Sentence examples for infinitesimal changes of from inspiring English sources
Assuming that the displacements of atoms, thus the infinitesimal changes of bond lengths, are along the axial direction, Poisson's ratio ν is often expressed as ν = − dε trans/dε axial, where ε trans and ε axial represent the transverse and axial strains, respectively.
To ensure a smooth search for an optimal set of choice probabilities, we require that arbitrary infinitesimal changes of {pa(w)} allowed in the space of choice probabilities can be caused by some set of infinitesimal changes {dwj}.
MCA defines coefficients that describe the effect of infinitesimal changes of parameters on system properties, like reaction fluxes or variable concentrations (Heinrich and Rapoport, 1974; Kacser and Burns, 1973).
We have applied perturbation theory to study the effects of infinitesimal changes on the material balance analysis of the unit operation.
An ideal flicker-free evolution could be achieved with infinitesimal change of Δk, but it would then take infinite time to transport atoms.
The main result is thus a new expression for the derivatives of the induced velocities obtained by including the effect produced by a change in wake pitch due to an infinitesimal change of the circulation.
Non-holonomic kinematic conditions, which can be expressed in terms of a coupled set of rigid body and modal elastic co-ordinates and velocities, restrict the infinitesimal change of system generalized co-ordinates.
Therefore, if initialized at a saddle point, any infinitesimal change of P will cause the differential system to further increase the value of the objective function and, thus, to move away from the saddle point.
Hence (dwidehat {X}^{k}_{u}) is the infinitesimal change of this number and (beta ^{k}_{u},dwidehat {X}^{k}_{u}) is the cost of this change, which has to be absorbed by the change in the value of the trading strategy.
In order to explore all possible patterns of state-dependent choice probabilities smoothly, we assume that an arbitrary pattern of {pas} and an arbitrary direction of infinitesimal changes {dpas} allowed in the space of probabilities can be expressed by some pattern of w and some direction of infinitesimal changes dw, respectively (see Methods).
So, for instance, in the later 18th century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function.
