By Albert H Beiler
1964, 1st ed., 1st printing. Lib Cong #64-13458;
This publication makes an attempt to give leisure facets of the idea of numbers.
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Extra resources for Recreations in the theory of numbers : the queen of mathematics entertains
T h e p a r a m e t e r s of t h e m o d e l of F i g . 2 4 6 c a n of c o u r s e b e e x p r e s s e d i n t e r m s of t h e p a r a m e t e r s of t h e m o d e l of F i g . 2 4 a . A s b e f o r e , i t i s e a s i e r t o c o n s i d e r t h e b e h a v i o r of t h e m o d e l i n F i g . 2 4 a if w e w i s h t o VISCOELASTICITY 35 P H E N O M E N A o b t a i n t h e creep a n d s t o r a g e c o m p l i a n c e s of a m a t e r i a l whose operator e q u a t i o n i s of t h e f o r m of e q u a t i o n ( 1 2 a ) .
19; alternatively, these moduli may be obtained by means of the relations given in Table I from the storage and loss compliances. These moduli are found to be ( ? ' ( ω ) = Ge + (6a) 1 + G"(«) = QTTr ^ - r (6b) t In Fig. 2 0 are plotted curves of J'(ω) — J and «/"(ω) against In ( 1 / ω τ ) and also a curve of J(t) — J against In (t/τ). In Fig. 2 1 are plotted similarly curves of G'(œ) — G , ( ? " ( ω ) , and G(t) — G . From these figures is g g e e Jlt)-Jg, ' - L O i ^ ^ / / y? \—"""Γ. -4 // // / / 1 / ι -2 ι ι 0 2 r 1 4 \r\(t/r), Ιη(1/ωτϊ F I G .
M r o w c a , a n d E . G u t h , / . Appl. Phys. 2 0 , 4 8 6 ( 1 9 4 9 ) . H . L e a d e r m a n , J. Appl. Phys. 2 5 , 2 9 4 ( 1 9 5 4 ) . H . F u j i t a , Buseiron-Kenkyu N o . 63, 48 (1953). F . Schwarzl and A . J . Staverman, 30 F . Schwarzl and A . J . Staverman, 31 32 33 34 35 36 J . D . Ferry, Eng. Chem. E . R . Fitzgerald, L . D . Grandine, J r . ,a n d M . L . Williams, 44, 703 (1952). 37 J . D . Ferry and M . Williams, 38 M. L . Williams and J . D . Ferry, J. Colloid Sei. 7 , 3 4 7 ( 1 9 5 2 ) .