Description:
Mathematical discussions and pursuits.
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metric spaces
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Hi! Is there an example of a complete metric space (X,d) and a continuous mapping f:X->X such that for all x,y\in X one has: 1) d(x,f(x))<c 2) d(f(x),f(y))\ge qd(x,y), here c and q>1 do not depend on x,y Thanks
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How does PIN entropy change if the probability distribution is known?
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Let us assume a user has to enter a 4 digit PIN to prove his identity. In the 4 digit PIN each digit should be unique. i.e. 0478 is a valid PIN but 1778 is not. If the user is equally likely to choose any digit, the entropy is: log (nchoosek(10, 4))/log(2) = 7.7142. How does the entropy change if we know that the user has 25%... more »
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f(2x)=4f(x)
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Which are the f such that f(2x)=4f(x) for all x (real) ? It looks like there is no other twice continuously differentiable solutions on R than x->C*x^2 (but there exists other continuous solutions, like x->x^2*sin (A log |x|), with appropriate A) Is there a simple proof (or even a counter-example)?... more »
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Solutions Manuals Wanted
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I am looking for instructor's solutions manuals for the standard "thermal physics"/"thermodynamics" textbooks used by the mainstream North American universities, electronic versions. Also, am interested in other physics and mathematics solutions manuals as well, mainly in the fields of mechanics, optics, statistical mechanics,... more »
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Mathematics education with Def of function.
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Hello teacher~ What's the base of the definition of function on modern math(set theory) ? 1) relation. 2) correspondence. Answer : (2). ------------------------------ ------------------------------ -------------------- How do you think about it ? Are you agree ? In fact, it need the knowledges of math education or history of function.... more »
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Still very frustrated with these issues
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...JS> [Leopard] no progress on the issues with Matlab. JS> JS> the UI issues are irritating. JS> JS> The performance issues are incredibly important. JS> JS> This is a HUGE productivity sink I fully agree with you. And as far as I see from this NG we are not the alone customers in our complains.... more »
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Illustrator and LaTeX
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Hi, I'm making some graphics for my supervisor's book, and I want to include some LaTeX notation in the actual image. I know that there is a way to do this with XFIG; however, I'm curious if there is a way to do the same with Illustrator. Does anyone know how to do this?
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Tractor and boat
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Here is a question I saw asked to some bright 11 and 12 year old children (who knew Pythagoras's equation): Imagine a vertical sea cliff. Floating in the sea some distance away from the cliff there is a boat, which is attached to a rope which goes diagonally up to the top edge of the cliff and then continues on the... more »
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