Sentence examples for by replacing the value from inspiring English sources

The existence results (Theorems 3.1, 3.3, 3.5, 3.6) for problem (4.1) can be obtained using the strategy followed in Section 3 by replacing the value of ω with the following one: omega_{1}= frac{1}{Gamma(alpha+1)}+frac{1}{|Theta|} biggl{ frac {|A|}{Gamma(gamma+alpha+1)}+ frac{|B|(logeta)^{alpha}}{Gamma (alpha+1)} biggr}.

Let R(x 0,q 0,s 0) denote the bit string generated by replacing the value x 0(q 0) of bit string x 0 at offset q 0 by a new value s 0. Both stochastic processes (({L^{1}_{t}})_{t in mathbb {N}}) and (({L^{2}_{t}})_{t in mathbb {N}}) are then simulated for k gen steps to generate the k gen new test cases begin{aligned} x_{1}:=Rleft(x_{0}, {L^{1}_{0}}, {L^{2}_{1}} right) end{aligned} (20).

Finally, by replacing the values from Table 2, as in the example above, and rearranging terms, expression (36) is reached.

Finally, by replacing the values of C and (C^{T}) found as such, we get the constraint (29) given in the second part of the corollary.

By replacing the values of VCC, Vt, L, and M in (18) and (19), it can be found out that the power consumption on the chip on which the circuit is implemented is reduced by a factor of (1/9).

To this end, frequencies that exceeded 0.05 Hz were removed using a low pass filter and clear technical artefacts (e.g., due to an optode losing contact to the scalp during measurement) were corrected by means of interpolation by replacing the values of the corresponding channels with the values of the circumjacent channels in a Gaussian manner (closer channels were taken more into account).

The matrix was transformed into a binary matrix by replacing the values of all correlations > 0.7 by 1, and assigning the others as 0. The resulting binary matrix induced the adjacency matrix of the coexpression network, in which genes form the nodes and two genes are connected by an edge if they are correlated above 0.7.

In these cases, missing scores were handled according to recommendations in the BRIEF-A manual, by replacing the missing value with the value 1 (never).

For each subcategory, if the expression value for a gene was missing in both duplicate measurements, imputation was performed by replacing the missing value with 1.

This paper overcomes this failure by replacing the initial value problem with the well-conditioned "least squares shadowing (LSS) problem".

The squareness of the resulting amplitude-modulated waveform may be relaxed by replacing the constant value (Omega_{l}) with an arbitrarily varying function of time in each segment.