The phrase "a periodical function" is correct and usable in written English.
It can be used in contexts related to mathematics, physics, or any field discussing functions that repeat at regular intervals.
Example: "The sine and cosine functions are examples of a periodical function, as they repeat their values in a regular pattern."
Alternatives: "a periodic function" or "a recurring function".
However, it could be considered a periodical function by parts, being defined as a range of period T equivalent to the radial distance to be studied.
Regarding these facts, we consider a case when, under the conditions of a complex stressed state (σ 33<σ 22=σ 11≤0), one of the components of the external stress, for example, σ 33, will be a periodical function with respect to coordinates.
The dissimilation of a maintainable system, (D_{m}), is described by a periodical function with recovered availability corresponding to the maintenance cycle T as follows: begin{aligned} D_mathrm{m} =left{ {begin{array}{ll} k, 1-mathrm{e}^{-t-T'}), 1-mathrm{et<0 k,(1-mathrm{e}^{-t-T'}&quad nTle t<(n+1)T,&quad, end{array}} righT'le
Because of the fact that the coefficients of (5) depend only on the parameter Λ, which is constant with regard to θ and z, and with regard to h, which is a periodical function on θ, one finds, as a result, the solution of the equation is periodical: begin{aligned} p(theta,z =p(theta+2pi,z). end{aligned} (9) It is easy to see that the equations of the mathematical model are nonlinear.
In our particular case, we do not have a periodical function.
Fourier Series Expansion: the basic idea of these series is that any periodical function (T) can be expressed as a trigonometric sum of sines and cosines where their frequencies are multiples of the fundamental frequency ω0, but at the same intervals in which the function is defined.
If (sigma= 1), (d=0), system (1.1) is the well-known Navier-Stokes equations (NS), Foias and Temam [5] proved spatial analyticity for solutions in Sobolev spaces of periodical functions in an elementary way.
Now, we need to introduce some concepts, definitions, and technicalities on almost periodical functions.
Then, in accordance with the relations presented in Appendix 1, the deformational characteristics of the media with isolated closed fractures are also periodical functions of coordinates.
The cases where the orders of the derivatives in VOFVDPM are varying with different linear and periodical functions of time are investigated.
The above numerical experiments investigate the dynamic behaviors of the VOFVDPM with different linear and periodical functions in the case (a=0).
