Future changes are only predictable if they are linear extensions of past trends; otherwise, future period effects are not predictable from past rates.
Let g : I n → ℝ be a piecewise linear extension of f.
Type 2 lesions are characterized by linear extension of contrast media into the superior labrum and the biceps anchor.
More recent neural network models such as back-propagation [8], [9] and basis function networks [10], [11] are simply non-linear extensions of the originally proposed models in the sense that they implement a mapping from stimulus to motor response by adapting (synaptic) weights in networks with fixed topology.
The SOM model may be viewed as non-linear extensions of standard regression models in the sense that it performs various non-linear mappings between the variables in the input, hidden, and output layers [ 42].
(widetilde{D} L^{p(x)}(Omega,mathrm{C}ell_{n}) rightarrow W^{-1,p(x)}(Omega,mathrm{C}ell_{n})), where the operator (widetilde{D}) can be considered as a unique bounded linear extension of the Dirac operator.
(widetilde{T}: W^{-1,p(x)}(Omega,mathrm{C}ell_{n}) rightarrow L^{p(x)}(Omega,mathrm{C}ell_{n})), where the operator (widetilde {T}) can be considered as a unique bounded linear extension of the Teodorescu operator.
(ii) (widetilde{T}: W^{-1,p(x)}(Omega,mathrm{C}ell_{n}) rightarrow L^{p(x)}(Omega,mathrm{C}ell_{n})), where the operator (widetilde {T}) can be considered as a unique bounded linear extension of the Teodorescu operator. .
(ii) (widetilde{D} L^{p(x)}(Omega,mathrm{C}ell_{n}) rightarrow W^{-1,p(x)}(Omega,mathrm{C}ell_{n})), where the operator (widetilde{D}) can be considered as a unique bounded linear extension of the Dirac operator. .
If pentanol is added to the synthesis solution in concentrations above 2.4 vol%, a linear extension of 5.6% was measured at a constant load of 0.6 MPa.
