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The Buchstab function omega(u) is defined by the delay differential equation {uomega(u)=1 for 1<=u<=2; (uomega(u))^'=omega(u-1) for u>2 (1) (Panario 1998). It approaches the ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.

The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...

Given A = |a_(11)-x a_(12) ... a_(1m); a_(21) a_(22)-x ... a_(2m); | | ... |; a_(m1) a_(m2) ... a_(mm)-x| (1) = x^m+c_(m-1)x^(m-1)+...+c_0, (2) then ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... ...

A (2n)×(2n) complex matrix A in C^(2n×2n) is said to be Hamiltonian if J_nA=(J_nA)^(H), (1) where J_n in R^(2n×2n) is the matrix of the form J_n=[0 I_n; I_n 0], (2) I_n is ...

The Jacobian of the derivatives partialf/partialx_1, partialf/partialx_2, ..., partialf/partialx_n of a function f(x_1,x_2,...,x_n) with respect to x_1, x_2, ..., x_n is ...

A procedure for decomposing an N×N matrix A into a product of a lower triangular matrix L and an upper triangular matrix U, LU=A. (1) LU decomposition is implemented in the ...