Rosin taken when melting it. It is soluble in alcohol, ether, benzene and chloroform. Rosin consists mainly of abietic acid, and combines with caustic alkalis to form salts (rosinates or pinates) that are known as rosin soaps. In addition to its extensive use in soap making, rosin is largely employed in making varnishes (including fine violin varnishes), sealing wax and various adhesives. It is also used for preparing shoemakers' wax, for pitching lager beer casks, and numerous other purposes such as providing backing surfaces to tin ware, copper ware, or even silver and gold vessels when embossing or engraving them (its
Envy-free cake-cutting many queries. As we show in the following subsection, it may be impossible to find an envy-free cake-cutting with connected pieces with a finite number of queries. An envy-free division with connected pieces for 3 or more agents cannot be found by a finite protocol. The impossibility proof uses a "rigid measure system" (RMS) - a system of "n" value measures, for which an envy-free division must cut the cake at very specific locations. Then, finding an envy-free division reduces to finding these specific locations. Assuming the cake is the real interval [0,1], finding an envy-free division using queries to