Further research by Dana Shew, Jan 30, 2012

The photograph that shows Adam Andrew, Carl W. Mueller, and Frank H. Dunne banners is likely the 1902 election. This is the only election that all three of them participated in at the same time. I initially thought the banners were from 1901 based on the article I sent you from Oct 2 1901, however I found another article that states that Andrew withdrew from the race that year. He ran in 1902 for the Railroad Commissioner and won. I don’t find him in another election between 1902 and 1907. He is still commissioner in 1905. Mueller was active in the German Republican party but only ran in the 1902 election based on what I could find. He was a county clerk deputy, on the finance committee of the Republican Primary League and a delegate of the German American Republican Club and the secretary of the German American League. See below PDF files.

Adam Andrew withdraws-SF Call Oct 1901.pdf
Adam Andrew RR Commissioner-SF Call 1902.pdf
Election results-Andrew, Dunne, Mueller-1902.pdf
Mueller county clerk-SF Call 1901.pdf
Mueller finance committee 39th Assembly Dist-SF Call July 1901.pdf
Mueller nomination-SF Call Sept 1902.pdf