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This equation is basically Pell's equation or the negative Pell equation and its solutions can be obtained similarly using the continued fraction expansion of . Whether or not x 2 − Δ y 2 = −4 has a solution determines whether or not the class group of K is the same as its narrow class group , or equivalently, whether or not there is a ...
This problem concerns the issue of whether questions that are easy to verify (a class of queries called NP) also have solutions that are easy to find (a class called P). Hosch, William L (11 August 2009). "P versus NP problem mathematics". Encyclopædia Britannica "P vs NP Problem". www.claymath.org (Cook, Levin)
In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p.That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of p n copies of g, and not fewer, is equal to the identity element.
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In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator [1] that encodes a great deal of information about the process.
The complexity class of decision problems solvable by an algorithm in class A with an oracle for a language L is called A L. For example, P SAT is the class of problems solvable in polynomial time by a deterministic Turing machine with an oracle for the Boolean satisfiability problem.
In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. [1]
Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for CMAC. [152]