Representational differential analysis

This would mean that the particles on the 170 mesh screen lie between 88 p,m and 125 p,m. This representation of the data is referred to as a differential analysis. In a cumulative analysis, the particles retained on each screen are summed sequentially starting from either the receiver or the screen with the largest aperture. 

Hubank, M. and Schatz, D.G. (1999) cDNA representational difference analysis a sensitive and flexible method for identification of differentially expressed genes. Methods Enzymol, 303, 325-349. 

CSTRs and other devices that require flow control are more expensive and difficult to operate. Particularly in steady operation, however, the great merit of CSTRs is their isothermicity and the fact that their mathematical representation is algebraic, involving no differential equations, thus maldng data analysis simpler. 

The Maxwell model is also called Maxwell fluid model. Briefly it is a mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus (E) in series with a dashpot of coefficient of viscosity (ji). It is an isostress model (with stress 5), the strain (f) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as d /dt = (l/E)d5/dt + (5/Jl)-This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis. 

Schematic representation of the application of the differential method for data analysis.

FIGURE 15.7 A representation of the results of the differential thermal analysis (a DTA curve) of a sample that melts at a particular temperature. 

In the above definitions, 9 represents a set of parameters of the system, having constant values. These parameters are also called control parameters. The set of the system s variables forms a representation space called the phase space [32]. A point in the phase space represents a unique state of the dynamic system. Thus, the evolution of the system in time is represented by a curve in the phase space called trajectory or orbit for the flow or the map, respectively. The number of variables needed to describe the system s state, which is the number of initial conditions needed to determine a unique trajectory, is the dimension of the system. There are also dynamic systems that have infinite dimension. In these cases, the processes are usually described by differential equations with partial derivatives or time-delay differential equations, which can be considered as a set of infinite in number ordinary differential equations. The fundamental property of the phase space is that trajectories can never intersect themselves or each other. The phase space is a valuable tool in dynamic systems analysis since it is easier to analyze the properties of a dynamic system by determining... 

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