Range of tan

As was pointed out by Newns (1967), for (4.99) to be complete, it is necessary to specify the range of the multi-valued function tan-1. First, we note that, if the unperturbed semi-infinite metal substrate has no surface states, then A(e) =0 outside the energy band. However, from (4.70), we see that poles may then occur in G a(e) at energies given by the solutions of — a r — A(e) = 0, (G.l)  

When a localized state does appear below the band, the contour C may be taken round all the eigenvalues between f and q, where the lowest 

---

The standard phase angle measuring system has been replaced with a lock-in amplifier (Princeton Applied Research Model 5204) to simplify automation of the measurement, to improve resolution of small angles, and to extend the range of tan 6 measurements. 

In order to improve BMI resins processability while retaining other important characteristics (excellent physical property retention at elevated temperatures and in wet environments, almost constant electrical properties over a wide range of tan-peratures, nonflammability, etc.), several modern approaches were utilized. 

---