Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely h nh (k) (h = f, g) sharing a nonzero polynomial of degree less than or equal to 3 with finite weight have common poles and obtain two results. The results in this paper significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
As a basis of this article served the catalogue of Czech social songbooks that the author made use of in the form of computer database for the Department of Ethnomusicology of the Institute of Ethnology of the Czech Academy of Sciences. On the basis of the recent analysis of these songbooks and with regard to results of previous researches, at first the origin and development of the Czech social singing in the first half of the nineteenth century is explained, including the characteristics of central personalities (A. J. Puchmajer, J. J. Ryba, V. J. Tomášek, V. Hanka, F. M. Kníže, A. Jelen, J. K. Chmelenský, F. Škroup, F. L. Čelakovský, F. J. Vacek Kamenický, J. K. Tyl, V. J. Picek and K. Havlíček Borovský) and publications (among others, Věnec ze zpěvů vlastenských [Garland of Patriotic Songs], 1835–1839, 1843–1844). In the second part the period of one hundred years of the phenomenon of Czech social songboks is reviewed (1848–1948); accentuated is, in especial, the foundational importance of Společenský zpěvník český [Czech Social Songbook] of J. B. Pichl (1851), realized with later musical cooperation of J. L. Zvonař (1863).