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The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

Consider the problem of comparing two real numbers x and y based on their continued fraction representations. Then the mean number of iterations needed to determine if x<y or ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

Let F(n,sigma) denote the number of permutations on the symmetric group S_n which avoid sigma in S_k as a subpattern, where "tau contains sigma as a subpattern" is ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function P(n) = p(1-p)^n (1) = pq^n, (2) where 0<p<1, q=1-p, and ...