Sentence examples for fractional relation from inspiring English sources

This fractional relation can be realized physically through hierarchical arrangements and in the limit of an infinite number of springs and dashpots [2].

For (betain 0,2 -{1}), the following Riesz fractional derivatives relation is valid: begin{aligned}[b]frac{partial ^{beta} phi_{i}(x)}{partial |x|^{beta}}& =i sum _{k=0}^{i }frac{(i + k-1 )! (k+1)!

The transformation stems from the Darcy fractional flow relations, combined with the equality between the flowrate and mobility ratio observed when steady-state conditions are maintained.

Another alternative PLP approach may be based on the fractional harmonic relations which exist between the fundamental frequencies in a musical chord, for example, for a major chord (consisting of dominant, third, fifth, and octave) it can be verified that,, and.

The viscoelastic material is assumed to follow a fractional Kelvin Voigt constitutive relation.

The material of the column is modeled using a fractional Kelvin Voigt constitutive relation, which leads to that the equation of motion is governed by a stochastic fractional equation with parametric excitation.

By modelling the wideband random excitation as Gaussian white noise and real noise and assuming the viscoelastic material to follow the fractional Kelvin Voigt constitutive relation, the motion of the column is governed by a fractional stochastic differential equation, which is justifiably and uniformly approximated by an averaged system of Itô stochastic differential equations.

The authors of [10] considered the relation between fractional Laplacian and fractional Sovolev space.

Time domain pulse responses simulated with algorithms of fractional calculus exhibit E I t relations closely related to experimental data.

In this paper, we obtain the correspondence relation between fractional factorial RPDs and the blocking schemes for full factorial RPDs.

The study starts by analyzing the memory properties of fractional operators and their relation with time delay.