Feasible roots, number

Number of feasible roots. Usually we are interested mostly in the feasible roots of the system (21). The feasible roots of system (21) are real roots satisfying constraints... 

If we add up the chemical equations of mechanism (46) multiplied by corresponding stoichiometric numbers (i.e. 1 and 2), we obtain the equation of net reaction (47). Note how the constant term of Equation (48) and exponents in its terms correspond to the Proposition 1 (and property (36)). The only feasible root of polynomial (48) is... 

It seems feasible to set r x dynamically based on the rate of decrease of the root-mean-square error. The goal is to achieve convergence in the fewest number of iterations while retaining the stability of the process. 

Previous hydroponic and soil pot research investigations have identified a number of Festuca rubra and Festuca arundinacea cultivars suitable for binding and holding various heavy metals on or within their root tissue (Kucharski and Sas-Nowosielska, 2004a). Festuca"s ability to tolerate heavy metal-contaminated soils, combined with proven cultivation methods, renders it an excellent candidate for phytostabilization projects at metal-contaminated sites where alternative remediation methods may not be economically feasible. 

Hory and Fox suggested that as the viscosity of a polymer solution will depend on the volume occupied by the polymer chain, it should be feasible to relate coil size and [rj]. They assumed that if the unperturbed polymer is approximated by a hydrodynamic sphere, then [Tjjg, the limiting viscosity number in a theta solvent, could be related to the square root of the molar mass by... 

In certain problems it may be necessary to locate all the roots of the equation, including the complex roots. This is the case in finding the zeros and poles of transfer functions in process control applications and in formulating the analytical solution of linear nth-order differential equations. On the other hand, different problems may require the location of only one of the roots. For example, in the solution of the equation of state, the positive real root is the one of interest. In any case, the physical constraints of the problem may dictate the feasible region of search where only a subset of the total number of roots may be indicated. In addition, the physical characteristics of ihe problem may provide an approximate value of the desired root. 

The most effective way of finding the roots of nonlinear equations is to devise iterative algorithms that start at an initial estimate of a root and converge to the exact value of the desired root in a finite number of. steps. Once a root is located, it may be removed by synthetic division if the equation is of the polynomial form. Otherwise, convergence on the same root may be avoided by initiating the search for subsequent roots in different region of the feasible space. 

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