Description:
Discussion of current mathematical research. (Moderated)
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call for papers
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( WE APOLOGIZE IF YOU RECEIVE MULTIPLE COPIES OF THIS MESSAGE ) ============================== =========================== ARPN Journal of Systems and Software Call for Research Papers [link] ============================== =========================== Dear Sir/ Madam,... more »
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a linear algebra problem
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I have linear algebra problem as follows: if a and b are n*1 vectors and matrix M>0 can we show (a'Mb)(a'Mb) <= (a'Ma)(b'Mb)? My thoughts are the above looks like cauchy-schwarz inequality |xy|^2 <= (x'x)(y'y) trying to apply this inequality to the above, but wasnt successful. Or did I went in entire wrong direction?... more »
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Stirling numbers question
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Hi! Do you know how to simplify the following sequence involving Stirling numbers of first kind (k-1)! \sum_{i=1}^{n-k+1} \frac{1}{i(n-i)!} s(n-i,k-1) Thank You, Magdalena
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Dimensional restrictions for these papers ??
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Hi... In my work with topological manifolds, i am using results from the following paper COUNTING TOPOLOGICAL MANIFOLDS, J. Cheeger and J. M. Kister, Topology Vol. 9 pp149-151, 1970 This article uses the main result (Theorem 5.1, i believe) from the following article of Kirby and Edwards Deformations of spaces of imbeddings, Ann. of Math. 2nd series, vol.... more »
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The johnson graph
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Hi everyone... Does anyone know of some good papers about the johnson graph ?? This graph has as vertex set all m-subset of {1, ..., n } and two vertices s1, s2 are adjacent if and only if |s1 \cap s2 | = m - 1. I have searhed over the internet but i can only find litte information about this graph... more »
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Z(t,t^-1) solutions to a(t)p(t)+b(t)q(t)=1
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Greetings. Suppose that p(t) and q(t) are Laurent polynomials with integer coefficients. I am looking for Laurent polynomials with integer coefficients for which a(t)p(t)+b(t)q(t) = 1. Over rationals, not integers, this could be unambiguously determined by the GCD algorithm. However, in integers, the GCD... more »
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Fourier series question
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Does there exist a nonzero (i.e. not equal to 0 a.e.) Lebesgue integrable function on [0, 2pi] whose Fourier series is 0, i.e. all its Fourier coefficients are 0 ? I don't think the famous Kolmogorov's example answers this question.
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E^(pi*sqrt(163)) and the solvable sextic 5x^6-640320x^5-10x^3+1 = 0
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Hello all, The sextics, 5x^6-15x^5-10x^3+1 = 0 5x^6-32x^5-10x^3+1 = 0 5x^6-96x^5-10x^3+1 = 0 5x^6-960x^5-10x^3+1 = 0 5x^6-5280x^5-10x^3+1 = 0 5x^6-640320x^5-10x^3+1 = 0 have some very interesting properties. 1. I'm sure some will also recognize the sequence {15, 32, 96, 960, 5280, 640320}. (Hint: Their cubes plus 744 are good approximations to... more »
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Brouwer's choice sequences as a basis for measure theory and probability theory
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In considering problems regarding the foundations of probability, I have thought that Brouwer's choice sequences could be an interesting basis for measure theory and probability theory. The class of choice sequences can be regarded both as the codomain and (in essence) as the domain of probability functions. A such approach could suggest possible solutions... more »
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