Sentence examples for obtained a formula from inspiring English sources
We obtained a formula that describes the propagation speed of the helical structure, which is proportional to the DMI strength but is not influenced by the strength of the exchange interaction.
From a study of the rainfall and its connection with the amount of the harvest, Sir Napier Shaw applied the method of harmonic analysis to the quantity in question, and obtained a formula according to which its fluctuations are periodic, the period being eleven years.
In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply-connected groups which have since been proven, particularly Weil's conjecture on Tamagawa numbers over number fields.
Recently Strichartz proved that if μ is locally uniformly α-dimensional on Rd, then, where 0 ⩽ α ⩽ d, and BT denotes the ball of radius T center at 0; if μ is self-similar and satisfies a certain open set condition, he also obtained a formula for the α so that 0 < lim supT → ∞ 1Td − α) ∝BT¦(μf)\̂s|2 < ∞.
We obtained a formula for determining the direction and stability of a Neimark-Sacker bifurcation.
We proved differentiability of a functional and obtained a formula for its gradient.
Furthermore, we obtain a formula with error term for the reconstruction of the potential.
In the courses of our investigation we also obtain a formula for the products of multiple Lévy Itô stochastic integrals.
As an application of the n-OCF, we obtain a formula for the effective elastic stiffness tensor pertaining to an orthorhombic aggregate of cubic crystallites.
Along the way, we obtain a formula for the adiabatic limit of the eta invariant for invertible perturbations of Dirac-type operators, a result of independent interest generalizing the well-known formula of Bismut and Cheeger.
We obtain a formula for the asymptotic behaviour of the Dirichlet heat kernel for large time in terms of the survival probability of a Brownian motion, under the assumption that the latter decays subexponentially for large time.
