katz
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Registered User
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1d |
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fundamental class is the sum of simplices of triangulation of the manifold? added 37 characters in body |
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2d |
answered | fundamental class is the sum of simplices of triangulation of the manifold? |
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May 20 |
answered | What’s the definition of continuous of set-valued functions? |
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May 13 |
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Isoperimetric inequality on a Riemannian sphere Frankel and I constructed metrics on a disk such that curve length grows very rapidly and the "obvious" curves in fact get very long before much of the area is swept out. Liokumovich et al. recently published some generalisations of this. It is possible that even the weaker version of your question admits of counterexamples. |
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May 13 |
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Isoperimetric inequality on a Riemannian sphere Just to make sure I understand what you are looking for: it seems plausible that by applying coarea to a suitable distance function one might be able to get a non-optimal bound similar to the one you asked for. Are you interested in the optimal value $2\pi$ for boundary length, or does the coarea argument get stuck on diameter issues? |
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May 12 |
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Isoperimetric inequality on a Riemannian sphere Can elaborate why you formulated the question in terms of "area between pi and 2pi" rather than in terms of the Cheeger constant, and how this might affect the answer? |
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May 10 |
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Leibnizian calculus textbook link for table of contents |
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May 10 |
answered | Leibnizian calculus textbook |
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May 10 |
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Leibnizian calculus textbook formatting as separate answer |
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May 8 |
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Leibnizian calculus textbook tagged NSA |
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May 8 |
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Leibnizian calculus textbook stroyan's book on multivariable |
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Apr 28 |
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Can nonstandard analysis be used to prove results in constructive or computable analysis? Thanks for a very interesting answer. Is there a home for this "Antonio Montalbán and me showed"? |
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Apr 24 |
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Intuitionistic logic as quantization of classical logic? tag |
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Apr 24 |
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Intuitionistic logic as quantization of classical logic? I am not too familiar with this material and am curious to find out more. Can you summarize why one might think of a Galois connection more in terms of intuitionistic logic as a quantisation of classical logic than vice versa, for example? The wiki page is written in such general terms that it is hard to tell how something like this could be applied. |
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Apr 23 |
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Intuitionistic logic as quantization of classical logic? Very interesting. I looked at the wiki article on "Galois connection" (incidentally, you could fix the link). Is this notion related to "equivalence of categories"? What would be a concrete example to illustrate the power of this notion as a means of clarifying the theory? |
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Apr 23 |
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Intuitionistic logic as quantization of classical logic? added phil tag |
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Apr 23 |
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Intuitionistic logic as quantization of classical logic? I note that in your "Practical Foundations" you use a similar analogy: "In classical logic, as in classical physics, particles enact a logical script, but neither they nor the stage on which they perform are permanently altered by the experience. In the modern view, matter and its activity are created together, and are interchangeable (the observer also affects the experiment by the strength of the meta-logic)." |
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Apr 23 |
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Intuitionistic logic as quantization of classical logic? Here is a relevant quote from MacTutor: "When the Dutch Mathematical Association announced a prize question in 1927 they gave Heyting an ideal topic on which to compete. They asked for a formalisation of Brouwer's intuitionist theories and Heyting's outstanding essay was awarded the prize in 1928. This essay was then polished and expanded by Heyting and published in 1930." See www-gap.dcs.st-and.ac.uk/~history/Biographies/… |
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Apr 23 |
asked | Intuitionistic logic as quantization of classical logic? |
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Apr 22 |
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In what ways did Leibniz’s philosophy foresee modern mathematics? added example from Levey |
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Apr 22 |
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Curvature of contour lines of a scalar field @Robert: thanks for your comments. Which reference would you cite for this? |
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Apr 22 |
accepted | Curvature of contour lines of a scalar field |
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Apr 21 |
answered | Curvature of contour lines of a scalar field |
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Apr 19 |
accepted | Extensions of Carathéodory’s theorem |
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Apr 18 |
answered | Why can an infinite-order polynomial be written as the ratio of two finite-order polynomials? |
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Apr 18 |
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Is there a lower bound for variance in terms of curvature? added 629 characters in body |
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Apr 18 |
answered | Leibnizian calculus textbook |
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Apr 18 |
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$f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $R$,how to show so is $f$ I don't feel bad! I feel enlightened :-) |
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Apr 18 |
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Only finitely many fundamental groups in $M(n,k,v,D)$? edited tags |
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Apr 18 |
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Was the early calculus inconsistent? Good point. Did you ever try seeing what Bos has to say about this? See ams.org/mathscinet-getitem?mr=469624 |
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Apr 18 |
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Only finitely many fundamental groups in $M(n,k,v,D)$? You might want to tag this in differential geometry and/or Riemannian geometry, as well. |
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Apr 18 |
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In what ways did Leibniz’s philosophy foresee modern mathematics? sp |
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Apr 18 |
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In what ways did Leibniz’s philosophy foresee modern mathematics? edited tags |
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Apr 18 |
answered | In what ways did Leibniz’s philosophy foresee modern mathematics? |
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Apr 18 |
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$f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $R$,how to show so is $f$ Oops, mea culpa, etc. This is what happens when a commoner thinks he knows something about analysis :-) |
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Apr 17 |
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$f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $R$,how to show so is $f$ "Vanishing of infinite order" means that it tends to zero faster than any polynomial $x^n$. The sine does not affect the order of vanishing at the origin. |
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Apr 17 |
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$f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $R$,how to show so is $f$ added 111 characters in body; added 8 characters in body; edited body |
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Apr 17 |
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geometric interpretation of Lie bracket sp |
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Apr 17 |
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geometric interpretation of Lie bracket added 293 characters in body |
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Apr 17 |
answered | geometric interpretation of Lie bracket |
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Apr 16 |
accepted | Nonstandard definition for the generator of a standard Ito diffusion |
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Apr 16 |
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Was the early calculus inconsistent? @Toby Bartels: I've thought about this for a few days but I am still not sure what point you are trying to make. Surely there IS a correct formula for the second derivative of a composite function, and there is a coherent theory of higher order differentials. |
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Apr 16 |
answered | $f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $R$,how to show so is $f$ |
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Apr 16 |
answered | Does some type of curvature require the space be an embedded manifold in a higher-dimensional space? |
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Apr 16 |
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Lapses of “the early proponents of the doctrine of limits” ...As far as Bolzano, I think there are very few errors there. Meanwhile, Cantor is notorious, among scholars who have actually bothered to look, for giving circular arguments "proving" that infinitesimals are contradictory. This is very rarely mentioned in received math history often focused on glorifing the "great triumvirate" (as Boyer put it) of Cantor, Dedekind, and Weierstrass. |
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Apr 16 |
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Lapses of “the early proponents of the doctrine of limits” @Joël: It is not clear whether Robinson is referring to early practitioners like d'Alembert, or more recent figures. Perhaps he was deliberately vague, and in fact referring to both. Concerning d'Alembert: based on what I have read, he is often presented in received history as a visionary pioneer of the "limit" concept, even though what he actually wrote about it is very thin stuff indeed, and the connection is almost a pun. I can try to look up some references if this interests you (Boyer is the "usual suspect")... |
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Apr 16 |
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Lapses of “the early proponents of the doctrine of limits” Excellent answer. You might want to elaborate a bit on Abel summation. |
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Apr 15 |
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Is there a lower bound for variance in terms of curvature? P.S. Robert, thanks a lot! You saved the day. |
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Apr 15 |
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Is there a lower bound for variance in terms of curvature? Yes, thanks. The formulation in terms of the subdomain $D$ is clearer because it consistently refers to domains in the $x,y$ plane. The reason I wanted a metric ball with respect to $g$ is because such a condition is more geometrically meaningful (it does not depend on the conformal parametrisation by the plane domain $\Omega$), but yours is much clearer as experience shows. |
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Apr 15 |
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Surfaces filled densely by a geodesic Good idea. I haven't spoken to him in years. Could you ask? |
