The phrase "and proceeding for" is not standard in written English and may cause confusion.
It could be used in contexts where you are describing a continuation or action that follows a previous statement, but it is not commonly used.
Example: "The committee discussed the proposal and proceeding for further evaluation was agreed upon."
Alternatives: "and moving forward with" or "and continuing with".
Starting about the middle of the 20th century and proceeding for several decades, organizational psychologists conducted many studies that correlated job satisfaction with performance.
Each run included four Markov chains, three heated and one cold, starting from random trees and proceeding for 250,000 generations.
It is easy to show that the expected number of times that a random walk starting at node v i and proceeding for k steps will visit node v j, denoted as, can be calculated as, where is the (i, j th entry of l-step transition probability matrix.
Similarly we define the k-step transition probability matrix P aug { k } = P aug k and calculate the expected number of times that a random walk starting at node v i and proceeding for k steps will visit node v j, H e aug { k } (v i, v j ) = ∑ l = 0 k p i j { aug, l }, where p i j { aug, l } is the (i, j th entry of the l-step transition probability matrix P aug { l }.
We first calculate He{ k}(A, B) as the expected number of times that a random walk starting at node A and proceeding for k steps, will visit node B; then we further define a n-dimensional vector H e { k } (v i ), ∀ v i ∈ V, where H e { k } (v i ) = (H e { k } (v i, v 1 ), H e { k } (v i, v 2 ),..., H e { k } (v i, v n ) ).
Given the one-step transition probability matrix Ppath as well as the l-step transition probability matrix P path { l } = P path l, ∀ l ≥ 0, we can calculate the expected number of times that a random walk starting at node v i α and proceeding for k steps will visit node v j β, EXP { k } (v i α, v j β ) = ∑ l = 0 k p i α, j β.
Turn left at the visitors' center and proceed for three and a half miles on Rockwell Road to the Jones Nose trailhead and parking area.
Newbury Street starts right at the Public Garden and proceeds for the length of the historic, beautiful, and romantic Back Bay neighborhood.
The products were then dried in a vacuum oven at 100 °C for 3 h and proceeded for characterization.
This suspension is then mixed with 0.7% agarose and proceeds for the experiment (Simon et al. 2013).
This sample is first diluted with 50 μl PBS and then mixed with equal volume of 1% LMA and proceed for the experiment (Bajpayee et al. 2005).
