By N. N. Lebedev
Recognized Russian paintings covers simple concept of the extra very important specified capabilities and their software to express difficulties of physics and engineering. most room dedicated to the applying of cylinder services and round harmonics. additionally explores gamma functionality, chance necessary and comparable capabilities, ethereal features, hyper-geometric services, extra. Translated by way of Richard Silverman.
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Additional resources for Special Functions & Their Applications (Dover Books on Mathematics)
6 b: decomposition rate constant, [ l/sec] ki: initiation rate constant, [Vmol-sec] k,: propagation rate constant, [I/mol*sec] ktc: termination rate constant by combination, [l/mol*sec] ktd: termination rate constant by disproportionation, [I/mol*sec] Kuo, J. F. and Chen, C. Y. Polym. J, 13, 453 (1981). 51 Methyl methacrylate Bulk polymerization Initiator: 2,2'-azobisisobutyronitrile Temperature: 25°C Initiation I R" + M Propagation Pi," + M Chain transfer +Y Termination by disproportionation P,O + PI," + PI," P,,O Termination by combination P,,O + + + + + + 2R" Pi'' Pnt i o PI, + Y" P, + PI, P,+,, kd ki kP ktW ktd(n,m) ktc(n,in) I: initiator, M: monomer, R" : primary free radical, P," : growing polymer radical containing n units of monomer, P,: dead polymer containing n units of monomer, Y: chain transfer agent.
6 0 ko: frequency factor, [-I E,: activation energy, [cal/mol] V,: activation volume, [ml/mol] P: pressure, [atm] T: temperature, [OK] K,: initiation rate constant, [ l/sec] K,: propagation rate constant, [I/mol sec] Kfi,,: monomer transfer rate constant, [Vmol sec] Kfsn:solvent transfer rate constant, [I/mol*sec] K,c: termination rate constant by combination, [I/mol*sec] Ktd: termination rate constant by disproportionation, [I/mol- sec] Kscn: short chain branching rate constant, [ l/sec] Shirodkar, P.
105, 212 (1967). , Makromol. , 114, 201 (1968). Methyl methacrylate 47 Bulk polymerization Initiator: 2,2'-azobisisobutyronitrile Temperature: 60°C C R + M Xr + M Xr + X, Xr + R 2R 2R +XI + + + + + Xr+l Pr + P, or Pr+, P, products C: initiator, R: primary radical, M: monomer, Ar: growing polymer radical with r monomer units, P,: dead polymer with r monomer units, Y: chain transfer agent. 41 x [C]: concentration of initiator, [mol/l] [MI: concentration of monomer, [mol/l] kd: decomposition rate constant, [ l/sec] ki: initiation rate constant, [Vmol esec] k,: propagation rate constant, [I/mol*sec] k,: termination rate constant, [Vmol-sec] kt,: primary radical termination rate constant, [Vmol-sec] k,,: rate constant between primary radicals, [I/mol- sec] R,: propagation rate, [mol/l-sec] Ito, K.