The peak of the loss modulus curve denotes the glass transition temperature (T g). Figure 7 denotes the glass transition temperature as 90°C and desired loss modulus values (minimum values) obtained for 10 to 20 wt.% SiC content.
where is the modulus operator and denotes the complex conjugate transpose operator.
Convolution of each LFP time series for each subject was carried out with an array of appropriately scaled wavelets to generate a complex time series for each frequency band between 1 and 80 Hz for the duration of each recording, the modulus of which denoted the instantaneous amplitudes for each frequency at all points during the recording.
|·| denotes the modulus of a complex number.
For a complex number a, |a| denotes the modulus.
Let ρ ( A ) = max { | λ | : λ is an eigenvalue of A }, where | λ | denotes the modulus of λ.
with m = 1, ⋯, M, n = 1, ⋯, M, a=2d cosθ, and b=2d sinθ, and m o d x,y) denotes the modulus operation after division of x by y.
where k ˜ : = max { | k ( t, s ) | : ( t, s ) ∈ D ε × [ 0, T ] }, and ω T ( k, | t 2 − t 1 | ) denotes the modulus of continuity of the function k on the set D ε × [ 0, T ].
defined on the bounded set Ω ⊂ C 1 ( [ 0, T ], E ), where the ordering is induced by the positive cone in R 2 and where mod C denotes the modulus of continuity of a subset Ω ⊂ C ( [ 0, T ], E ).a Such a μ is an m.n.c. in C 1 ( [ 0, T ], E ), as shown in the following lemma (proven in [16]), where the properties of μ will be also discussed.
defined on the bounded Ω ⊂ C 1 ( [ 0, T ], E ), where the ordering is induced by the positive cone in R 2 and where mod C denotes the modulus of continuity of a subset Ω ⊂ C ( [ 0, T ], E ).a It was proved in [19] that the function α given by (7) is an m.n.c. in C 1 ( [ 0, T ], E ) that is monotone, non-singular and regular.
Now let ρ denote the modulus of continuity of ξ.
