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Each monomer molecule that adds to a reactive center regenerates the reactive center. Polymer growth proceeds by the successive additions of hundreds or thousands or more monomer molecules. The growth of the polymer chain ceases when the reactive center is destroyed by one or more of a number of possible termination reactions. The typical step and chain polymerizations differ signi cantly in the relationship between polymer molecular weight and the percent conversion of monomer. Thus if we start out step and chain polymerizations side by side, we may observe a variety of situations with regard to their relative rates of polymerization. However, the molecular weights of the polymers produced at any time after the start of the reactions will always be very characteristically different for the two polymerizations. If the two polymerizations are stopped at 0.1% conversion, 1% conversion, 10% conversion, 40% conversion, 90% conversion, and so on, one will always observe the same behavior. The chain polymerization will show the presence of high-molecular-weight polymer molecules at all percents of conversion. There are no intermediate-sized molecules in the reaction mixture only monomer, high-polymer, and initiator species. The only change that occurs with conversion (i.e., reaction time) is the continuous increase in the number of polymer molecules (Fig. 1-1a). On the other hand, highmolecular-weight polymer is obtained in step polymerizations only near the very end of the reaction (>98% conversion) (Fig. 1-1b). Thus both polymer size and the amount of polymer are dependent on conversion in step polymerization. The classi cation of polymers according to polymerization mechanism, like that by structure and composition, is not without its ambiguities. Certain polymerizations show a linear increase of molecular weight with conversion (Fig. 1-1c) when the polymerization



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Siegman showed that for those lasers the perfect cavity mode expansion of the radiation field breaks down and one must use instead the actual modes of the open laser cavity, which are nonorthogonaL Thus, the breakdown of the Gardiner-Collett Hamiltonian, the need to adopt the.

a b g b bs 2 2 2-48

12Notice that unlike the constant coupling strength advocated by Barnett and Radmore [37] and Gardiner and Collett [225], among others, the frequency-dependent Vn(k) given by (9.57) does not make the phase shift integral in the Fano diagonalization method diverge. Moreover, (9.57) is practically flat (constant) within the cavity resonance peaks but falls off between peaks.

The integral in Eq. 2-46 yields simple integrals for s values of 0, 1, and 1. The dependencies of a, b, and g on t in these instances are 1. For s 1, that is, k2 k1 ,





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How to convert Word to PDF using C# and VB.NET | WinForms - PDF
31 Oct 2018 ... Steps to convert word document to PDF programmatically : Create a new C# console application project. Install the Syncfusion.DocToPDFConverter.WinForms NuGet packages as reference to your .NET Framework application from NuGet.org. Include the following namespaces in the Program.cs file.

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natural cavity modes rather than perfect cavity modes, and the emergence of excess noise in lasers are all connected.

b 1 g a 1 2t 2-49

2. For s 0, that is, k1 ) k2 , where k1 has some value and k2 ! 0: B0 groups do not react (g 1) and

80 60 40 20 0 0

3. For s 1, that is, k2 ) k1 , where k2 has some value and k1 ! 0: B groups do not react b 1 and

-:--... 1 2 3 4 5

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For almost all other values of s the integral in Eq. 2-46 must be numerically evaluated. The results of such calculations are presented in graphical form in Figs. 2-3 and 2-4 as plots of a, b, and g versus log t for s values of 1 and larger [Ozizmir and Odian, 1980]. There is no need for plots for s < 1, since the B and B0 groups have interchangeable roles due to the symmetry of the reaction system. a at any time is exactly the same for s z or s 1=z, where z is any number. The only difference for an s value of z or 1=z is whether it is the B or B0 type of group, which reacts rapidly while the other reacts slowly. Figure 2-3 gives b and g as a function of t. When s 1 both b and g decay at the same rate according to Eq. 2-49. As s increases the b plots move sharply above the plot for s 1 since B groups react more slowly with A. Although k2 is xed, increasing values of s help move the g plots gradually below the plot for s 1, since B groups reacting more slowly with A leaves comparably more [A] for

Figure 9.3 Here we show the coupling strength Vn (k) in relation to the cavity resonances. The thin line is a plot of 1 (k)12; the peaks show the cavity resonances corresponding to k o, kl, and k2. The thick dotted line is a plot of sin2 ([k - kIJL)j(k - kI)2 properly scaled to appear in the figure. Notice how VI (k) is practically flat inside the n = 1-mode Iinewidth and falls off as it approaches the next modes. We have used an energy reflectivity Irl2 of 96% (i.e., = 0.2).

To name a field, click the Click to Add link at the top of the field column. Click the type of field you want to add (here, Text).

Fig. 2-3 Decay in b and g with time in the polymerization of A A with B B0 . b plots are indicated by 4; g plots, by *. Values of s are noted for each curve. After Ozizmir and Odian [1980] (by permission of Wiley-Interscience, New York).

Another interesting feature of this derivation is that even though we have not adopted the rotating-wave approximation, there are no counterrotating terms in (9.56). This absence of counterrotating terms is a consequence of a n 2(k) and i32(k,k') vanishing in the high-Q approximation. It guarantees that the master equation derived from (9.56) is of the Lindblad form [411], as (6.68), derived in 6.

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NET Source Code for fast Converting PDF pages to Word (.doc/ .docx) Document with .NET XDoc.PDF Library on C# class, ASP.NET web forms (aspx), ajax, ...

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I want to convert pdf to Word using C# | The ASP.NET Forums
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