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Nanoscience and Technology: An International Journal

Publication de 4  numéros par an

ISSN Imprimer: 2572-4258

ISSN En ligne: 2572-4266

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.3 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.7 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.7 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00023 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.11 SJR: 0.244 SNIP: 0.521 CiteScore™:: 3.6 H-Index: 14

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AVERAGING EQUATIONS OF MATHEMATICAL PHYSICS WITH COEFFICIENTS DEPENDENT ON COORDINATES AND TIME

Volume 8, Numéro 4, 2017, pp. 367-375
DOI: 10.1615/NanoSciTechnolIntJ.v8.i4.70
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RÉSUMÉ

Differential equations with variable coefficients describe the processes proceeding in inhomogeneous materials in which mechanical characteristics change either abruptly or continuously in the boundary area between the phases. One of the general approaches to solving equations with variable coefficients is the use of the averaging method, which implies some of the ways to represent the solution of the initial equation in terms of a solution of an equation with constant coefficients. In the present paper, an integral formula has been obtained which presents the solution of the original linear differential equation of the second order with the coefficients depending on the coordinates and time, through the solution of the same equation with constant coefficients (the concomitant equation). The kernel of the integral formula includes the Green function of the original equation and the difference of the coefficients of the original and concomitant equations. From the integral formula an equivalent representation of the solution of the initial equation in the form of a series of all possible derivatives of the solution of the concomitant equation is obtained. The coefficients of the series are called structure functions. They depend substantially on the form of the inhomogeneity and tend to zero as the coefficients of the original equation tend to the constant coefficients of the concomitant equation. A system of recurrence equations satisfied by the structural functions is written. Examples of calculation of the structure functions are given.

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