Кафедра інженерії програмного забезпечення

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https://elar.khmnu.edu.ua/handle/123456789/581

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Перегляд Кафедра інженерії програмного забезпечення за Автор "Bedratyuk, L."

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  • Ескіз
    Документ
    The double star sequences and the general second zagreb index
    (2019) Белратюк, Леонід; Bedratyuk, L.
    For a simple graph we introduce notions of the double star sequence, the double star fre- quently sequence and prove that these sequences are inverses of each other. As a consequence, we express the general second Zagreb index in terms of the double star sequence. Also, we calculate the ordinary generating function and a linear recurrence relation for the sequence of the general second Zagreb indices.
  • Ескіз
    Документ
    The inverse and derivative connecting problems for some hypergeometric polynomials
    (Прикарпатський національний університет імені Василя Стефаника, 2018) Белратюк, Леонід Петрович; Бедратюк, Ганна Іванівна; Bedratyuk, L.; Bedratyuk, A.
    Given two polynomial sets { P n ( x )} n ≥ 0 and { Q n ( x )} n ≥ 0 such that deg ( P n ( x )) = deg ( Q n ( x )) = n. The so-called connection problem between them asks to find coefficients α n,k in the expression Q n ( x ) = n ∑ k = 0 α n,k P k ( x ) . The connectionproblem for different typesof polynomials has along history, and it is still of interest. The connection coefficients play an important role in many problems in pure and applied mathematics, especially in combinatorics, mathematical physics and quantum chemical applications. For the particular case Q n ( x ) = x n the connection problem is called the inversion problem associated to { P n ( x )} n ≥ 0 . The particular case Q n ( x ) = P ′ n + 1 ( x ) is called the derivative connecting problem for polynomial family { P n ( x )} n ≥ 0 . In this paper, we give a closed- form expression of the inversion and the derivative coefficients for hypergeometric polynomials of the form