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The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...

Every sufficiently large odd number is a sum of three primes (Vinogradov 1937). Ramachandra and Sankaranarayanan (1997) have shown that for sufficiently large n, the error ...

Differential Equations

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

For some constant alpha_0, alpha(f,z)<alpha_0 implies that z is an approximate zero of f, where alpha(f,z)=(|f(z)|)/(|f^'(z)|)sup_(k>1)|(f^((k))(z))/(k!f^'(z))|^(1/(k-1)). ...