Addition-subtraction network

Another stream of the study of temporal networks concerns a model network whose history involves cross-links added at a certain stage, a part of which is subsequently removed so as not to be present in the final stage of deformation (called an addition-subtraction network). On the basis of such model composite networks, Flory [14] calculated the stress relaxation, and found that it obeys slow dynamics including a logarithmic dependence of the stress, which is closer to power law rather than exponential. 

Flory s intuitive argument was later confirmed by Fricker [15] with minor modification by a replica calculation. Owing to the rather arbitrary assumption about chain creation and annihilation, the addition-subtraction network model is difficult to apply to real physical gels. 

Substrate Treatment. When the desired image is developed in the resist, the pattern created provides a template for substrate modification. The various chemical and physical modifications currently used can be classified into additive and subtractive treatments. Examples of additive treatments include the insertion of dopants (by either diffusion or ion implantation) to alter the semiconductor characteristics and metal deposition (followed by lift-off or electroplating) to complete a conduction network. In most cases, however, the substrate material is etched by a subtractive process. 

Transient — Subcycle disturbance in the AC waveform evidenced by a sharp, brief discontinuity of the waveform. This may be of either polarity and may be additive or subtractive from the nominal waveform. Transients occur when there is a sudden change in the voltage or the current in a power system. Transients are short-duration events, the characteristics of which are predominantly determined by the resistance, inductance, and capacitance of the power system network at the point of interest. The primary characteristics that define a transient are the peak amplitude, the rise time, the fall time, and the frequency of oscillation. Figure 1.12 shows a transient voltage waveform at the output of a power transformer as the result of switching-in of a motor containing power factor correction capacitors. 

The percolation model suggests that it may not be necessary to have a rigid geometry and definite pathway for conduction, as implied by the proton-wire model of membrane transport (Nagle and Mille, 1981). For proton pumps the fluctuating random percolation networks would serve for diffusion of the ion across the water-poor protein surface, to where the active site would apply a vectorial kick. In this view the special nonrandom structure of the active site would be limited in size to a dimension commensurate with that found for active sites of proteins such as enzymes. Control is possible conduction could be switched on or off by the addition or subtraction of a few elements, shifting the fractional occupancy up or down across the percolation threshold. Statistical assemblies of conducting elements need only partially fill a surface or volume to obtain conduction. For a surface the percolation threshold is at half-saturation of the sites. For a three-dimensional pore only one-sixth of the sites need be filled. 

Polyesters derived from maleic anhydride and 2,2-di(4-hydroxyphenyl)pro-pane were copolymerised with styrene and then studied by CP/MAS NMR [39] spectroscopy. The three dimensional-crosslinked network formed by the polymerisation was examined using spin-lattice relaxation times in the rotating frame. A correlation between reaction conditions and the structure of the resulting material was found. The degree of residual unsaturation was determined by subtraction of two relaxation times from a linear additivity model used for erosslinked polymer systems. 

ANN = artificial neural network AR = approximate reasoning BAM = bidirectional associative memory FAM = fuzzy associative memory FL = fuzzy logic LP = linear programming OLS = ordinary least squares PCCF = partial cross correlation function SSC = spectrum-structure correlation sup = supremum = fuzzy addition = fuzzy subtraction O = fuzzy multiplication Q = fuzzy division Q = relation. 

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