By Cruz-Barroso R., González-Vera P., Njåstad O.

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**Additional info for On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands**

**Example text**

Discussions, 2, 310 (1947). 5"C M + hv Qr + M Q'r + Q n = Q I + Qo = Q'r+l = Qr rate=f( I) kP + Qn kt M: monomer, Qtr: an active "half-chain" of length r units, Qr: an inactive "half-chain" of length r units. 9 k,=5 X 1OSexp(-4400 cal/RT) k,= 1O8 f(1): rate of initiation, [mol/l*sec] k,: propagation rate constant, [l/mol*sec] k,: disproportionation termination rate constant, [I/mol*sec] 45, 323 (1949). Mackay, M. H. and Melville, H. , Trans. , Photo-induced bulk polymerization Temperature: 0°C 2M + 2X or D2 X + M + X D2 + M + D1 + R DI + M - t P2 + R R + M + PI + R D2+X+DI+Q D I + X + P Z + Q R + X + P I + Q 2x 24 + M: monomer, X: active center, Q: dead center, D2: initial polymer growing at both ends, DI: polymer growing at one end, R: growing transfer polymer, PI: dead transfer polymer, Pz: dead initial polymer.

8, 529 (1952). Copyright 0 1952 John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc. 3 Ri: R,: R,: kt,: initiation rate, [mol/l*sec] propagation rate, [mol/l*sec] termination rate, [mol/l*sec] termination rate constant by combination, [l/mol*sec] ktd: termination rate constant by disproportionation, [I/moI*sec] k,: propagation rate constant, [I/mol*sec] [I]: concentration of initiator, [mol/l] [Ma"]: average monomer concentration, [mol/l] [C*]: radical concentration, [mol/l] f I: initiator efficiency, [-3 Van Hook, J.

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.

### On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands by Cruz-Barroso R., González-Vera P., Njåstad O.

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