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The fracture network in shale gas reservoirs has a plurality of extending frontiers and the propagation paths of fractures are difficult to predict in advance.
Your discoveries have extended the frontiers of human knowledge.
For years, some politicians have progressively extended the frontiers of their entitlements.
The leading HVC protease inhibitors have tested and extended the frontiers of synthetic chemistry.
The surrender of Toledo in 1085 not only extended his frontiers to the Tagus River but also had great symbolic value.
After dissolving his marriage to Urraca, Alfonso I extended his frontiers to the Ebro River by seizing Zaragoza in 1118.
Those three have extended the frontiers of my mind and have made my job both supremely challenging but rewarding.
In serving political purposes and testing human moral qualities, great voyages of discovery have always inspired risk takers and extended human frontiers of thought and action.
The kingdom extended its frontiers to include Galicia to the southwest and Cantabria to the east before the end of the 8th century.
Carver pioneered a form that others have borrowed; Greene ultimately extended the frontiers of "Greeneland" over a long writing life that could encompass the wisdom and acceptance of mature years.
The imperial state extended its frontiers to include southern Kyushu during the 8th century and conquered the Ezo (Emishi) people in northern Honshu following a series of campaigns (late 8th early 9th century).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com