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Let D be a domain in R^n for n>=3. Then the transformation v(x_1^',...,x_n^')=(a/(r^'))^(n-2)u((a^2x_1^')/(r^('2)),...,(a^2x_n^')/(r^('2))) onto a domain D^', where ...

If Omega subset= C is a domain and phi:Omega->C is a one-to-one analytic function, then phi(Omega) is a domain, and area(phi(Omega))=int_Omega|phi^'(z)|^2dxdy (Krantz 1999, ...

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...

The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let f be a function over the reals" means "Let f be a ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

A set A of integers is productive if there exists a partial recursive function f such that, for any x, the following holds: If the domain of phi_x is a subset of A, then f(x) ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

A multivalued function, also known as a multiple-valued function (Knopp 1996, part 1 p. 103), is a "function" that assumes two or more distinct values in its range for at ...