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Nov
29
comment Hahn-Banach theorem with real extended valued function
@LuisSilvestre: that sounds right, if you take the lower semicontinuity requirement to refer to the finest locally convex topology. Do you have a reference for that version of Hahn-Banach? I'm currently writing a paper which uses this and would like to attribute it appropriately.
Nov
20
answered Combinatorial Databases
Nov
14
revised What is the BRST-anti-BRST formalism?
corrected tags
Nov
14
suggested approved edit on What is the BRST-anti-BRST formalism?
Nov
12
awarded  Necromancer
Nov
12
answered Examples of common false beliefs in mathematics
Nov
11
answered Big list of repositories of mathematical preprints and postprints
Oct
29
comment Under what conditions there is a one-to-one mapping between a product of matrices and the sequence of matrices leading to the product?
The answer strongly depends on whether your matrices are invertible or not. If they are, then the question is equivalent to asking whether the group they generate is free, and techniques like the ping-pong lemma should apply. If they are not all invertible, then you are asking whether the monoid that they generate is free, which is a more difficult problem and undecidable even for 3x3-matrices with integer coefficients, see this paper and references therein: arxiv.org/abs/0808.3112 This implies that there cannot exist any simple necessary and sufficient conditions.
Oct
27
comment General additive function of probability
@PiotrMigdal: hi again! I just came across the exact same problem. The papers that Carlo linked to indeed seem to make additional assumptions about the particular form of $H$. I can email the papers to you if you like. Have you found a satisfactory answer in the meantime? BTW one simple observation is that all linear combinations of Rényi entropies satisfy your conditions as well, so Carlo (resp Rényi) must have had something else in mind.
Oct
4
awarded  Yearling
Sep
15
comment Results true in a dimension and false for higher dimensions
Is this related to the accepted answer on Brownian motion?
Aug
22
comment Continuous relations?
@EricWofsey: Presumably the idea is that continuous relations should generalize continuous functions in the same way as ordinary relations generalize functions.
Jul
24
comment Both NP-hard but different
Are you considering the 0-1 knapsack problem? And how do you compare the size of a knapsack instance to the size of a TSP instance? By the number of variables (=edges for TSP)?
Jun
13
comment Why are polynomials so useful in mathematics?
@GerryMyerson: another way of saying that is that $K[x]$ is the free unital $K$-algebra on one generator. Similarly, $K[x_1,\ldots,x_n]$ is the free $K$-algebra on $n$ generators.
May
21
awarded  Excavator
May
21
revised Are there any books that take a 'theorems as problems' approach?
edited body
May
7
comment Why are smooth numbers called “smooth”?
@WillJagy: en.wikipedia.org/wiki/Mouse_%28set_theory%29
Apr
22
comment Entropy for Haar measure on $O(n)$
@Asaf: okay, good, then we perfectly agree! I just wanted to make sure that the basic concepts are not forgotten.
Apr
21
comment Entropy for Haar measure on $O(n)$
Kolmogorov-Sinai entropy is then a derived quantity defined in terms of the Shannon entropy of a partition, and it measures the scaling of this Shannon entropy with time. As far as I can see, the OP's question is about "entropy" in the sense of Shannon entropy, not Kolmogorov-Sinai entropy.
Apr
21
comment Entropy for Haar measure on $O(n)$
@Asaf: "entropy is defined by a dynamical system, not just a space". I disagree with this statement. Arguably, the most basic notion of entropy is Shannon entropy, which assigns to every finite probability space a number measuring its effective size: en.wikipedia.org/wiki/Shannon_entropy