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The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...

R(p,tau)=int_(-infty)^inftyint_(-infty)^inftyf(x,y)delta[y-(tau+px)]dydx, (1) where f(x,y)={1 for x,y in [-a,a]; 0 otherwise (2) and ...

A recurrence plot is defined as a plot of the quantity R(t,tau)=H(epsilon-||f(t)-f(tau)||), where H(x) is the Heaviside step function and ||f|| denotes a norm. A recurrence ...

An analytic function f(z) whose Laurent series is given by f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n, (1) can be integrated term by term using a closed contour gamma encircling ...

The time required for a given principal to double (assuming n=1 conversion period) for compound interest is given by solving 2P=P(1+r)^t, (1) or t=(ln2)/(ln(1+r)), (2) where ...

The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

The secant numbers S_k, also called the zig numbers or the Euler numbers E_n^*=|E_(2n)| numbers than can be defined either in terms of a generating function given as the ...

A species of structures is a rule F which 1. Produces, for each finite set U, a finite set F[U], 2. Produces, for each bijection sigma:U->V, a function F[sigma]:F[U]->F[V]. ...

A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially ...