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The mode of a set of observations is the most commonly occurring value. For example, for a data set (3, 7, 3, 9, 9, 3, 5, 1, 8, 5) (left histogram), the unique mode is 3. ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...

Let f(z) be an analytic function of z, regular in the half-strip S defined by a<x<b and y>0. If f(z) is bounded in S and tends to a limit l as y->infty for a certain fixed ...

Let g(x_1,...,x_n,y) be a function such that for any x_1, ..., x_n, there is at least one y such that g(x_1,...,x_n,y)=0. Then the mu-operator muy(g(x_1,...,x_n,y)=0) gives ...

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient ...

Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

A vector space V with a ring structure and a vector norm such that for all v,W in V, ||vw||<=||v||||w||. If V has a multiplicative identity 1, it is also required that ...

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

There are several meanings of "null vector" in mathematics. 1. The most common meaning of null vector is the n-dimensional vector 0 of length 0. i.e., the vector with n ...

The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...