Sentence examples for decreasing solutions from inspiring English sources

Let DS r denote the set of all eventually positive decreasing solutions of (4).

The main result of [1] is the following theorem about the existence of positive, decreasing solutions of (1.1) (see [1, Theorem ] and its proof).

Our result, combined with asymptotic theorems from [2] or [3], yields asymptotic formulas for the positive, monotone decreasing solutions of (1.6).

Without loss of generality, we restrict our study to eventually positive decreasing solutions of (1); such a set is denoted as DS.

Theorem 1.1 indicates that (1.1) admits decreasing solutions for every small ϵ and the proof can be carried over to show that this system also admits increasing solutions.

The first theorem applies to the positive, monotone decreasing solutions of (1.6) provided that zero is a hyperbolic equilibrium of (1.6).

Decreasing solution pH enhanced pressure inactivation of HAV.

The minimum [Cl−] required for pit initiation increases with decreasing solution temperature, ie with decreasing solution aggressiveness.

It was found that the degradation efficiency increased with increasing temperature, treatment time and pressure, and decreasing solution concentration.

Extractable P increased with decreasing solution pH in all soils until the acid soluble P was depleted.

The reduction rate of Cr VI) increased with increasing total chromate concentration, [Cr VI ], and equivalent concentration of organic compounds, [OCs], and decreasing solution pH.