In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The article is devoted to the issue of word-formation motivation, which does not lose its relevance and plays a role not only in disclosing formal-semantic relations between words of one language and has not only theoretical, but also applied significance. The authors consider word-formation motivation consistently in its varieties in a comparative way on the materials of so different languages as Russian and Arabic and approach the mechanism of achieving semantic equivalence of translation. To the greatest extent, word-formation activity today, due to objective reasons, affects some special branch (technical, medical, etc.) vocabulary, which is increasing from year to year in national dictionaries. This extensive material, selected

Small and Medium Enterprises (SMEs) in Iraq have experienced low performance due to the limited usage of accounting information systems (AIS) and the inability to exploit knowledge of management capabilities (KMC). These deficiencies have led to competitive pressures in the marketplace that have adversely affected their sales and production. This study investigates the role of AIS in terms of operation support, knowledge support, regulatory support, and the role of KMC, including knowledge acquisition, knowledge transfer, and knowledge utilized to enhance organizational performance in Iraqi SMEs. The target population was managers and owners in SMEs using AIS in Iraq’s cities. A non-probability purposive sampling technique was use