Pure and Applied Mathematics Journal

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Volume 6, Issue 2, April 2017

  • Clones of Self-Dual and Self-K-Al Functions in K-valued Logic

    M. A. Malkov

    Issue: Volume 6, Issue 2, April 2017
    Pages: 59-70
    Received: 17 February 2017
    Accepted: 24 February 2017
    Published: 10 March 2017
    DOI: 10.11648/j.pamj.20170602.11
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    Abstract: We give a classification of dual functions, they are m-al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and self- -al... Show More
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  • Generalization of Kalmar’s Proof of Deducibility in Two Valued Propositional Logic into Many Valued Logic

    Chubaryan Anahit, Khamisyan Artur

    Issue: Volume 6, Issue 2, April 2017
    Pages: 71-75
    Received: 13 February 2017
    Accepted: 15 March 2017
    Published: 22 March 2017
    DOI: 10.11648/j.pamj.20170602.12
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    Abstract: This paper focuses on the problem of constructing of some standard Hilbert style proof systems for any version of many valued propositional logic. The generalization of Kalmar’s proof of deducibility for two valued tautologies inside classical propositional logic gives us a possibility to suggest some method for defining of two types axiomatic syst... Show More
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  • Shallow Water 1D Model for Pollution River Study

    Antoine Celestin Kengni Jotsa, Vincenzo Angelo Pennati, Antonio Di Guardo, Melissa Morselli

    Issue: Volume 6, Issue 2, April 2017
    Pages: 76-88
    Received: 25 February 2017
    Accepted: 23 March 2017
    Published: 15 April 2017
    DOI: 10.11648/j.pamj.20170602.13
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    Abstract: In this paper a finite element 1D model for shallow water flows with distribution of chemical substances is presented. The deterministic model, based on unsteady flow and convection-diffusion-decay of the pollutants, allows for evaluating in any point of the space-time domain the concentration values of the chemical compounds. The numerical approac... Show More
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