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A linear combination of basis quaternions with integer coefficients.

The repeated application of a transformation.

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

A method for constructing magic squares of odd order.

The sum of sets A and B in a vector space, equal to {a+b:a in A,b in B}.

An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

A set A of integers is recursively isomorphic to set B if there is a bijective recursive function f such that f(A)=B.

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

Stochastic optimization refers to the minimization (or maximization) of a function in the presence of randomness in the optimization process. The randomness may be present as ...

A function f:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) is a trapdoor one-way hash function if f is a trapdoor one-way function and is also a one-way hash function, i.e., if, ...