Tom Copeland
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Registered User
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Apr 16 |
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Does the derivative of log have a Dirac delta term? @Liviu, anticipating? Check the dates. Dirac was famous for his terseness, originality, and ingenuity, as reflected in his presentation. |
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Apr 16 |
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Does the derivative of log have a Dirac delta term? @Terry, given the earlier stated answers below, your comment seems at best redundant. Maybe you could expand on it as an answer and provide some new details for those not already familiar with the theory of distributions |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? Really, weren't the results for the limiting case of the derivative of the log worked out fairly rigorously by Cauchy and Poisson in their work on potential theory long before 20'th century mathematicians put a formal dress on them? |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? Dirac would have known all these results from electrostatics to corroborate his assertion. |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? Terry, you're missing a derivative. d/dz log(z)=1/z then look at limits as in the Poisson kernel. |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? Dirac's bachelor's degree was in electrical engineering at a British university, so I'm sure he was familiar with and influenced by Heaviside's style of mathematics. |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? For those who may be a little confused about the absolute value sign, just switch to polar coordinates and restrict to the real line. |
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Apr 15 |
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Does the derivative of log have a Dirac delta term? I'm sure Dirac was thinking that ln(x)=ln|x|+i H(-x)π, where H(x) is the Heavside step function. |
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Apr 10 |
awarded | ● Popular Question |
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Jan 16 |
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Motivation of Virasoro algebra @Muon : Actually, you mean $z^{n+1}$. I'll expand on my comment later. I think a good answer to your questions would involve combining ideas in Khesin and Wendt's The Geometry of Infinite-Dimensional Groups, Ovsienko and Tabachnikov's Projective Differential Geometry Old and New, and the book I cited earlier in a tight narrative, but that's beyond me at the moment. |
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Jan 12 |
awarded | ● Yearling |
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Jan 9 |
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History of the Sampling Theorem @Eremenko : the paper you cite in the edit is precisely the one in my answer. Why the repetition? Luke in the cited paper states, "The first scientist to formulate the sampling theorem precisely and apply it to problems of communication engineering is probably V. A. Kotelnikov." (1933) |
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Jan 9 |
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Hopf Algebra for a physicist For a physicist with an interest in QED perhaps a good place to start is Sec. 3.3 Fusion, Splitting, and Hopf Algebras in E. Zeidler's book Quantum Field Theory II Quantum Electrodynamics. |
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Jan 7 |
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History of the Sampling Theorem Don't confuse the son J. M. (1929, and later in his book in 1935) with the father E.T. (1915) who is actually given the majority of the credit for a bandwidth analysis. (I guess you see what you look for.) If you're concerned about accreditation to Russians, you might want to confirm (or not) the chronology at the website linked to in my answer which notes Kotelnikov (1930), as well as other nationalities (Ogura, 1920). |
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Dec 27 |
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Motivation of Virasoro algebra As a first step at understanding the relations, I always recall that $exp(-c \cdot z^2d/dz)f(z)=exp[c \cdot d/d(1/z)]f(1/(1/z))=f(1/(c+1/z))=f(z/(cz+1)),$ a special conformal transformation. Note $zd/dz=d/d(ln(z))$ for the dilatation. |
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Dec 27 |
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Motivation of Virasoro algebra Try Ch. 9: Conformal Invariance Sec. 9.1: Energy momentum tensor-Virasoro algebra of the book Statistical Field Theory Vol. 2 by Itzykson and Drouffe. Maybe you could work around pg. 514 on translations, complex dilatations, and special conformal transformations related to $d/dz, zd/dz,$ and $z^2d/dz$.The central charge is discussed in the next sub-section from a physical and mathematical perspective. |
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Dec 26 |
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The Dedekind Eta Function in Physics Final update |
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Dec 26 |
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The Dedekind Eta Function in Physics deleted 3 characters in body |
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Dec 26 |
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The Dedekind Eta Function in Physics More specifics |
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Dec 24 |
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The Dedekind Eta Function in Physics Deleted remark confusing Dirichlet eta with Dedekind |
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Dec 24 |
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The Dedekind Eta Function in Physics Specifics |
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Dec 24 |
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The Dedekind Eta Function in Physics New info |
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Dec 21 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) I wonder if the first curve could be lifted off the plane onto a double torus with one torus nested inside the other but sharing its circle of max radius with that of the other torus. |
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Dec 20 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) We're essentially looking at solns. around $z=0$ and infinity of the eigenfunction eqn. $\exp(t\cdot z^2 \frac{\partial }{\partial z}) f(z)=f[z/(-tz+1)]=\epsilon(t) f(z)$ for some $t$. The simplest case being $f(z)=\exp(-\lambda/z)$. |
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Dec 20 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) Hi Dan--the results above depend on $\eta$ being a modular form. I don't see how to get the necessary periodicity with any polynomial under shear transformations. Scan my notes on Infinigens at my little "arxiv website" for details. |
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Dec 20 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) Extra info |
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Dec 19 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) Refined discussion |
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Dec 17 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) Added another figure |
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Dec 17 |
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A Dedekind Eta trajectory / horocyclic flow (Reference request) Better graphics |
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Dec 17 |
asked | A Dedekind Eta trajectory / horocyclic flow (Reference request) |
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Dec 11 |
awarded | ● Disciplined |
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Dec 7 |
revised |
The Dedekind Eta Function in Physics added 463 characters in body |
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Dec 5 |
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Conjugation: The nature of the beast--spawn, perspectives, broadest formulation Quandles and racks would have been a good example of an answer. |
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Dec 3 |
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The Dedekind Eta Function in Physics deleted 1 characters in body |
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Dec 3 |
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The Dedekind Eta Function in Physics added 402 characters in body |
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Dec 3 |
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The Dedekind Eta Function in Physics added link, fixed typos |
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Dec 3 |
asked | The Dedekind Eta Function in Physics |
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Nov 29 |
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Geometric / physical / probabilistic interpretations of Riemann zeta(n>1)? See also Itzykson and Zuber's "Matrix Integration and Combinatorics of the Modular Group" lpthe.jussieu.fr/~zuber/MesPapiers/iz_CMP90.pdf |
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Nov 28 |
awarded | ● Good Question |
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Nov 27 |
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Are there other nice math books close to the style of Tristan Needham? added 179 characters in body |
