office door where he worked all day and every evening, Tuckerton would come downstairs into the lounge area between our rooms and mine once he was ready to eat dinner around eight pm each night and tell us what paper he read today. One of these papers turned out to be very influential for me: “On the Theory of Dispersed Waves Reflected from Two Plane Parallel Mirrors With Different Indexes”, written by the late Sir Arnold Sommerfeld, the famous German theoretical physicist, in English so that it could appear in the Zeitschrift für Physik volume CXLVII published in Berlin in March 1931. This article gave a beautiful analytical solution to such a problem; the most interesting bit being the case when one object has index n=1 and the other has index m>n. We were left wondering how you might generalise the method if, say, both objects have any arbitrary values of their indices. If only such methods existed back then….. Soon enough we learned that such a thing did exist thanks to a series of lectures given by Alfred Schildkraut during April of 1956. These talks were later expanded upon and revised in book form by Gerd Fischer [GF] and appeared as Inverse Problems: Their Formulation And Solution in December 1957 by Springer Verlag publishers. It took us some time to understand all parts of these papers properly especially since we had little access to books like they used to be made before the advent of computers; but eventually everyone in the department got up to speed sufficiently well Below is a long blog post about 2018 and my plans for the future. I know that many of you don’t want to read this, but it would mean a lot if at least one person took time out of their day to tell me why they didn’t like what was said here so I can improve in the coming years! I hope everyone had an amazing holiday season. Mine was fun and relaxed with very little stress, which made it even better than expected! It feels good to be home after two months away on tour though. There are some things I want to share from last year before moving forward into 2019… In 2017, I released four albums: The New Beginning EP; Moments That Make Us Who We Are Volumes One & Two; and This Is Alive (with Derek Minor). In total those projects sold over 35k units combined worldwide – not bad considering how young I am as well as releasing them all independently. They were also critically acclaimed by media such as Hypebeast who called “This Is Alive” album-of–the week while Noisey gave Volume One five stars saying that “it will make you think twice about everything else being pushed down your throat”. The first half of 2018 brought us more music when I dropped my first ever full length studio project titled ‘Closer To You.’ This record was entirely produced by Grammy winning producer Joel Hamilton whose credits include work with Bob Dylan, Tom Waits, TV On The Radio etcetera amongst others – proving once again just how talented he truly is both behind microphone AND soundboard alike! Not only did we release another single off Closer To You entitled “Pray For Me,” which has racked up millions upon millions views since its release date back in June 2016 alone – but our most recent track featuring Johnnyswim hit number seven on iTunes Top Songs chart shortly after dropping earlier this month too!! Overall sales have surpassed expectations thanks largely due to strong word-of-mouth marketing campaigns launched via social media platforms including Instagram where fans could purchase limited edition merchandising items ranging anywhere between $4-$5 depending on size/quantity desired during preorder period leading up until launch date itself.” Below is a long blog post about 2015 and what happened, but before that I wanted to make sure you read the two articles below from today. The first article is by James Rickards called “Bernanke’s Great Depression” - it talks about his book “The New York Times best seller The New Case for Gold”, which he said sold more than any other economics or finance title in history since publication on September 9th. He also says it has become required reading at the Federal Reserve Board of Governors and at every major central bank around the world. It was just released as an audiobook, and Jim believes this will be even better received because of the narrator’s voice. You can purchase it here: http://amzn.to/1HgYf6R . The second piece is written by my friend David Galland who wrote “Learning From Ben Bernanke”. Here are some excerpts if you don’t have time to read all three pages… Here’s one last quote from Ben that should send chills down your spine…“If we had done something like quantitative easing earlier – I mean, when Lehman failed [in September 2008] – then I think the crisis would not have been as bad.” In fact, he goes so far as to say “I wish we had done QE3” back in late-2011 (when stock markets were plunging). That’s right; despite the overwhelming evidence showing how destructive easy money policies are, with their ability to inflate asset bubbles, distort capital allocation decisions, create moral hazard problems among borrowers, encourage risk-taking across many different areas of the economy, and ultimately lead to financial market instability followed by economic downturns, Ben still thinks they’re great ideas! And so does Janet Yellen, whom he unsuccessfully pushed into the Fed chairmanship position after she was passed up once during President Obama’s initial search process due to her perceived lack of leadership qualities. So there you go. Even though Mr. Bernanke is now out of office, he remains very much engaged in the conversation regarding monetary policy going forward, and continues to advocate the use of extraordinary measures including negative interest rates. If anything, he may well have learned nothing from the experience of the past seven years, especially given recent comments suggesting that the next recession could come as soon as early 2017." I am happy to announce our new partnership with Global Financial Advisor, Inc., a company founded and run by Dr. Mike Cobb, PhD in Economic History, MBA, CFP®, AIF® , CLU, ChFC and author of the books “Understanding Bit Below is a long blog post about 10 things that I am learning in the midst of my life. I have been on this path for over two years now and it has not always easy, but it’s definitely worth it! Sometimes we get so caught up in what we don’t want to be doing or who we don’t want to become…but if you take time to reflect upon yourself then maybe just one little thing will shift your perspective into positivity again. This article might give some insight as well: https://www.google.com/amp/s/www .youtube . com / watch?v=hRX9x7EAQYk%3Famp&gts = 1 > 5 Minutes To Change Your Life – YouTube

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