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The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

The number of different triangles which have integer side lengths and perimeter n is T(n) = P(n,3)-sum_(1<=j<=|_n/2_|)P(j,2) (1) = [(n^2)/(12)]-|_n/4_||_(n+2)/4_| (2) = ...

An integral embedding of a graph, not to be confused with an integral graph, is a graph drawn such that vertices are distinct points and all graph edges have integer lengths. ...

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

A general integral transform is defined by g(alpha)=int_a^bf(t)K(alpha,t)dt, where K(alpha,t) is called the integral kernel of the transform.

Integration by parts is a technique for performing indefinite integration intudv or definite integration int_a^budv by expanding the differential of a product of functions ...

An interior point method is a linear or nonlinear programming method (Forsgren et al. 2002) that achieves optimization by going through the middle of the solid defined by the ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...