For example, the scalar
perturbations at the linear level reveal that F(T, [THETA]) cosmology can be free of ghosts and instabilities for a wide class of ansatzes and model parameters [13,14].
Moreover, it is known--as a consequence of more general results in  and following previous results for the scalar
field--that, for the Dirac field in globally hyperbolic space-time with compact spatial sections, all pure Fock Hadamard states lead to unitarily equivalent quantizations.
When a scalar
IM is used, if ln(EDP|IM) is assumed to have a Gaussian distribution, then the estimated conditional probability of exceeding an EDP level edp given IM = im is computed as 
Then, for a scalar
type spectral operator A in a complex Banach space (X, [parallel]*[parallel]), equalities (18) are true; the scalar
type spectral operators T (t[absolute value of A]), t > 0, are understood in the sense of the Borel operational calculus and the function T(*) defined by (17) is replaceable with any nonnegative, continuous, and increasing on [0, [infinity]) function F(*) satisfying condition (20).
Figure 4 plots the theoretical SNR using (15) of the forward adaptive scalar
compandor in the assumed variance range, for L = 32 levels log-uniform quantizer used for variance quantization and different number of quantization levels N for the adaptive quantizer.
The influence of the scalar
dissipation rate on a steady state diffusion flamelet is best illustrated by the well-known S-shaped curve, which is shown in Figure 4 .
Each opening of interest on the vehicle needs a separate passive scalar
The above integral equation is equivalent to the summation of CSB vector and scalar
In contrast to the other estimation methods (DVT, MSCT, and FPT), which directly observe the electrode in relation to anatomic structures, MRI-based estimation indirectly observes the electrode via the diminution of the scalar
The Gram determinant  (composed from pairwise scalar
products of the current and voltage IV vectors) equals to square of the vectorial IP (8)
The Report describes a series of mechanical characterization tests that apply to both feet and pylons, of which 10 tests generate scalar
values to check against thresholds and 3 tests require observation of the components' behavior during evaluation to confirm whether the component passes or fails to achieve a certain motion.