Text: topmost specialize in producing outdoor leisure furniture, which sells well in europe, american, australia, southeast asia, etc., having won a good reputation.

Correct capitalization: Topmost specialize in producing outdoor leisure furniture, which sells well in Europe, American, Australia, Southeast Asia, etc., having won a good reputation.

Text: note that the lhs of the equations involve only geometric quantities and the rhs only physical quantities.

Correct capitalization: Note that the LHS of the equations involve only geometric quantities and the RHS only physical quantities.

Text: and he kissed all his brethren, and wept upon them: and after that his brethren talked with him.

Correct capitalization: And he kissed all his brethren, and wept upon them: and after that his brethren talked with him.

Text: you can enjoy them anytime without dvd discs, or burn them to blank discs by burning software.

Correct capitalization:
You can enjoy them anytime without DVD discs, or burn them to blank discs by burning software.