Sentence examples for a result assuming that from inspiring English sources

As a result, assuming that (M=1), we can recover asymptotics for the ground state energy ({mathsf {E}}) with the Scott correction term but with the remainder estimate (O(Z^{5/3}+ Z^{4/3}B^{1/3})).

As a result, assuming that an apprentice only performs skilled tasks, and not accounting for a firm's training expenditures, "fair" apprentice pay in relation to that of a skilled worker would be approximately 8% during the first year of training.

As a result, assuming that (M=1) if (Z^{4/3}le Ble Z^3), we can recover the asymptotics for ({mathsf {E}}) with the Scott correction term but with the remainder estimate (O(B^{4/5}Z^{3/5}+ Z^{4/3}B^{1/3})).

First, a P-value only shows the probability of getting a result assuming that the null hypothesis is true and does not reflect the probability of getting a result assuming an alternative hypothesis to the null hypothesis is true.

(comparison result) Assume that, are lower and upper solutions of the boundary value problem (1.1).

This is likely a robust result, assuming that the timescales for the thermochemical destruction of sulfuric acid, and subsequent depletion of the reservoir, are likely to occur at somewhat longer timescales than the microphysical processes observed here (Krasnopolsky 2007).

This is an expected result, assuming that stomach contents are composed of food items ingested during the last few hours whereas dental microwear texture records the physical properties of items eaten over periods of days or weeks.

We also prove a partial nonperturbative result assuming that the function v belongs to some particular Gevrey classes.

This result was used in [123] to prove a semiglobal solvability result assuming that one metric is close to the Euclidean and the other has bounded curvature.

Later in [28] Vitanza proved an existence theorem for a Dirichlet problem, under weaker assumptions than those introduced by Miranda in [29], and a W 3, 2 regularity result assuming that the partial derivatives of the coefficients of the highest and lower order terms belong to a vanishing Morrey space depending on the dimension.

Asaad and Shaalan (Theorem 3.8 in [3]) proved the following generalization of Baer's result: Assume that a finite group G is the product of the supersoluble subgroups H and K. Assume further that G' is nilpotent.