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In computer science, the count-distinct problem [1] (also known in applied mathematics as the cardinality estimation problem) is the problem of finding the number of distinct elements in a data stream with repeated elements. This is a well-known problem with numerous applications.
() = (), where = = (/), μ(n) is the Möbius function, li(x) is the logarithmic integral function, ρ indexes every zero of the Riemann zeta function, and li(x ρ / n ) is not evaluated with a branch cut but instead considered as Ei( ρ / n log x) where Ei(x) is the exponential integral.
The first such distribution found is π(N) ~ N / log(N) , where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N).
For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, " a AND NOT a " is unsatisfiable. SAT is the first problem that was proven to be NP-complete —this is the Cook–Levin theorem .
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After spending the holidays at home, No. 3 Iowa State is ready to hit the road for its Big 12 Conference opener on Monday night. And Cyclones coach T.J. Otzelberger knows exactly what he wants his ...
(Reuters) - Ukraine possesses a laser weapon capable of shooting down airborne targets at an altitude of more than 2 kilometres (1.2 miles), the country's drone forces commander said on Monday.