Sentence examples for by a simple expression from inspiring English sources
The flat on flat contact normal traction distributions are approximated for fretting fatigue by a simple expression.
For a favourable isotherm it was found that the theoretical equation of the breakthrough curve can be represented with sufficient accuracy by a simple expression proposed by ourselves.
The catalyst effectiveness factor is given by a simple expression that depends solely on the Thiele modulus and first series coefficient which is found by numerical solution of the dual-series using the method of weighted residuals.
Furthermore, a unified criterion to predict the critical buckling of substrate-supported graphene is given by a simple expression, which could be of great help in design and manufacture of graphene-based electronics and devices.
In sum, Paul agrees with Gregory that what is signified by a simple expression is different from what is signified by a complex expression, and that what is signified by a complex expression is also real, but disagrees with him about the meaning of the term 'res'res
Therefore, the reaction time is calculated by a simple expression: tprecursor = zprecursor2 × (topt/ zopt2), where opt indicates a measured optimal reaction time for a species with a known charge state.
If (g > g^{ast }); then one is (x_{I_{1,2}} = 0), whereas the others can be found by inverting a simple expression relating g and (x_{I_{1}}) along the solution branch: -x_{I_{1}} + frac{alphamu_{E}}{sqrt{N}}tanh(g x_{I_{1}}) = 0quad Rightarrowquad g = frac{1}{x_{I_{1}}} tanh^{-1} biggl( frac{sqrt {N}x_{I_{1}}}{alphamu_{E}} biggr).
When using an exponential function, the expression for Ω in eq 43 becomes rather complex and computationally expensive; the time dependence of the energy loss was therefore emulated by a simpler expression.
In order to achieve a simpler expression of the WIR, by employing the matrix inversion lemma and after some manipulations, we have WIR = ( D - k 2 s T R x s ) ( s T R x - 1 s ) ( s T s ) ( 1 - k l ) 2.6565).
The failure map can be described by a simple mathematical expression to give a simple force-based criterion for combine loading of solder joints.
In GDQ, the weighting coefficients for derivative approximations are given by a simple algebraic expression and a recurrence relationship, together with arbitrary choice of grid points.
