1347 
APPENDIX A 
PROPERTIES OF f_(p) and Yq(p) FUNCTIONS 
i. The basic equations for the functions f(D) and Yale) 
and their derivatives are as follows: 
5 P c 4 We 
Ald) = on UG) = ae feo, ce ; / (la 
( #, the sign of (F -1)) 
Pip) = e, Vie) = —— (¥ =1) +y(Qle- &° (la! 
n : 5 
wad te (pay ae ge ace 
4, "4 OH Cc i+¥ ~ l+2x 
jo vl), =n el y+ “s 
th nt oe peu ipae ae vo ee 
-2y "Lu F 1 (1a" 
-1 
Also Vr(p)= ea ey 1) (1b 
Cn gS 
2. Proof of (8a'), (8b‘) 
For any real, mn <zero value of A, B 
a® - 20 B + BY > O 
ti ca 
Let a? = (F-1)§" ¥ Be = ioe ?) 
then, ( F-1)€ > an - eVy(F-1)" we (1- FO ob ‘ ae + 
GO a F) do 
= 59 = 
