PEARLS model

Steady-state B) is the interesting one, of course, since steady-state (A) corresponds to complete washout of cells. Stability analysis has shown that the two cannot coexist at the same holding time either (A) is stable and (B) is unstable, or (S) is stable and (A) is unstable. Moreover, since (B) is a node if it is stable, we see that Monod s model will not predict oscillations— even damped ones—about a steady state of nonzero cell concentration. Hence, in this sense, there has been no improvement over the Verhulst-Pearl model. 

PMA belongs to the most common and most important weak PEs. The behavior of its aqueous solutions has been a subject of numerous studies [112-118], which started in early 1950s with the paper by Katchalski [112], The most important achievements were made by Strauss et al. [113-116], Morawetz et al. [117], and by Ghiggino et al. [118], It was soon recognized that PMA differs from other PEs, e.g., from chemically similar poly(acrylic acid). In 1985, Ghiggino and Phillips [118] were the first to propose the necklace of pearls model specifically for PMA on the basis of indirect fluorescence studies, i.e., more than 10 years before a similar model by Dobrynin became popular and generally recognized (however, their paper is almost unknown). 

Soutar et al. [125] measured the time-resolved anisotropy, r(f), for dilute solutions of PNIPAM, randomly labeled by ca. 5 mol.% acenaphthylene in water, methanol, and in the whole region of their mixtures at temperatures covering the LCST dependence (see Fig. 7) on the composition of the solvent mixture. They found that the anisotropy decays are double exponential in all cases. They used the string of pearls model for the system in pure water and in water-methanol mixtures, where they ascribed the short time to the rotation of probes in the highly solvated parts of the PNIPAM chain and the long time to the rotation of probes in coiled dehydrated parts. Because they also observed the double-exponential... 

Pearl, J. (2000), Causality Models, Reasoning and Inference, Cambridge University Press, New York. 

We now present the simplest analytical model [32] for the origin of qmax> the mechanism of growth of smectic pearls, and the growth of density fluctuations in the very early stages of nucleation of lamella. 

To address why a certain average distance is maintained between two smectic pearls at a very early stage, let us consider a model chain of N beads with only two smectic pearls (containing N and N2 beads) connected by a strand of m (=N-Ni- N2) beads (Fig. 6). 

The focus of this chapter is on an intermediate class of models, a picture of which is shown in Fig. 1. The polymer molecule is a string of beads that interact via simple site-site interaction potentials. The simplest model is the freely jointed hard-sphere chain model where each molecule consists of a pearl necklace of tangent hard spheres of diameter a. There are no additional bending or torsional potentials. The next level of complexity is when a stiffness is introduced that is a function of the bond angle. In the semiflexible chain model, each molecule consists of a string of hard spheres with an additional bending potential, EB = kBTe( 1 + cos 0), where kB is Boltzmann s constant, T is... 

Fig. 7 Model of the mechanism for ORR at the Cu/Modified Black Pearls Carbon Black cathode. (Reprinted from 222, with permission from Elsevier). 

Pearl LN, Taylor WR. A structural model for the retroviral protease. Nature 1987 329 351-354. 

Eq. (2.14) is identical in form to that derived by Debye (21) in his "pearl-necklace in shear model, where a Stokes law molecular friction factor was also assumed. 

Even if allowed by the CPT theorem, the non-conservation of CP symmetry was hard to accept - not least because it was not consistent with the Standard Model. In 1972, Kobayashi and Maskawa predicted that CP violation would be consistent with the Standard Model provided that three generations of quarks exist (and only two were known at the time). The subsequent discoveries of the r lepton by Pearls (1975) and of the top and bottom quarks at the Fermilab confirmed the existence of a third family, this resulted in the incorporation of the CP violation into the Standard Model. 

Reeves, R.H., Pearl, I.H., "Reaction Products Formed Upon the Alkaline Peroxide Oxidation of Lignin-Related Model Compounds", Tappi, 1965, 48(2), 121. 

Kirkwood and Riseman (1948) did not encounter this problem, because they used the bead-rod or, in other words, pearl-necklace model of macromolecule (Kramers 1946), in which A is a number of Kuhn s stiff segments, so that N present the length of the macromolecule. 

Parameter values were chosen so that Ub models a stiff covalent bond, whereas the repulsive portion of ii j, approximates a hard sphere potential of diameter au, which was set equal to the bond length a so that the chain becomes the familiar pearl necklace model. 

Pearl, J. (1999). Graphs, structural models, and causality. In Computation, Causation, and Discovery, 95-140. MIT Press, Menlo Park. 

Quantitative Structure Activity Relationship (QSAR) is a method that makes predictions by the quantitative description of molecular properties with the use of descriptors of the chemical structure (Dearden 2003). This means QSAR models describe the quantitative or calculated relationship between a chemical structure and their biological activity (e.g. toxicity) with the help of chemical descriptors that are generated from the molecular structure (Durham and Pearl 2001). This relationship is described in from of a mathematical equation (e.g. log 1/C = a tt + b a +. .. + const). QSAR models generally show better predictivity if all compounds of a dataset involved in the prediction are derived from a congeneric series of compounds, that means they should all act by the same mechanism of action, since the physico-chemical and structural descriptors used in the QSAR reflect the same mechanism of action. Sometimes it is difficult to determine the mechanism of action, so series of compounds involved in a QSAR model are often restricted to a given chemical class in the hope that this will ensure a single mechanism of action (Dearden 2003). 

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