Shape Expressions

Theory. The velocity (v) of particle sedimentation during centrifugation depends on the angular velocity co of the rotor, its effective radius (teff, the distance from the axis of rotation), and the particle s sedimentation properties. These properties are expressed as the sedimentation coef cient S (1 Svedberg, = 10 s). The sedimentation coef cient depends on the mass M of the particle, its shape (expressed as the coef cient of friction, f), and its density (expressed as the reciprocal density v, partial specific volume ). 

Reproductions of the example artwork listed above (or other reproductions with shapes expressing movement, direction, mood, and emotion). 

Comparing this scheme with its common shape expressed by reactions (2.14) and (2.15a), it should be noted that it gives the best display for the role of the intermediate substance X, which is common to both conjugated reactions as the bifurcation factor of the reaction system, and the inducer is expended in amounts providing A expenditure in both reactions. 

Similar to a Voigt profile, this line shape expression is a convolution of Equation (11) and a Gaussian distribution to account for inhomogeneous broadening [12,31]. This profile is the best profile currently employed for the analysis of spectra exhibiting significant overlap of modes of different phases. 

The Net value undergoes a transfer function that mimics the signal threshold from the biological neuron. A typically used transfer function has a sigmoidal shape expressed by... 

This had been found earlier by Wobschall et and by Beauchamp 28). Line shape expressions are obtained by summing the power absorption of all ions over the analyzer region... 

The shape group method (SGM), reviewed in ref. [2], has been proposed for the analysis of three-dimensional shape properties of formal molecular bodies. For example, by choosing the electronic charge isodensity contours G(a) (of various density values a) as the physical property P for shape representation, and by taking the family of Betti numbers b as the topological tool for shape description [2], the similarity of the geometrical shapes of two molecules, A and B, is transformed into an equivalence of their topological shape, expressed as... 

Prud hommeaux, E., Gayo, J.E.L., Solbrig, H.R. Shape expressions an RDF validation and transformation language. In Proceedings of the 10th International Conference on Semantic Systems (SEMANTICS), pp. 32-40 (2014)... 

It is seen, in the first three experiments, that the shape expressed the character indicating that a cylinder formed between the discs would be unstable, and, from the first to the third, this character was less and less marked finally, in this third experiment, for which the ratio was 3.18, which was already extremely close to the sought limit. The three last experiments expressed, on the contrary, the character of the stability of the cylinder, and this stability was decreasing from the fifth experiment to the seventh, for which the ratio was 3.13 and which had very low stability. 

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