Sentence examples for using the following condition from inspiring English sources

Samreen and Kamran [20] also obtained useful results for such mappings by using the following condition, which is weaker than ((mathcal{P})) ((mathcal{P'})):  for any ({f^{n}x}) in X such that (f^{n}x to yin X) with ((f^{n+1}x,f^{n}x) in E(G)) there exist a subsequence ({f^{n_{k}}x}) of ({f^{n}x}) and (n_{0}inmathbb{N}) such that ((y,f^{n_{k}}x) in E(G)) for all (kgeq n_{0}).

The PCR reaction was carried out in a Rotor-Gene 2000 real-time thermal cycling system (Corbett Research, Australia), using the following condition: 95°C for 2 min, followed by 40 cycles of 95°C for 15 s, 55°C for 20 s, and 72°C for 20 s.

Detail information of qRT-PCR Primers were provided in Additional file 4. qRT-PCR was performed with an ABI7300 real-time PCR system (Applied Biosystems, Foster City, CA), using the following condition: 95°C for 30 s followed by 40 cycles in 95°C for 5 s, 60°C for 30 s and 72°C for 31 s.

Following denaturation (94° for 5 min ., PCR was performed for 32 cycles using the following condition (94° for 30 sec., 45° for 30 sec, 72° for 1 min ., followed by a 5 min. extension at 72°.

A bound on tail probabilities for quadratic forms in independent random variables is seen by using the following condition.

Hanson and Wright (1971) obtained a bound on tail probabilities for quadratic forms in independent random variables using the following condition: for all n ≥ 1 and all x ≥ 0, there exist positive constants M and γ such that P ( | X n | ≥ x ) ≤ M ∫ x + ∞ e − γ t 2 d t. (3.4).

Quantitative PCR was performed in triplicate with an Applied Biosystems Prism 7500 Fast Sequence Detection System Applied Biosystemss) using the following conditions: 10 min, 95 °C; followed by 40 cycles of 30 s; 95 °C, 60 s; 60 °C.

The reverse primer was then added and quantitative PCR was performed using the following conditions; 94°C for 15 mins, followed by 40 cycles of denaturation/amplification (95°C for 30 secs, 60°C for 60 secs).

PCR was performed using the following conditions: 95ºC for 2 min, followed by 50 cycles at 95ºC for 15 s and 60ºC for 1 min.

Amplification and real-time measurement was performed in the 7500Fast ABI system (Applied Biosystems, Foster City, CA, USA), using the following conditions; 15 min at 95°C followed by 40 cycles of 15 s at 95°C and 1 min at 60°C.

The reactions were conducted in an Eppendorff Realplex Mastercycler using the following conditions: 95°C for 2 min, followed by 40 cycles of 95°C for 15 s, 60°C for 15 s and 68°C for 20 s.