Sentence examples for vanishes I from inspiring English sources

It is shown that there are four cases, depending on the critical level(s) where the Doppler shifted frequency vanishes: (i) for propagation upstream the critical levels are outside the duct (case II); (ii) for propagation downstream there may be two (case IV), one (case I) or no (case III) critical level inside the duct.

Under the property of zero mean of noise n(t) and sensor error represented by ΔA, the expectation of the cross-terms vanishes (i,e., E [ D y ° p ] = 0 and E [ D p y ° ] = 0 ), and it follows, E [ D y ̃ y ̃ ( t, f ) ] = E [ D y ° y ° ( t, f ) ] + E [ D pp ( t, f ) ] (15).

Caputo: The projectile reaches its maximum height when its vertical component vanishes, i.e., (dot{y}=0).

Thus, the radial chloride flux at the om − oa interface (r = r oa ) vanishes, i.e. q_{oa} (r_{a},theta ) = 0 (15).

The magnetic field line coordinate system is identical to the spherical coordinate system when the solar rotation vanishes, i.e., when α=0.

In order to guarantee the global exponential stability of system (1), we assume that the system tends to its equilibrium point and the stochastic noise contribution vanishes, i.e., (rho(x^,y^,y^,t) = 0); (i,j = 1,2,ldots,n).

In addition, the shock speed σ does not vanish, i.e., there is not a stationary shock.

For non-polar media the spin and its production vanish, i.e., s i =0 and ε ijk σ jk =0.

Furthermore, suppose that G 1 ( x, a ), G 1 ( b, t ), G 2 ( a, t ), G 2 ( x, b ) do not vanish i d e n t i c a l l y in ( a,b ).

Roots are values of the independent variable which cause a function to vanish, i.e. to be equal to zero.

"Were you on board when Rebecca Coriam vanished?" I ask.