The phrase "an arbitrary inequality" is correct and usable in written English.
It can be used in mathematical or philosophical contexts to describe a relationship that is not based on any specific rule or principle.
Example: "In this study, we will explore the implications of an arbitrary inequality in the distribution of resources."
Alternatives: "a random inequality" or "an unprincipled inequality".
The speech, given 50 years ago, expressed the hope of a young African American leader -- the hope that the country of his birth would forsake the twin evils of racism and arbitrary inequality and accept the salvation of peace and equal opportunity.
401(k) plans create stark, arbitrary inequalities between retirement cohorts because retirement income varies wildly with financial market conditions.
For an arbitrary, the following inequality is well known [19]: (A3).
If Ω ( l p + 1, α ) = 0 for all l ∈ N = { 1, 2, … }, then equation (9) has an analytic solution of the form g ( z ) = z + ∑ n = l p + 1, l ∈ N ζ n z n + ∑ n ≠ l p + 1, l ∈ N γ n z n. in a neighborhood of the origin, where ζ l p + 1 is an arbitrary constant satisfying the inequality | γ l p + 1 | ≤ B l p + 1, and the sequence { B n } n = 1 ∞ is defined in (19).
Then, by the Cauchy inequality, we have I 1 ≤ μ 1 ∑ | p | = | q | = m 1 2 ( | D q u N | 0, Q τ 2 + | D p u N | 0, Q τ 2 ) ≤ m ′ μ 1 | u N | m, Q τ 2. By the Cauchy inequality and the interpolation inequality (3.3), for an arbitrary positive number ε1, we have I 2 ≤ ε 1 | u N | m, Q τ 2 + C 1 | u N | 0, Q τ 2, where C1 = C1 ε1) is a nonnegative constant independent of u N, f and τ.
Constitutive equations are derived by means of the free energy imbalance inequality for an arbitrary three-dimensional deformation with finite strains.
As a consequence, we show that d-tuples of commuting strict contractions obeying an additional positivity constraint satisfy the d-variable von Neumann inequality for an arbitrary operator-valued bounded analytic function on the polydisk.
However, our approach provides proofs for the approximation of the corresponding function by the inequality of an arbitrary degree.
Since M 1 > M is an arbitrary large number, then the inequality ∑ ℓ = M ∗ M 1 − 1 ω ( ℓ + 1 ) ω < 0. holds.
The zero solution of the system of equations of neutral type (1.1) is called exponentially stable in the metric if there exist constants, and such that, for an arbitrary solution of (1.1), the inequality (2.1).
