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Partial Differentiation of Real Ternary Functions Cover

Partial Differentiation of Real Ternary Functions

Formalized Mathematics
Volume 18 (2010): Issue 1 (March 2010)
By: ,   and    
Open Access
|Jan 2011
References

References

  1. [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences., 1():107-114, 1990.
    Search in Google Scholar
  2. [2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets., 1():529-536, 1990.
    Search in Google Scholar
  3. [3] Czesław Byliński. Functions and their basic properties., 1():55-65, 1990.
    Search in Google Scholar
  4. [4] Czesław Byliński. Functions from a set to a set., 1():153-164, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Partial functions., 1():357-367, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. The sum and product of finite sequences of real numbers., 1():661-668, 1990.
    Search in Google Scholar
  7. [7] Agata Darmochwał. The Euclidean space., 2():599-603, 1991.
    Search in Google Scholar
  8. [8] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces R., 15():65-72, 2007, doi:10.2478/v10037-007-0008-5.
    Open DOISearch in Google Scholar
  9. [9] Krzysztof Hryniewiecki. Basic properties of real numbers., 1():35-40, 1990.
    Search in Google Scholar
  10. [10] Jarosław Kotowicz. Convergent sequences and the limit of sequences., 1():273-275, 1990.
    Search in Google Scholar
  11. [11] Jarosław Kotowicz. Real sequences and basic operations on them., 1():269-272, 1990.
    Search in Google Scholar
  12. [12] Xiquan Liang, Piqing Zhao, and Ou Bai. Vector functions and their differentiation formulas in 3-dimensional Euclidean spaces., 18():1-10, 2010, doi: 10.2478/v10037-010-0001-2.
    Open DOISearch in Google Scholar
  13. [13] Konrad Raczkowski and Paweł Sadowski. Real function continuity., 1():787-791, 1990.
    Search in Google Scholar
  14. [14] Konrad Raczkowski and Paweł Sadowski. Real function differentiability., 1():797-801, 1990.
    Search in Google Scholar
  15. [15] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers., 1():777-780, 1990.
    Search in Google Scholar
  16. [16] Walter Rudin.MacGraw-Hill, 1976.
    Search in Google Scholar
  17. [17] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers., 1():445-449, 1990.
    Search in Google Scholar
  18. [18] Edmund Woronowicz. Relations defined on sets., 1():181-186, 1990.
    Search in Google Scholar
  19. [19] Bing Xie, Xiquan Liang, and Hongwei Li. Partial differentiation of real binary functions., 16():333-338, 2008, doi:10.2478/v10037-008-0041-z.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/v10037-010-0005-y | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
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Language: English
Page range: 39 - 46
Published on: Jan 5, 2011
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Related subjects:
Computer sciences,
Artificial intelligence,
Computer sciences, other,
Mathematics,
Logic and set theory,
General mathematics

© 2011 Takao Inoué, Bing Xie, Xiquan Liang, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 18 (2010): Issue 1 (March 2010)
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