First, the hyperelastic part presents the effects of fiber fabric and the interaction between the rubber and the fiber fabric; the viscoelastic part is described by Prony series functions, also the temperature effect on the mechanical response for the fabric reinforced rubber composites is considered in the hyper-viscoelastic constitutive model.
The expansion of radial profiles is represented by the series of weighted orthogonal functions which are GL CHFs: ℑ k n r, θ = − 1 K 2 n + 1 2 π n 2 K ! n + K ! 1 2 r n L K n 2 πr 2 e − πr 2 e jnθ (4).
Regarding the current density of discrete points as unknown parameters, the vector expression of K Bn, which is the coefficient of K, will be obtained by the series formula of Bessel function according to the linear distribution assumption of current between the adjacent discrete points.
Nakamura [19] studied the ((3+1))-dimensional Toda equation, and its solutions are expressed by the series expansions of the Bessel functions.
The Wright function is defined by the series representation, convergent in the whole z-complex plane [12] W ( z ; α, β ) = ∑ k = 0 ∞ z k k !
In that sense, this procedure is possible by using the series where the incomplete gamma function.
By extending the Taylor series, the function f(b R,b I ) is refined, but in exchange, the resulting expression is cumbersome.
Mathematical approximations are given by the multicomponent exponential or sine-series functions [4].
First, we find the solution of integral equation in terms of reproducing kernel functions in series, then by truncating the series an approximate solution obtained.
The SNPs associated with ABA-dependent signalling pathways played a major role in the plant's response to stress by regulating a series of functions including flowering, root development, auxin metabolism, guard cell functions, and scavenging reactive oxygen species (ROS).
