Description:
Mathematical discussions and pursuits.
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General Physical Constant Theorem.By Aiya-Oba
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Planck mass times 0.009, plus the product of any fundamental physical constant in negative powers greater than minus 4, and planck mass times 0.991, invariably equals planck mass time 0.009.-Aiya-Oba (Philosopher) Thus, p(0.009) + Q(p x 0.991) = p(0.009). Where p, is planck mass (10^-5), and Q, can be any fundamental... more »
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z^2 represented as a complex power series
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Hi all, Is there a way to represent z^2 as a power series of the form \sum c_n (z-a)^n between n=0 and infinity, where z is a complex number of the form x+iy, i^2= -1 and a= -i?
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Roots to nth Degree Polynomial
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[link] The polynomal is expressed as the equation of a plane and an orthogonal basis set up using the unit normal, the unit vector pointing from the intersection of the normal with the plane, to the intersection of the plane with the coordinate axes. From there the space curve in x is projected onto... more »
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Hard trigonometry integration
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integration of sin^4(x + sin 3x) dx from x = 0 to x = pi. any idea.? ------------------ Here is I tried If Let f(x) = sin(x + sin 3x) I find that f(x) = f(-x) There are 3 value of x such that f(x) = 0, f(0) = f(pi) = 0 and f(some value) = 0. no symetry about x = pi/2 ---------------- Can anyone solve this problem.?... more »
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legendre transform and convex function
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By "convex function", here, I mean a function whose first derivative is strictly increasing. Legendre transform applied to a convex function still gives a convex function. Please, can you give a proof (or an hint about it) of the statement ? Warmest regards mercury
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A new definition of Cardinality.
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Hi all, As far as I know, all the definitions of cardinality are limited in a way or another, lets take them one after the other: 1) Von Neumann's Cardinals: A cardinal is the least of all equinumerous ordinals. 2) Frege-Russell Cardinals: A cardinal is an equivalence class of sets under equivalence relation... more »
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Closed forms for certain types of sums
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Hi I'm trying to figure out how to derive the closed form for the following types of sums (a) Sum[a <= k <= b](floor(k/m)) (b) Sum[a <= k <= b](ceiling(k/m)) (c) Sum[a <= k <= b](k mod m) I'm not asking for a ready made formula that you happen to know. I'm asking for a step-by-step derivation. Note: A typical method for deriving the sum of a sequence of integers... more »
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relation between mutual information and statistical difference
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Hi guys, I was wondering if there is a relation between Shannon Mutual Information and statistical difference. More precisely, let A be a random variable over X_A and B over X_B. Let U be a random variable over X_A with uniform distribution. What I would like to show is that the following are equivalent (at least for 0<n<=1):... more »
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Ci ∩ Cj
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Four planar curves are defined as follows: C1:x^3 + x^5 - 3*x*y^2 - 10*x^3*y^2 + 5*x*y^4 = x/(x^2+y^2), C2:3*x^2*y + 5*x^4*y - y^3 - 10*x^2*y^3 + y^5 + y/(x^2 + y^2) = 3 C3:-1 + x^4 + x^6 + 3*y - 6*x^2*y^2 - 15*x^4*y^2 + y^4 + 15*x^2*y^4 - y^6 =0, C4:-3*x + 4*x^3*y + 6*x^5*y - 4*x*y^3 - 20*x^3*y^3 + 6*x*y^5 = 0... more »
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