Analysis Fact @AnalysisFact
Daily tweets about real and complex analysis and related topics. From @JohnDCook. JohnDCook.com/math Joined December 2009-
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All finite dimensional linear operators are continuous.
Well, waddya know -- looks like a NEW VIDEO! youtube.com/watch?v=5RHSS-…
Well, waddya know -- looks like a NEW VIDEO! youtube.com/watch?v=5RHSS-… https://t.co/G3eCn7qgRu
How faithful can a map be? Quantifying and minimizing distortion. johndcook.com/blog/2023/05/1…
A linear operator is continuous if and only if it maps the unit ball to a bounded set.
Fatou's lemma: the integral of the lim inf is at most the lim inf of the integrals. en.wikipedia.org/wiki/Fatou%27s…
Diagram of relationships between kinds of topological vector space johndcook.com/blog/topologic…
Stoke's theorem: The integral of curl F over a surface equals the integral of F around the boundary of that surface.
Summation by parts is the discrete analog to integration by parts. en.wikipedia.org/wiki/Summation…
Oldies but goldies: I Daubechies, Orthonormal bases of compactly supported wavelets, 1988. Defines orthogonal wavelet bases which generalize the Haar basis. The construction is a mathematical gem that uses the Bezout theorem. fr.wikipedia.org/wiki/Ingrid_Da…
Fixed points of the Fourier transform johndcook.com/blog/2023/03/1…
Octave means johndcook.com/blog/2023/10/1…
New post: Arc length of a general Archimedean spiral johndcook.com/blog/2024/04/1…
'Real analysts cannot do without Fourier, complex analysts cannot do without Laurent, and numerical analysts cannot do without Chebyshev.' -- Lloyd N. Trefethen
How well does an interpolating spline fit a function? johndcook.com/blog/2023/02/1…
Hohmann transfer orbit johndcook.com/blog/2020/06/1…
Algebra Etc. @AlgebraFact
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@AnalysisFact Curiously, this structure appears in the roots of the Reissner-Nordstrom radial function:
@AlgebraFact @JohnDCook That was interesting. Thank you.
@AnalysisFact Reminds me of x.com/normonics/stat…
Things you only notice when you tinker: Fully connected networks with nodes arranged regularly on a circle Evens have filled centers, odds have empty centers
@LorenzoWVilla it's obvious a priori after youve seen it from tinkering
@AnalysisFact This is why people invented differential forms instead of tensors. I mean, why let tensors confuse you with their coordinate systems, when you can instead be confused in all possible coordinate systems at once?
@AnalysisFact Thanks for making my head hurt first thing in the morning today
@AnalysisFact Beware, there's a mistake: there's no 1/n in the right hand side!
Oldies but goldies: W. Fenchel, On conjugate convex functions, 1949. The Legendre-Fenchel transform extends the Legendre transform to arbitrary dimensions. |x|^2/2 is the only fixed point of the transform. en.wikipedia.org/wiki/Legendre_…
Several decibel values are near integers. How does base 10 compare to other bases? johndcook.com/blog/2022/08/1…
Asked to integrate the impossible integral, with passing reference to Man of La Mancha. Another interesting post by John Cook, @AnalysisFact
To integrate the impossible integral johndcook.com/blog/2020/05/1…
@AnalysisFact Grats! It’s a pleasure to follow and read the content you provide here ;)
@AnalysisFact I was always wondering how to find the branch it belongs to, like especially when using Newton’s method to approximate after solving where there is no context given
@AnalysisFact Surely then, it is a reference to the term from chemistry
@AnalysisFact Important: You need also continuity of the function! @JohnDCook arxiv.org/abs/1702.04877
@AnalysisFact Doesn’t this definition also give the alternative formulation that like 0!! is sqrt(2/π)?