User hany - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T12:57:03Z http://mathoverflow.net/feeds/user/7886 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/45185/pseudonyms-of-famous-mathematicians/45325#45325 Answer by Hany for Pseudonyms of famous mathematicians Hany 2010-11-08T17:07:44Z 2010-11-08T17:07:44Z <p><a href="http://arxiv.org/find/all/1/all%3A+polymath/0/1/0/all/0/1" rel="nofollow">D. H. J. Polymath</a> is a pseudonym for a collective of mathematicians (some of them may be not professional mathematicians).</p> http://mathoverflow.net/questions/43848/two-sequences-whose-difference-converges-to-zero/43858#43858 Answer by Hany for two sequences whose difference converges to zero Hany 2010-10-27T19:22:05Z 2010-10-27T19:22:05Z <p>For sequences of real numbers there is a French term: "suites adjacentes" (may be translated as adjacent sequences) which means that the two sequences satisfy $\lim_{k\to\infty}(A_k-B_k)=0$, but with $A_k$ decreasing and $B_k$ increasing.</p> http://mathoverflow.net/questions/43792/riemann-stieltjes-derivative/43843#43843 Answer by Hany for "Riemann-Stieltjes derivative" ? Hany 2010-10-27T18:00:13Z 2010-10-27T18:00:13Z <p>Let $G:[0,1]\longrightarrow[0,1]$ be a continuous increasing function that is constant on each subinterval of the complement of the Cantor ternary set $K$ and satisfying $G(0)=0, G(1)=1$.</p> <p>The Riemann-Stieltjes integral with respect to $G$ cannot be 'differentiated'. Consider a function $F(x)$ and suppose there is some Riemann-Stieltjes integrable function $h$ such that $$F(b)-F(a)=\int_a^b h(t)dG(t),\quad \forall a,b \in[0,1]$$ Then, as the R.H.S. vanishes on any interval contained in the complement of $K$, $F$ must be constant on each such interval. So $F(x)=x$ for example cannot satisfy the above formula.</p> http://mathoverflow.net/questions/43381/what-numbers-can-be-approximated-pretty-well-by-rationals/43560#43560 Answer by Hany for What numbers can be approximated "pretty well" by rationals? Hany 2010-10-25T18:53:36Z 2010-10-26T19:35:50Z <p><a href="http://books.google.com.eg/books?id=rey9wfSaJ9EC&amp;printsec=frontcover&amp;dq=Hardyand+wright+number&amp;source=bl&amp;ots=avj7HPEGSa&amp;sig=ZBqVYG6xeXOSbwcC5mUxM-ql_uQ&amp;hl=ar&amp;ei=pdHFTLeQOca54gb28OC6Aw&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=10&amp;ved=0CEgQ6AEwCQ#v=onepage&amp;q&amp;f=false" rel="nofollow">Hardy and Wright</a> devoted a chapter (chapter 9) to these questions. One interesting theorem related to your question is theorem 196.</p> http://mathoverflow.net/questions/12085/experimental-mathematics/42197#42197 Answer by Hany for Experimental Mathematics Hany 2010-10-14T19:11:37Z 2010-10-14T19:11:37Z <p>Didn't the work of Candès and Tao on compressed sensing begin by a computer experiment by Candès that gave results "too good to be true"? See: <a href="http://www.ams.org/samplings/math-history/hap7-pixel.pdf" rel="nofollow">http://www.ams.org/samplings/math-history/hap7-pixel.pdf</a></p> http://mathoverflow.net/questions/41245/proof-that-bases-etc-exist-in-early-linear-algebra-course/41271#41271 Answer by Hany for Proof that bases etc. exist in early linear algebra course? Hany 2010-10-06T13:32:49Z 2010-10-06T13:32:49Z <p>I do not really know what is the level of the course and what else is in the syllabus, but there are many excellent books in linear algebra that cover abstract vector spaces almost painlessly. A good book to find this stuff is Axler's "Linear Algebra Done Right".</p> http://mathoverflow.net/questions/40528/spencer-browns-claimed-proof-of-the-four-color-theorem Spencer-Brown's claimed proof of the four color theorem Hany 2010-09-29T19:59:59Z 2010-09-30T09:38:36Z <p>I read on <a href="http://en.wikipedia.org/wiki/G._Spencer-Brown" rel="nofollow">Wikipedia</a> that G. Spencer-Brown gave a non-computer based proof of the four color theorem. As I'm not an expert in the subject I'm unable to verify that claim. Does any one have an idea about the proof or a reference to a serious discussion of the subject?</p> http://mathoverflow.net/questions/34251/the-dual-group-of-mathbb-q The dual group of $\mathbb Q$ Hany 2010-08-02T12:13:34Z 2010-08-20T09:49:13Z <p>What is the dual group of the additive group of rational numbers equipped with the standard topology inherited from $\mathbb R$? As a group, this dual group is isomorphic to $\mathbb R$ (see the answer of Ekedahl given below), but it should be equipped with the topology of uniform convergence on compact subsets of $\mathbb Q$. What are the properties of this group? Is it locally compact? what are its connected components? does it have more natural structure? </p> http://mathoverflow.net/questions/45185/pseudonyms-of-famous-mathematicians/45206#45206 Comment by Hany Hany 2010-11-08T19:56:32Z 2010-11-08T19:56:32Z If you mean by Al-Khoresmi &quot;Abu Ja'far Muhammad ibn Musa Al-Khwarizmi&quot; then I think he does not qualify. It was customary at the time to use geographic names of family origin as family name. This means that he had the name &quot;Al-Khwarizmi&quot; all his life and that his father, brothers and sons (if he had any) had the same name. http://mathoverflow.net/questions/44705/cardinalities-larger-than-the-continuum-in-areas-besides-set-theory/44709#44709 Comment by Hany Hany 2010-11-03T21:43:00Z 2010-11-03T21:43:00Z For the example of measurability I would say it is still within the realm of set theory (descriptive set theory). I think there are results on infinite dimensional topology that require a space of very large cardinality, but the ideas and techniques are borrowed from model theory. Actually it seems that whenever we study questions of infinite cardinals we require tools from model theory or set theory. http://mathoverflow.net/questions/44265/question-about-schauder-bases-in-c0-1/44280#44280 Comment by Hany Hany 2010-10-30T22:29:33Z 2010-10-30T22:29:33Z The usual example in $C([0,1])$ is $\vert t-\frac 12\vert$. Its Fourier series does not converge uniformly. http://mathoverflow.net/questions/44265/question-about-schauder-bases-in-c0-1 Comment by Hany Hany 2010-10-30T20:27:30Z 2010-10-30T20:27:30Z Actually if a trigonometric series converges uniformly to a function $f$, then the series must be the Fourier series of $f$. This is statement 1.41 on page 6 of Zygmund's {\it Trigonometric Series}. http://mathoverflow.net/questions/43864/describe-subsets-of-the-integers-closed-under-the-binary-operation-axby/43905#43905 Comment by Hany Hany 2010-10-28T07:09:15Z 2010-10-28T07:09:15Z Wouldn't $(1)$ be the set of all integers of the form $F(A+B)$ where $F$ is a polynomial with positive integer coefficients? http://mathoverflow.net/questions/43848/two-sequences-whose-difference-converges-to-zero/43858#43858 Comment by Hany Hany 2010-10-27T21:56:04Z 2010-10-27T21:56:04Z Yes. I thought it may suggest a suitable terminology. http://mathoverflow.net/questions/43792/riemann-stieltjes-derivative/43794#43794 Comment by Hany Hany 2010-10-27T16:48:50Z 2010-10-27T16:48:50Z The existence of the Radon-Nikodym derivative requires that the measure $dF$ be absolutely continuous with respect to Lebesgue measure which is not satisfied by a pure jump function where the support of the measure is a finite or countable set. http://mathoverflow.net/questions/43538/wonderful-applications-of-the-vandermonde-determinant/43548#43548 Comment by Hany Hany 2010-10-26T19:20:51Z 2010-10-26T19:20:51Z Another application is to prove that for any $0&lt;\alpha_1&lt;\cdots&lt;\alpha_n$ the family $$\sin \alpha_1x,\cdots,\sin\alpha_nx$$ is linearly independent in $C^{4(n-1)}(\mathbb R)$. http://mathoverflow.net/questions/42215/does-constructing-non-measurable-sets-require-the-axiom-of-choice Comment by Hany Hany 2010-10-15T08:46:26Z 2010-10-15T08:46:26Z There is an interesting discussion on: <a href="http://www.math.niu.edu/~rusin/known-math/99/AD_AC" rel="nofollow">math.niu.edu/~rusin/known-math/99/AD_AC</a> http://mathoverflow.net/questions/41493/explicit-isomorphism-between-distributions-and-universal-enveloping-algebra/41496#41496 Comment by Hany Hany 2010-10-08T11:25:15Z 2010-10-08T11:25:15Z @Najdorf- It seems that $D.\delta_e$ should act as $D$ according to $$&lt;(D.\delta_e)\varphi,\psi&gt;=&lt;\delta_e\varphi,D\psi&gt;$$ http://mathoverflow.net/questions/34251/the-dual-group-of-mathbb-q/34254#34254 Comment by Hany Hany 2010-08-10T14:45:05Z 2010-08-10T14:45:05Z @Edgar: Thanks for the correction. http://mathoverflow.net/questions/34251/the-dual-group-of-mathbb-q/34254#34254 Comment by Hany Hany 2010-08-06T09:02:18Z 2010-08-06T09:02:18Z @Victor: Consider $X={\mathbb R}\cup\{\infty\}$ with the topology consisting of the discrete topology on $\mathbb R$ and with a base of neighborhoods at $\infty$ consisting of intervals $]k,\infty]$ with $k\in{\mathbb N}$. Compact sets in this space are finite, but the space is not discrete.