Complementary equation

Since PB and WO32 are respectively anodically and cathodically coloring electrochromic materials, they can be used together in a single device121-125 so that their electrochromic reactions are complementary (Equation (15)) ... 

This equation is linear and could be solved exactly, whereas the complementary equation for U (f, t) = Ca (r, t) + Cyt, (r, t) is non-linear. We restrict ourselves to those problems whose solutions could be expressed through... 

As is usual in cost accounting practice, there ae a variety of methods for establishing the complementary equations—for allocating the costs—and which method is most equitable depends upon the circumstances. 

This constrained relationship between the two rectilinear coordinates 2xi and 2x3 defines implicifly fhe locus offhe seam in fheplane (2xi, 2xs) (fhe complementary equation being /2 (2x2) = f Qx2 = 0, i.e., 2x2 = 0, ia the fiill three-dimensional space). The graph of the seam is a parabola given by the explicit equation... 

The orbitals are those of C, in all cases, but there would be complementary equations for D. 

Another feature of the present theory is that it provides a formalism for deducing a complete mathematical representation of a phenomenon. In particular, beginning with the balance equations for (1) the pertinent constraints (e.g. volume, alone, for "simple compressible flows"), (2) the energy and (3) the availability, the needed complementary equations are deduced namely, the equations reflecting inertial effects (e.g., the momentum equation), and the constitutive relations. In this paper, the theory is applied to two specific cases. The first case is simple compressible flows to illustrate the theory in familiar circumstances. (Where some assumptions inherent in the traditional governing equations also come to light.) The second case is chemically reactive flows here the added generality of ideality over reversibility is needed, since the states visited are not at internal equilibrium. As... 

Step 1. Solve the equation obtained by deleting the inhomogeneous term. This homogeneous equation is called the complementary equation, and the general solution to this equation is called the complementary function. 

Since = 1, it can be derived from equation (5) that one complementary equation of the form... 

If Zc (t) is a general solution to the complementary equation and Zp t) is a particular solution to the inhomogeneous equation, show that... 

The solution to the complementary equation is the same as for the unforced harmonic oscillator ... 

Other complementary equations of the hydrocracking model are as follows ... 

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