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 Yearling
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Apr
25
revised More about self-complementary block designs
I clarified that I am only interested in the case where n is odd, and I gave an example of such a design
Apr
20
revised More about self-complementary block designs
made nature of obstacle more explicit
Apr
19
asked More about self-complementary block designs
Apr
6
comment Multidimensional integrals that diverge by oscillation
It's worth mentioning that for the Heaviside function on ${\bf R}$, $\int (f - f \circ T)$ is NOT equal to 0 when $T$ is a nontrivial translation. So some restrictions apply to the sort of functions $f$ that satisfy this equality. Come to think of it, isometry-invariance is not what I need for my intended application.
Apr
6
comment Multidimensional integrals that diverge by oscillation
I found the online link oeiras mentioned; it is on page 4 of the pdf file sebastiaoesilva100anos.org/Publicacoes/Lista/Publicacoes.pdf, or one can go to sebastiaoesilva100anos.org/Publicacoes/publicacoes.html and click on the leftmost book on the lowest shelf. The former links gives just the article; the latter gives the whole book.
Apr
5
comment Multidimensional integrals that diverge by oscillation
Christian's reply points to a discrepancy between what I asked for and what I want. (Though I would assert that his $\overline{p}$ needs to be 0, and also one must check that his definition is truly a definition by verifying that a function $f$ can be written in the form $g+p$ in at most one way; so it's a one-paragraph triviality, not a one-sentence triviality.) But I think other respondents correctly divined that I'm looking for a theory that would have these properties as a consequence of having a "correct" point of view rather than by ad hoc fiat (an admittedly subjective distinction).
Apr
5
comment Multidimensional integrals that diverge by oscillation
Also, I'd be very interested to know of follow-up literature that builds on e Silva's theory. The book "Introduction to the Theory of Distributions" (by J. Campos Ferreira, R. F. Hoskins, and Jose Sousa-Pinto) looks like it has a lot of what I want, but it defers the treatment of the multdimensional theory to "a later volume" that as far as I can tell was never published (though maybe I'm just googling ineptly).
Apr
5
comment Multidimensional integrals that diverge by oscillation
Thanks, oeiras! While I wait for my library to get me a copy of the English version, can you tell me whether e Silva's definition is isometry-invariant ($\int f = \int (f \circ T)$ for all isometries $T$ of ${\bf R}^n$)? If (as I suspect from what I've seen) e Silva's definition for multivariate distributions uses induction on dimension, proving isometry-invariance could be nontrivial. Also, I'm hoping his definition satisfies $\int (f - f \circ T) = 0$ for a broad class of functions $f$ with $\int f = \infty$; without that, I doubt my Leech-lattice-packing integral would be tractable.
Apr
4
comment Multidimensional integrals that diverge by oscillation
Here's an example: Let $f_1$ and $f_2$ be the indicator functions of two (unrelated) Leech-lattice packings of balls in ${\bf R}^{24}$. (By "unrelated" I mean that they differ by some generic isometry of ${\bf R}^{24}$.) The theory should have the property that $f_1 - f_2$ integrates to 0. Actually, it'd be nice if the theory could handle distributions, since for my purposes it might be nicer to work with the difference between the Dirac combs associated with the centers of the balls in the packing.
Apr
4
asked Multidimensional integrals that diverge by oscillation
Mar
20
comment Self-complementary block designs
Yes, Dima's surmise about the intended meaning of "self-complementary" is correct.
Mar
19
asked Self-complementary block designs
Mar
14
revised Integer sets with forbidden differences
Joseph O'Rourke's proposed title is better than mine.
Feb
28
revised Integer sets with forbidden differences
added 117 characters in body
Feb
26
revised Integer sets with forbidden differences
edited title
Feb
26
revised Integer sets with forbidden differences
edited title
Feb
26
asked Integer sets with forbidden differences
Feb
23
answered What's wrong with the surreals?
Jan
29
awarded  Yearling
Jan
17
comment Nice sign-expansions of special surreal numbers
And thanks yet again, Mark!