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The globular shape of dendritic polymers also results in lower hydrodynamic volume and lower viscosity compared to linear polymers Dendritic polymers have potential for use as additives to polymers and oils to modify their viscosity, melt behavior, and lubricating properties; and to aid in compatibilizing mixtures of different materials The difference between linear and dendritic polymers has an analogy in nature For example, there are globular and elongated (more often called brous) proteins The brous proteins have strong secondary attractive forces and are used to construct such materials as bone, skin, and nails Globular protein molecules do not attract each other strongly and are soluble in aqueous media, and this ts their biological functions Globular proteins perform catalytic, transport, regulatory, hormonal, and other functions that require their solubility in blood and the other aqueous media of cells and tissures.



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Instead of going from Maxwell equations to a quantum description of light as we have done so far, let us take the reverse route. Let us forget about classical electrodynamics for the moment and try to obtain a wave equation for a frees quantum of light. This is what Oppenheimer called an extreme quantum theory of light [472]. This section is very much in the spirit of [472], with the crucial exception that here we will allow for the possibility that the light quantum might have a nonvanishing rest mass. As discussed in Section 3.1, this will allow us to define a position operator that will have localized eigenstates in the nonrelativistic limit. So an ordinary first-quantization wavefunction description will be possible. On the other hand, we will see that instead of Maxwell equations, this approach leads us to a different description where there is no gauge freedom for the potentials: Proca equations. Maxwell equations are recovered only if we take the limit of vanishing rest mass. Our derivation of the Proca equations will be quite different from the usual textbook derivation, where a so-called mass term is added to the ordinary Lagrangian of the electromagnetic field. Even though this popular textbook derivation is how Proca eventually derived his equations in [498], we think that his earlier failed approach to the problem in [497] is more enlightening. In [497], Proca starts to look for a wave equation for the photon the same way as Dirac did for the electron. But then he follows an idea by Lanczos [383, 384] that both generalizes and gives some insight into Dirac's method to get an equation of first order in time from an equation that is





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Jan 16, 2019 · Export (Convert) Image to PDF using iTextSharp in ASP. ... then the Image file will be added into the iTextSharp PDF document and ultimately ...

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Another (obvious) difference between linear and dendritic polymers is that dendritic polymers have a much larger number of chain ends The interesting situation arises when the dendritic polymers are synthesized by methods that result in functional groups such as NH2, OH, or COOH at the chain ends Such polymers carry a large number of derivitizable functional groups and hold promise as carrier molecules for drug delivery, gene therapy, catalysis, and sensors [Frechet and Tomalia, 2002; Stiriba et al, 2002] Two types of dendritic polymers have been developed: hyperbranched polymers and dendrimers 2-16a Random Hyperbranched Polymers.

second order in time (Le., the Klein-Gordon equation). So we present a derivation of Proca equations along the lines of [497] but not quite. 9 If the photon has a nonvanishing rest mass m, however small, its energy-momen tum relation is given by

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Hyperbranched polymers are produced in a one-pot synthesis using a multifunctional monomer such as ABf where f is 2 or greater [Bolton and Wooley, 2002; Galina et al., 2002; Kim, 1998; Voit, 2000]. Hyperbranched polymers are more correctly called random hyperbranched polymers because the branching occurs in a random manner. For an AB2 multifunctional monomer such as a diamino or dihydroxy carboxylic acid, f 2 and the product has a structure described by LXII. With increasing conversion AB2 adds to LXII to produce higher X n polymer. The random hyperbranched polymer at every stage of its growth has a single

You can use a keyboard shortcut to insert a page break as you type in your document; press + . You can insert a line break by pressing + . You can change the page number style. Click the Page Number button on the Insert tab and then click Format Page Numbers.This opens the Page Number Format dialog box. Select the style you want.

unreacted A group. The number of unreacted B groups is given by Eq. 2-241 [Kim, 1998]. LXII has X n 13 and 14 unreacted B groups. The number of unreacted B groups increases with increasing X n and f .

-;;- )

Unreacted B groups 1 X n f 1 2-241

- PI -

A hyperbranched polymer is often characterized by the degree of branching DB [Holter et al., 1997; Jo and Lee, 2001; Kim, 1998; Lee et al., 2000]. For the hyperbranched polymer produced from AB2, there are three different types of repeat units: dendritic, linear, and terminal units de ned as units having two, one, and no B groups reacted, respectively. The degree (fraction) of branching (DB) is given by

(3.19)

DB D T D T L 2-242

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Merge multiple image files into a single PDF file with ASP.NET C#
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iText copies the bytes of a JPG straight into the PDF. Not a single byte is changed​. If you say that your JPGs have clipping paths (I've never heard of such a thing) ...












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