A device for the graphical solution of the simultaneous equations A = f (D, C, K), which equations can be represented by nomographs, e.g., Larson's Nomograph, having two spaced vertical axes bounding two families of curves. The device comprises a first straight line defining means (e.g...
One method permits data to be taken at multiple wavelengths to generate linear plots, from which the concentrations can be determined; this method is applicable to mixtures of two or three components. The second method is a graphical technique for the solution of simultaneous equations. For 3-com...
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The minimum can be found by setting the partial derivatives ∂S/∂a, ∂S/∂b, and ∂S/∂c to zero and solving the resulting simultaneous equations, as for the linear least-squares regression case above. Standard computer packages to estimate the parameters a, b, and c by numeric...
h ybrid algorithm, com bining lo cal propagation with pluggable cycle solv ers, allo wing constrain ts to range o v er arbitrary ob jects, while at the same time satisfying constrain ts represen ting sim ultaneous equations o v er the reals. 1 In tro duction A v ariet y of researc...
It is found that a pair of simple simultaneous equations can often be solved easily by substitution. Another approach consists of algebraic addition and subtraction. The relationship between current and voltage in a resistive circuit can be portrayed by a linear equation. It is observed that ...
This chapter describes the use of simultaneous equations and graphical solutions in electrical problems. Presentation on a graph or chart is a forceful method of representing data and presenting the relationships between data. Data with only two variables that are related to each other, so that ...
Simultaneous solution of these equations always leads to a kinetic equation of non-Markovian type. Rules of the Graphical Technique. Let us consider an atom interacting with an electromagnetic field and a thermostat. We will write the Hamiltonian of the entire system in the form...
The construction of Branin trajectories for locating the stationary points of a scalar function of many variables involves, in the general case, the numerical solution of a set of simultaneous ordinary differential equations, or some equivalent numerical procedure. For a function of only two variables...
The graphs are based on the simultaneous solution of the equations representing nine complexing equilibria and three stoichiometric summarizations, using a fixed value of ionic strength equal to 0.1. Solubility relationships for aluminum hydroxide and cryolite also are shown graphically, using the same ...