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In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

The average power of a complex signal f(t) as a function of time t is defined as <f^2(t)>=lim_(T->infty)1/(2T)int_(-T)^T|f(t)|^2dt, where |z| is the complex modulus (Papoulis ...

Although the inner shaded region has the same area as the outer shaded annulus, it appears to be larger. Since the rings are equally spaced, A_(inner) = pi·3^2=9pi (1) ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

A topology arising from a sheaf of continuous functions. It derives a natural topology from the projection operator. Etale spaces are examples of space that are not T2.

Let f(theta) be Lebesgue integrable and let f(r,theta)=1/(2pi)int_(-pi)^pif(t)(1-r^2)/(1-2rcos(t-theta)+r^2)dt (1) be the corresponding Poisson integral. Then almost ...

A filtration of ideals of a commutative unit ring R is a sequence of ideals ... subset= I_2 subset= I_1 subset= I_0=R, such that I_iI_j subset= I_(i+j) for all indices i,j. ...