Sentence examples for above manipulations from inspiring English sources

What the above manipulations actually prove is the following: Given any summability method that is linear and stable and sums the series 1 − 2 + 3 − 4 +..., the sum it produces is.

All of the above manipulations resulted in the abolition of state alternations, although as physostigmine was metabolized, a return to alternations into the deactivated state began taking place (Figure S1).

The above manipulations of the optimality condition are by no means the only ways to derive a fixed-point equation for power optimization.

Now, we introduce the tampered region detecting method for the above three manipulations, respectively.

In most cases under the above admissible manipulations, authentication are correctly passed with average authRatio s higher than 1.2543, namely, only the perceptual quality is degraded and the semantic meaning is preserved.

However, none of the above mentioned manipulations appear to be a requirement for successful viral reprogramming of human T-cells.

88 89 Thus, the raw ordinal scores should not be summed into a single total, and the above mathematical manipulations (subtraction or division) of rehabilitation indices (table 4) may not be valid.

2) After the above genie manipulation is performed, the maximum of the T 2 and R 1 signaling dimensions are equal to (d_{mathsf {sum}}^{mathsf {max}}) in constraint (16), and since the scattering intervals are overlapped, the channel model becomes the Hilbert space equivalent of the well-studied MIMO Z-channel [35, 36].

The first relationship of (iii) can easily be proved by using the definition of (k_{1}) with the homogeneity of k and the second one follows from the above by simple manipulation.

On the other hand, the nonprehensile manipulations mentioned above often involve much faster time scale associated with the object motion.

At this step, by applying some basic manipulations, the above problem can be finally casted to a standard form of GP which is readily (8) as desired.