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4 2 The black line is the branch cut. Lemma $$lim_{Deltato0^+}left(int_{gamma_1}+int_{gamma_2}right)f(z)ln(z-s)dz=-2pi iint_{pe^{itheta}}^{qe^{itheta}}f(t)dt$$ where $arg(z-s)in[theta,theta+2pi)$ , $f$ being holomorphic on the path of integration. Many advanced users on this site use this lemma without stating, letting alone proving it. I wrote a proof here, but it is quite long. Is there a shorter proof of this lemma? complex-analysis complex-integration share | cite | improve this question asked Nov 19 '18 at 0:27 Szeto 6,436 2 9 26 ...

5 I just tried to replace my chain for the first time - Shimano, 9-speed, labeled as CN-GH53. After I inserted the special pin, the joint is somewhat more stiff compared to the other ones. On the insertion side, it seems to protrude from the plate about as much as the regular pins (so almost not at all), and on the other side, where the guiding part of the pin was, it's protruding by about 0.5 mm. Is this normal, and will it get better once lube penetrates the link, or did I mess something up? I did notice that before I pushed it in enough to be aligned with the regular pins on the one side, the joint couldn't move at all and it got better once I got it further, but I don't want to push it in too far by accident. chain ...