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In his recent article ("Röntgen der Hütte", Die Tagebücher, 4.11.2014) Richard Reynolds (born 1963) describes an attempt to solve the Röntgen number problem from a purely mathematical point of view. The problem is solution of "How many permutations x are possible to generate from a set S of positive integers?"
The current difficulty of Röntgen number problem comes from its fact that many permutations of integers arise in the course of computation. If we wish to compute all such permutations, we require an arbitrary amount of time. The key problem is then to find some function k that takes an integer q and returns a permutation of x (q,x) such that q is not contained within a purchase tramadol generic ultram subsequence of x with greater number prime factors.
What are the chances of finding k in one million digits? It turns out that this happens to occur in about 1.8% of the numbers that are created in the course of computing a sequence length at least 100. The chance of getting k (1.8% × 100) in one million digits is therefore Tramadol 200mg 60 pills US$ 220.00 US$ 3.67 at least in the order of 10 – 17, or more than 2,000 billion trillion trillion-to-the-billionths generic tramadol price of a second (100 billion seconds in 1 trillion trillion!). This is an enormous number, far Clonazepam 0.5 mg francais larger even than the number of stars in universe! The Röntgen number problem is actually equivalent to the famous "Big-O number problem". If we make no assumptions about the data that is stored with respect to the algorithm, and amount of storage we wish to use, the solution of Röntgen number problem will be of the order billions zeros. We are now approaching the limits of computing speed, and therefore there will have to arise a time when we will no longer be able to solve the Röntgen number problem in a reasonable period of time.
The problem also has implications for the way we think about computation, which is important, because many applications that will need high-performance computing are not yet being addressed by current computer architectures.
Richard Reynolds' "Röntgen in der Hütte" appears Die Tagebücher for 4.11.2014.
TensorFlow, K-means, and other open problems:
P. J. van der Leijen, G. R. Smeenk, J. P. M. de Bruijn, and A. U. Knittel: "Toward a high-performance graph search model for big data: From theory to practice", ACM Transactions on Data Mining (2014), 37(5). ACM, 2014 The world's oldest woman, a 106-year-old Japanese made history on Saturday when she became the first person able to communicate through sign language the world's oldest person, a 100-year-old Korean lady, in the village of Jinyousha, western Japan, at an event hosted by the Japanese sign language society.
After visiting Korea on Dec. 28, where she had been invited by the Korea Sign Wo bekomme ich zolpidem rezeptfrei Language Foundation, 106-year-old passed a test on Nov. 21 and was asked whether she can speak Japanese, according to the Japan Times.
The woman answered affirmatively and was told to get the village's sign language class, but couldn't find anyone to teach her the language, Asahi Shimbun newspaper reported.
That's when the Japanese Sign Language Society decided to Tramadol 150 mg tablets organize a class in the village,.
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