Proof. is equivalent to the function, which is decreasing.
Note that and therefore the claim is equivalent to the function being decreasing on.
Note that and therefore the claim is equivalent to the function being increasing on.
Note that p ∞ is equivalent to the function m both at 0 and at ∞ in terms of asymptotic behavior.
We observe that the condition (h0) holds, for example, if Ω is an unbounded open set with the cone property, or if the open set Ω has not the cone property but the weight function ρ is equivalent to the function dist (see [6]).
The weak formulation (2) is equivalent to the function equation left { textstylebegin{array}{l} frac{mathrm{d}u}{mathrm{d}t}+mu Au+B u)+G u)=f x,t),quad mbox{for }t>tau, u tau)=u_{tau}, end{array}displaystyle right.
Finding this extreme is equivalent to the function optimization problem, for which a large number of algorithms exist.
The form of the readout is equivalent to the functions of weighted, summed inputs used in neural network learning rules.
Continue until the point where the tangent line crosses is equivalent to the functions zero.
In the narrowband channel, the LSSUS expression when presented in the time-frequency domain can be deem to be equivalent to the channel correlation function (CCF) in [2] as will be explained in Section 4. To parameterize the non-WSSUS channel in time-scale domain using the LSSUS assumption, a stationarity degree estimation method is presented.
Nevertheless, choosing in particular and, the -monogenicity of the corresponding diagonal matrix, denoted by, is seen to be equivalent to the -monogenicity of the function.
