Math

Rule-based integration
There is much to say about the Rubi. One tiny example. The VM machine says: Mathematica 7.0.1.0 returns Integrate[1/(Sqrt[2] + Sin[z] + Cos[z]), z] unevaluated (!). Rubi returns -(2/(1 + (-1 + Sqrt[2]) Tan[z/2])) which is a correct answer. Best wishes, Vladimir Bondarenko VM and G... 24 Jul 2010 01:38

Exchange of the "oracle machine" and the "oracle" in the polynomial-time hierachy
Hi there! The polynomial-time hierarchy (PH) is simply defined in a recursive manner. For example, for all k>=0, the \Sigma_{k+1} complexity class is defined as NP^\Sigma_k. My question is, whether on can write \Sigma_{k+1} as \Sigma_k^NP ? This is somehow counterintuitive, but I saw a variation of it in ... 9 Jun 2010 08:37

Crankfest!
WM <mueckenh(a)rz.fh-augsburg.de> writes: On 9 Jun., 12:57, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: The antidiagonal is not equal to any of the numbers on the list. What is unclear about that? It is unclear how this can be accomplished in the binary tree with countably many different ... 9 Jun 2010 08:37

manipulating spectral norm of matrix with normalized columns
Hello: I am using an iterative method that requires a matrix and vector input (solve special Ax=b for x), such that the matrix has normalized columns (norm = 1), and this matrix has a spectral norm (biggest singular value) < a certain constant (for example, 1) for convergence. For any matrix A, I can influenc... 10 Jun 2010 05:37

constructible = unconstructible
Binary Tree The complete infinite binary tree contains all real numbers between 0 and 1 as infinite paths i. e. infinite sequences { 0, 1 }^N of bits. 0, / \ 0 1 / \ / \ 0 1 0 1 / 0 ... The set { a_k | k in N } of nodes a_k of ... 13 Jun 2010 19:24

"NO BOX CONTAINS THE BOX NUMBERS THAT DON'T CONTAIN THEIR OWN BOX NUMBER" ~ XEN
(from the "Xenides dies" thread) For *all* N, the sequence differs from the Nth entry in the list at the Nth digit (and possibly other positions as well). It is new because for *every* sequence in the list, the question "is it the same as this sequence" is answered "no". So you think the antidiago... 9 Jun 2010 20:56

Longitude determination with an astrolabe
don't know, why, that link didn't work to Maui's Tanawa. http://www.21stcenturysciencetech.com/articles/fall01/Tanawa/tanawa.html thus quoth: For our first "proof-of-principle"experimental observations of the motion of the Moon, in order to determine longitude on Earth, our measurements were done with a "strippe... 9 Jun 2010 02:06

Cosmic Blackbody Microwave Background Radiation proves Atom Totality and dismisses Big Bang Chapt 3 #150; ATOM TOTALITY
Archimedes Plutonium wrote: II. Cosmic characteristics and features; support Chapter (3) uniform blackbody 2.71 K cosmic microwave background radiation and Dark Night sky: Olber's Paradox fully answered Before I can do the DeBroglie thermodynamics of an electron cavity, I need to know the large number of C... 9 Jun 2010 02:06

Obummer talks about himself while he coats our coastline with OIL
This is not a obama resource, this is AGR if you keep yerself locked on babylon politics you may miss the solution. The solution may be locked inside you, but being wrapped in the swagg blankets of politics, it cannot get out. Put yer obama bash blanket away and listen to the wind. The wind is where the answers ar... 9 Jun 2010 01:00

Countable infinities?
There are some infinities that can be passed through in finite time like distance for Zeno's paradox. They still are all uncountable by any definition. Mitch Raemsch ... 9 Jun 2010 17:35