The phrase "after examining this" is correct and usable in written English.
It can be used when referring to a review or analysis of a particular subject or item before drawing a conclusion or making a decision.
Example: "After examining this report, I believe we need to adjust our strategy moving forward."
Alternatives: "upon reviewing this" or "after analyzing this".
But, after examining this, and switching the light on and off, I decided that one was more than enough.
After examining this Socratic project, we will follow Plato as he develops the project in his own directions.
After examining this mixed record, I came away with heightened admiration for those reporters like Mowrer and CBS's William Shirer who were consistently right.
After examining this history in detail, Lord Justice Leveson concluded that the Caryatid team had made mistakes in handling victims of the hacking and had failed to follow leads to other perpetrators but had acted in good faith, primarily because officers had to deal with far more serious crime involving terrorist plots to commit mass murder.
Pocock shows that Machiavelli's prime emphasis was on the moment in which the republic confronts the problem of its own instability in time, which Pocock calls the "Machiavellian moment". After examining this problem in the works of Machiavelli, Guicciardini, and Giannotti, Pocock turns to the revival of republican ideology in Puritan England and in Revolutionary and Federalist America.
After examining the basis of this claim, the fact-checking Web site Politifact rated it as "true," saying, "If anything, Clinton understated the number of people who have benefited from the program".
The rest of the models in the survey were selected after examining the publications citing this work in Scopus (52 papers) and Google Scholar (92 papers)2, and including the studies which proposed a generative model for the structure and growth of online discussion threads.
After examining the studies in this review, it is difficult to make any firm conclusion regarding the effect of surgeon or unit volume on mortality.
This picture, after examining the hard facts, becomes even more clear that this phase "the prison industrial complex" is inherently and explicitly linked to race, especially when one looks at the fact that more than 8.3 million children, namely over 2/3 of Black and Latino children, have at least one or both parents under some form of community or correctional supervision.
I came to this conclusion after examining the use of the word "willful" in the civil copyright infringement context and applying that use to the criminal statute.
The study's authors came to this conclusion after examining the results of 33 randomized clinical trials involving more than 1,800 people.
