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The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

A symmetric block design (4n+3, 2n+1, n) which is equivalent to a Hadamard matrix of order 4n+4. It is conjectured that Hadamard designs exist for all integers n>0, but this ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

The hemisphere function is defined as H(x,y)={sqrt(a-x^2-y^2) for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a. (1) Watson (1966) defines a hemispherical function as a function S ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->..., the module B_i of i-boundaries is the image of d_(i+1). It is a submodule of C_i and is ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

For x(0)=a, x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)]. (2) If a/b=n, then x = 1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a (3) y = ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...