Search Results for ""

The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

A quantity displayed below the normal line of text (and generally in a smaller point size), as the "i" in a_i, is called a subscript. Subscripts are commonly used to indicate ...

The Fibonacci chain map is defined as x_(n+1) = -1/(x_n+epsilon+alphasgn[frac(n(phi-1))-(phi-1)]) (1) phi_(n+1) = frac(phi_n+phi-1), (2) where frac(x) is the fractional part, ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

A vector difference is the result of subtracting one vector from another. A vector difference is denoted using the normal minus sign, i.e., the vector difference of vectors A ...

The bandwidth of a matrix M=(m_(ij)) is the maximum value of |i-j| such that m_(ij) is nonzero.

Consider the Fibonacci-like recurrence a_n=+/-a_(n-1)+/-a_(n-2), (1) where a_0=0, a_1=1, and each sign is chosen independently and at random with probability 1/2. ...

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...