Time reversal, in physics, mathematical operation of replacing the expression for time with its negative in formulas or equations so that they describe an event in which time runs backward or all the motions are reversed.
Through replacing the expression of y ~ i pos from Equation 30 into Equation 31, it follows that J SAM pos = J SAM + μ i 2 κ ( i ) 2 ∑ l = P + 1 L c | y ~ i - l | 2 - 2 μ i ℜ Ξ i H y ~ i ∗ κ ( i ).
Consequently, as there are two minimum paths and since the two minimum paths have a Hamming distance of 1 and have the same weight, the conditioned bit error probability for RA scheme is obtained by replacing the expression of the minimum distance in Equation (12), thus obtaining the following expression P b | h i = 1 2 e r f c d min h 1,..., h L N R N 0, (13).
Proof First, in view of (3.2), we have to prove that m 2 ( 1 − ε κ ) 2 ≥ m 4 + κ ε κ 4 ε κ 2, which is equivalent to κ ≤ m 4 2 ε κ − 1 ε κ 4 ( 1 − ε κ ) 2. By replacing the expression of κ given by (2.9), we obtain 1 ≤ m 4, which implies that (3.5) holds for all m ∈ N.
Finally, by replacing the expression of G k into E k and using similar techniques as in [35] we obtain E k = I − α k, k T k † H k, k † · · α k, k 2 H k, k T k T k † H k, k † + R v k − 1 α k, k H k, k T k = = ( I + T k † R H k T k ) − 1, where R H k = α k, k 2 H k, k † R v k − 1 H k, k.
Sequentially replacing the expression for L into the equation for M and that for M into the equation for Y, we obtain the reduced form of model 4 (equation 4): Y = (β 0 + α 0 β m + α l β m γ 0 + β l γ 0 ) + (β x + α x β m + α l β m γ x + β l γ x ) X + (β c + α c β m + β l γ c + α l β m γ c ) C + (β m ϵ m + α l β m ϵ l + β l ϵ l + ϵ y ).
The unit was adopted in October 1933 by a committee of the International Electrotechnical Commission and is in widespread use today, although it has not entirely replaced the expression "cycles per second".
If t is finite, we must replace the expression in (22) by ([29], Eq. (32)).
telling us we may replace the expression on the left in a formula by the one on the right.
(23)–(25) have replaced the expression for w i in the PCA model, ∘ is the element-wise Hadamard product, and the product notation in 26 and 27 denotes independent draws.
The extraordinary boost in the understanding of the genetic and epigenetic mechanisms underlying the development and progression of different types of cancer, is offering an unprecedented hope for the development of precise therapeutics able to interfere or replace the expression of target genes.
