Двойственные сетевые модели больших систем

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  • 30.1

    76

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  • 77

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  • 30.1

    78

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  • 79

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  • 30.1

    80

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  • 81

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  • 30.1

    82

    . 1.

    , , , . . . , - - C - C = A: (1) mC (mCt mC)-1 mCt + jA (jAt jA)-1 jAt = = mC (mCt mC)-1 mCt + mC (mCt mC)-1 mCt = I.

    (1) mC = jA , jA = mC - , I . , . - .

    - ( ), ( ) Z I, (Z = Y1), : (2) mC (mCt Z mC)1 mCt + Y mC (mCt Y mC)1 mCt Y = Y = (Z)1.

    , Z Y. . .

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  • 83

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  • 30.1

    84

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  • 85

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  • 30.1

    86

    () - () ; - . ( ) , .

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  • 87

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  • 30.1

    88

    (11) ==+= =

    =

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    nnp )(1

    00

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  • 89

    . . , - , - ( ). - - . . - . 2008-2009 .

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    1. .. : . . 2- ., . .: . .; ; 2000. 607 .

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  • 30.1

    90

    5. ., .., . - . . . .: -, 1958. 640 .

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    7. .. . .: , 2007. 496 .

    8. ., . , -: . . / . .. . .: , 1984. 455 .

    DUAL NETWORK MODELS OF LARGE-SCALE SYSTEMS Andrey Petrov, Moscow State Mining University, Moscow, Doc. Sc., professor (helen_pet@mail.ru). Abstract: The tensor method of dual networks was developed to calculate changes of processes in large-scale systems caused by changes in the structure of links. Dual networks are constructed as dual graphs, and have an invariant of structural transformations. The dual invariant has fundamental character that turns up in the form of the law of preservation of a stream of energy. The invariant provides methods to calculate chains and network models of large-scale systems of variable structure, including network models of economic systems. This paper describes the method and its applica-tions for simulation of a product flow network and a dual network of cash flows. Keywords: processes and structure modeling, economics, tensor method, dual networks, sustainable development, invariant, product and cash flows.

    . .

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