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does anyone know why in Illustrator, I don't see the "stripes" like the picture below but when I export it into pdf, I see a lot of these stripes? I am doing science, I need to export into pdf for my paper. Thank you very much!

enter image description here

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This is unfortunately something you can not fix with simple export options, or even quickly at all. Objects simply have to overlap because there is a well known, but ignored, error in the way most (if not all) vector engines render the shapes.

I have explained this in more detail here and here, and you can see a nice way to avoid it here

Simply put the programmers have made a assumption that opacity equals coverage. This is not true, it will not work. How severe the lines are depend heavily on the PDF viewer and method used to rasterize used. In general a commercial printer, should have no need for subpixel renders so there would be no coverage issues to be had, despite what your PDF preview says. Ask the printer for a proof. However for cheap home printers i wouldn't go and take this bet.

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