Sentence examples for be rewritten as partial from inspiring English sources

By using the continuity equation (partial _{t} n + c,partial _{j}(nu_{j})) the latter can be rewritten as partial _{t} u_{i} + cu_{j}, partial _{j} u_{i} pmfrac{2c}{e} u_{i} ^{perp} u_{j}^{perp},partial _{j}V = 0 (60) which is decoupled from the continuity equation for n.

Condition (5.4) can be rewritten as (5.7).

then Theorem 2.8 can be rewritten as follows, let and.

Observe that (3.1) can be rewritten as (3.4).

If μ denotes the set of all positions of (K_{1}) in which either (t gK_{1})subset K_{0}) or (t gK_{1})supset K_{0}), then the fundamental kinematic formula of Blaschke (1.14) can be rewritten as int_{mu}dg+ int_{{gin G_{2} : partial K_{0}cappartial (t gK_{1}))neqemptyset}} chibigl(K_{0}cap t gK_{1}) bigr), dg=2pi bigl(t^{2}A_{1}+A_{0} bigr)+tP_{0}P_{1}.

Furthermore, Eq. 4 can be rewritten as: n_{ 1} left( {partial D/ partial z} right)_{ 1} = n_{ 2} left( {partial D/partial z} right)_{ 2} = C (5 where C is a constant and can be obtained from a calibration of RI- ∂D/∂z).

Eq. 8) can be rewritten as frac{partial u}{partial t}=frac{varphi hboxleft left|nabla uright|right)}{left|nabla uright|}varDelta u+nabla left(frac{varphi hboxleft left|nabla uright|right)}{left|nabla uright|}right cdot nabla u (9).

It is not difficult to show that varepsilon^ = -{bigllangle logbigl(1 - f^{ mathrm {me}}bigr) bigrrangle } and that the constraint equations (14) may be rewritten as frac{partial varepsilon^{partial A} = n,qquad frac{partial varepsilon^{partial B_{i}} = nu_{i},qquad - frac{partial varepsilon^{partial C} = ne, (21) where (i = 1,ldots,d).

Using the definition of Riemann-Liouville tempered fractional derivative, Eq. (1.1) can be rewritten as frac{partial (e^{lambda t}u x,t))}{partial t} = _{0}D_{t}^{1 - alpha} biggl[ - frac{partial}{partial x}F x) + frac{partial^{beta}}{ partial vert x vert ^{beta}} biggr]bigl(e^{lambda t}u x,t) bigr).

We first note that Eq. (10) may be rewritten as frac{partial}{partial t}P x,t)=frac{partial}{partial x} bigl[ B x P_{x} bigr] + alpha P_{x}+beta P, (12) where (alpha=-A+B_{x}), (beta=-A_{x}+B_{xx}), and each subscript (bullet _{x}) denotes a partial derivative with respect to x.

The laws of conservation of mass and conservation of momentum can be rewritten as frac{{partial left( {gamma rho } right)}}{partial t} + {text{div}}left( {gamma rho varvec{u}} right) = 0, (7) frac{{partial left( {gamma rho varvec{u}} right)}}{partial t} + {text{div}}left( {gamma rho varvec{u} times varvec{u}} right) = - gamma nabla p (8 where γ is the porosity.