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For what value of x is f(x)=x^(1/x) a maximum? The maximum occurs at x=e, where f^'(x)=x^(-2+1/x)(1-lnx)=0, (1) which is zero at x=e and gives a maximum of ...

A stochastic resonance is a phenomenon in which a nonlinear system is subjected to a periodic modulated signal so weak as to be normally undetectable, but it becomes ...

A superabundant number is a composite number n such that sigma(n)/n>sigma(k)/k for all k<n, where sigma(n) is the divisor function. Superabundant numbers are closely related ...

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

Term rewriting systems are reduction systems in which rewrite rules apply to terms. Terms are built up from variables and constants using function symbols (or operations). ...

Consider expressions built up from variables and constants using function symbols. If v_1, ..., v_n are variables and t_1, ..., t_n are expressions, then a set of mappings ...

The versine, also known as the "versed sine," is a little-used trigonometric function defined by versin(z) = 2sin^2(1/2z) (1) = 1-cosz, (2) where sinz is the sine and cosz is ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...