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An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two elements. For example, the swapping of 2 ...

cos(pi/8) = 1/2sqrt(2+sqrt(2)) (1) cos((3pi)/8) = 1/2sqrt(2-sqrt(2)) (2) cot(pi/8) = 1+sqrt(2) (3) cot((3pi)/8) = sqrt(2)-1 (4) csc(pi/8) = sqrt(4+2sqrt(2)) (5) csc((3pi)/8) ...

A triple integral over three coordinates giving the volume within some region G, V=intintint_(G)dxdydz.

The subset {0} of a ring. It trivially fulfils the definition of ideal since it is a group (specifically, the zero group), and it is closed under multiplication by any ...

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

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 ...

A multiple integral is a set of integrals taken over n>1 variables, e.g., int...int_()_(n)f(x_1,...,x_n)dx_1...dx_n. An nth-order integral corresponds, in general, to an ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

An abstract machine is a model of a computer system (considered either as hardware or software) constructed to allow a detailed and precise analysis of how the computer ...

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...