1. The numerical partial derivative is introduced to simplify the GPS network adjustment model.

2. The canonic OC expansion of the first-order Boolean partial derivative of the OC type logic function was discussed.

3. Extremal multi - function, multi - function partial derivative method.

4. Based on the definitions of Boolean difference and partial derivative of logical functions, the tabular method calculating Boolean difference and partial derivative was presented.

5. With the terminal value of the partial derivative for boundary variates and their differetial equation, the variates can be solved by backward derivation of the differetial equation.

6. We will replace the partial derivative by an ordinary derivative.

7. A discussion of the relations between continuity, partial derivative, directional derivative and differentiability of binary function is helpful for us to study binary function.

8. In this paper, the formula of partial derivative of second order on compound function of many varables is established.

9. The difference between an ordinary and a partial derivative was at first not explicitly recongized.

10. So the methods given in this paper can be used to get some simple inverse Z transform. The partial derivative method and deconvolution method are of practical use.

11. That was this symbolic vector operator in which the components are the partial derivative operators.

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12. For each cyclic dynamic stress, the incremental strain is obtained in terms of the first partial derivative of the known formula for the uniform load with respects to the cyclic number.

13. Then, a new method testing the double fault of combinational circuits based upon Boolean partial derivative is proposed.

14. Convolutional differentiator (CD) is obtained by inverse Fourier transform of bandlimited Fourier spectra of partial derivative operator. CD is symmetric or antisymmetric and decays rapidly.

15. We also give the matrix forms of the interface partial derivative with multiple complex interfaces.