Description:
Mathematical discussions and pursuits.
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Normed Vector Spaces, Inner Product Spaces
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A vector space has a field over which it is built. Now for Normed Vector spaces, one of the axioms is ||cV|| = |c| ||V|| This sort of implies that the field should be one with an absolute value function. So it should be something like R, or C. But are there examples of Normed vectors spaces where there is another... more »
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complex numbers and the law of cosine
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I am trying to find an angle in an obtuse triangle. The only way I can figure to do this is to use the law of cosine. Here's the problem: c^2=a^2+b^2-2ab cos C B=arccos((c^2-a^2-b^2)/(-2ab)) were: a = 3.105 b = 3.803 c = 6.944 When I solve for the angle B I get a complex number (), why? Visualizing the problem show that the angle should be solvable. Is... more »
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a question about Fourier series
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Hey all, I guess this is related to Fourier series: how to show A_n(t) = \sum_{k=0}^n sin(kt)/k is uniformly bounded (in n and t)? Should be easy but cant figure it out... Can someone shed some light on this? Thx a lot! Best, YH
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The 2008 Nobel Prize in Physics.
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The 2008 Nobel Prize in Physics. Fermilab and symmetry breaking Source: [link] My comment. Quotations from: Fermilab and symmetry breaking Yoichiro Nambu, Makoto Kobayashi and Toshihide Maskawa won the 2008 Nobel Prize in Physics for their work on symmetry breaking in the... more »
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Tangent space question
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Hi all Let U be a neighbourhood of the origin in |R^n, and let F(U) denote the space of C^oo real-valued functions on U. We may define the tangent space T at the origin to be the space of derivations of F(U), i.e. the space of |R-linear maps D: F(U) -> |R such that, for any f, g in F(U) D(f * g) = D(f) * g(0) + f(0) * D(g).... more »
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prove equivalence (of categories) is a full functor
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Given that a functor F:A->B is an equivalence, how can it be proved that F is a full functor. Since F is an equivalence, we know that there exists a functor G:B->A, such that GF is isomorphic to 1A, the identity functor on A, and FG is isomorphic to 1B, the identity functor on B. That is, there exists a natural transformation,... more »
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subrings of ZxZ
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What are all the subrings of ZxZ if we require (0,0) and (1,1) to be in the subring? the whole ring is a subring subset of all pairs of form (a,a) is a subring I believe that's all. Am I right?
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Passing through every quantity
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When there is a continuous change there is a passage through every quantity. This applies in the calculus of physics. There can pass through different sizes of infinity of the infinitely small at the same rate. This is speed through distance. The limit for speed is light speed. You can pass through the same size infinity of the infinitely small... more »
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Test Bank And Solution Manual
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[link] is the place where you can find or ask for a comprehensive solution manuals and test banks in digital formats. Those instructors’ resources save your time and effort and let you definitely understand what you are studying and get an amazing marks as well.
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