Constant term

This is written in terms of zt-, the moduli of the roots Zk-, since the roots are either real or come in mutually complex conjugate pairs. In any case, this constant term can be absorbed in the polynomial P t) in Eq. (15).]... 

The actual invariants in invariant properties of a lamina include not only U., U4, and U5 because they are the constant terms in Equation (2.93) but functions related to U-), U4, and U5 as shown in Problem Set 2.7. The terms U2 and U3 are not invariants. The only invariants of an orthotropic lamina can be shown to be... 

There are in principle also energy levels associated with nuclear spins. In the absence of an external magnetic field, these are degenerate and consequently contribute a constant term to the partition function. As nuclear spins do not change during chemical reactions, we will ignore this contribution. 

Similar, although less well documented, is Bryson s observation that a constant term must occasionally be included in the Hammett equation, i.e. A K = ap +a, which means that the intercept is significantly different from the equilibrium constant for the parent compound. 

To facilitate trial-and-error work, the following constant terms are calculated ... 

For rotating cylinders the exponent x for Reynolds number is very often unity for turbulent flow, and therefore L may be included in the constant term for a particular geometry of cynlinder. 

But since x — 1) contains a constant term, if A x 1) is a conventional polynomial, then A x-, )/ x — 1) must also be a conventional polynomial. Thus, all reachable configurations represented by the generating function 1) have the form... 

Each of the functional equations (4.1) - (4.10) determines a unique power series. The constant term of the first five solutions is equal to, of the second five it is zero. The other coefficients are positive moreover, they are integers except in the case of equation (4.8). The sequence of coefficients does not decrease. 

That is to say, however many different factors contribute to the constant term that is independent of the concentration, the other term that depends on the concentration should, at extreme dilution, be of the form — In yB. Since we identify1 the entropy with A (In Wtk + hi Wcf), (58) is the form that we have obtained in each of the examples examined above. 

Referring to equation [40], we can see that we require the absorbance at each wavelength to equal zero whenever the concentrations of all the components in a sample are equal to zero. We can add some flexibility to the CLS calibration by eliminating this constraint. This will add one additional degree of freedom to the equations. To allow these non-zero intercepts, we simply rewrite equation [40] with a constant term for each wavelength ... 

Fukuda et a/.9 62 have argued that, in most copolymcrizations, penultimate substituents should mainly influence the enthalpy for addition to monomer. It was proposed that enthalpy change (-A/7yk) is given by the cq. 16 (refer Scheme 7.5) which contains a constant term (A 1 0) and the stabilization energies of the product propagating radical (6)0, the reactant propagating radical (t/y) and the monomer (Ljf). 

Hence there can be no constant term in the derived series, i.e., the coefficient of T in the series (12) must be zero. 

The number of terms required in equation (2.19) depends upon the substance and the temperature interval. For small temperature differences, heat capacity changes with temperature are small and Cp can be represented reasonably well by the constant term a. For larger temperature changes a and b are used in equation (2.19), and over very large temperature ranges, higher power terms are included. Tables of the coefficients for equation (2.19) for a number of substances are summarized in the literature,2 with an abbreviated list3 summarized in Table 2.1. 

The constant term within the brackets has a value of 172.3005 in SI units (J-K- -mor1). 

Now relation (29) contains only two terms in its right-hand side, since the contribution of the Em-constant term in the Eq. (22) is now incorporated into the second linear right-hand side term of Eq. (29). 

Equation (17) is similar to Eq. (13) in both cases the outcome is that AE measures a difference in electronic energy. However, Eq. (17) is more complete since it consists of measurable quantities while Eq. (13) is incomplete for a constant term, which turns out to be dropped. This is a consequence of the approach used to separate AE into the various components. 

The constant term includes the contributions from the reference electrode. 

In purely electrochemical experiments the constant term is unknown. Therefore, from a measure of Ea=0t no information can be derived about the interfacial structure. However, if two metals are compared,... 

Equation (28) shows that the constant term is eliminated. Nevertheless, A

derive information about AX. There is no way to avoid this it is a consequence of the nature of the electrode potential [see Section I.2(ii)]. 

It is seen that the composite curve is hyperbolic, consisting of the sum of a constant term value (A) that describes the multi-path effect, a... 

---