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A quadratic form Q(x) is indefinite if it is less than 0 for some values and greater than 0 for others. The quadratic form, written in the form (x,Ax), is indefinite if ...

A binary quadratic form is a quadratic form in two variables having the form Q(x,y)=ax^2+2bxy+cy^2, (1) commonly denoted <a,b,c>. Consider a binary quadratic form with real ...

For a quadratic form Q in the canonical form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2, the rank is the total number r of square terms (both positive and ...

A quadratic field Q(sqrt(D)) with D>0.

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)

The system of partial differential equations del ^4u = E(v_(xy)^2-v_(xx)v_(yy)) (1) del ^4v = alpha+beta(u_(yy)v_(xx)+u_(xx)v_(yy)-2u_(xy)v_(xy)), (2) where del ^4 is the ...

The system of ordinary differential equations (dm)/(dt) = lambdamxm+gammax1 (1) (dgamma)/(dt) = lambdagammaxm. (2)

A linear system of equations is a set of n linear equations in k variables (sometimes called "unknowns"). Linear systems can be represented in matrix form as the matrix ...

The signature of a non-degenerate quadratic form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2 of rank r is most often defined to be the ordered pair (p,q)=(p,r-p) of ...