# independent equations

## independent equations

[‚in·də′pen·dənt i′kwā·zhənz]
(mathematics)
A system of equations such that no one of them is necessarily satisfied by a solution to the rest.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
If we want to decode [s.sup.[1,1]] , we need to provide 6 interference-free linear independent equations. Moreover, although user [2,1] and user [2,2] only can receive the ICI signal in time slot 1, the overheard ICI signal in time slot 1 is still useful to eliminate ICI signal in step two.
Irrigation ecology 0.048 ** 0.021 _cons 0.840 *** 0.033 /athrho -0.46942 ** 0.207234 /lnsigma -2.706 *** 0.061 rho -0.438 0.168 sigma 0.067 0.004 lambda -0.029 0.013 Log likelihood 261.944 Waldtest rf (15) 4.95 *** LR test of independent equations (1) 3.84** Irrigation Ecology Variables Coef.
Therefore, there are a total of seven independent equations needed for the complete solution of all actual elastic-plastic stress and strain components at the notch root.
However, the number of linear independent equations generated by XSL attacks in the academic field is disputed, and the validity of the attack is questioned [6, 7].
Based on our experience, we should transform the coupled equations into two independent equations. Inspired by [38, 39], (39) can be written with the following form:
Without loss of generality, in the following, the first (n - 1) equations for [[alpha].sub.1], [[alpha].sub.2], ..., [[alpha].sub.n-1] are taken as independent equations. Let [alpha]' = [[[alpha].sub.1] [[alpha].sub.2], ..., [[alpha].sub.n-1]] be n - 1 dimensional vector diffusion process.
In this system, there are three independent equations and four unknowns [rho], p, L, and G.
It can be separated into two independent equations given by
Number of observations = 140; Censored observations = 54; Uncensored observation = 86; Wald Chi-square = 25.39 (0.00); p = -0.4945; LR test of independent equations (p = 0) = 2.67 (0.10)
The tests for independent equations (lack of self-selection) are rejected for each specification and point to a self-selection of bankers on company boards.
For single vibrator or slot, as well as for the absence of electromagnetic interaction between them, system (9) splits into two independent equations:

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