Description:
Mathematical discussions and pursuits.
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5*z^4+K*z^3+k*z^2+K*z+5
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f[z,k,K]=5*z^4+K*z^3+k*z^2+K*z +5 where k,K is a real number. Show that all roots zj of f[z,k,K]=0 lie on the unit circle the complex plane if and only if ____________. (condition of k, K)
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Billiards
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Hello, suppose to have a ball on a smooth rectangular billiard table. When the particle hits the boundary it reflects from it without loss of speed. I have two questions. (I) Given a point P on the billiard table, and a positive integer M, does there exist a trajectory P(t), with P(0)=P, such that the ball passes again... more »
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bijective tetration ?
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is there an analytic bijective tetration known ? details : 1) bijective from A <-> B where A is the complex plane with real part > -2 and B is the complex plane apart from at most a finite set of complex numbers. 2) analytic on A. (see 1) ) 3) with tetration i mean base e tetration with f(-2)= -oo, f(-1) = 0 , f(0) = 1 and f(x+1) = exp(f(x)).... more »
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I choose three (#2)
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Here are three blogs on science and physics (except for one) that I found interesting today. [link] (pseudo-science to the extreme, but this guy has lots of followers who are nearly as nutty as the cranks usenet. =) [link] [link] (I love that show)... more »
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proof that a + b is unique for any cardinal numbers a,b
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Definition: given sets A, B, C, where A and B have no elements in common, we write a + b = c when there is a one to one correspondence between the elements of C and the totality of elements of A and B. Prove that for any cardinal numbers a, b, a + b is a unique cardinal number. suppose we have the sets A, B, C, D where... more »
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When t^4-z^4=d*w^p
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Given t,z are odd integers, t>z. When t^4-z^4 is representable in the form of d*w^p, where d is integer, w is integer >1, p is prime >=7?
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Math/CompSci Interview Question - Thoughts?
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I was posed the following question in a technical interview for a Software Engineering position by a major multinational NASDAQ company: [Paraphrasing] "You are given an array of 1,000,000 32-bit integers. One int value x occurs 500,001 times or more in the array. Specify an algorithm to determine x."... more »
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I found this interesting stuff with Riemann's ZF
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RZF --> Zeta Function While working with integrals of fractional parts, I came out with this... which I haven't quite seen before (on the internet, or books that I own)... Namely, the equation RZF(n) = 1/(n-1) - integral _1 ^oo 1/r^(1/n) dr 0 < n < 1, n belongs to N I myself am doubtful about the correctness of this equation... But I... more »
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5*z^4 - 11*z^3 + K*z^2 - 11*z + 5
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f[z,K]=5*z^4 - 11*z^3 + K*z^2 - 11*z + 5 where K is a real number. Show that all roots zj of f[z,K]=0 lie on the unit circle the complex plane if and only if ____________. (condition of K)
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