Symmetrical patterns exist in the nature of inequalities, which play a basic role in theoretical and applied mathematics. In several studies, inequalities present accurate approximations of functions based on their symmetry properties. In this paper, we present the following rational approximations for Bateman’s G-function G(w)=1w+2w2+∑j=1n4αjw2−2j−1+O1w2n+2, where α1=14, and αj=(1−22j+2)B2j+2j+1+∑ν=1j−1(1−22j−2ν+2)B2j−2ν+2ανj−ν+1,j>1. As a consequence, we introduced some new bounds of G(w) and a completely monotonic function involving it.
Symmetrical patterns exist in the nature of inequalities, which play a basic role in theoretical and applied mathematics. In several studies, inequalities present accurate approximations of functions based on their symmetry properties. In the paper, we prove the completely monotonic (CM) property of some functions involving the function Δ(l)=ψ″(l)+ψ′(l)2 and hence we deduce a new double inequality for it. Additionally, we study the CM degree of some functions involving the function ψ′(l). Our new bounds takes priority over some of the recently published results.
Glycosylation of small molecules based heterocycles can improve the biological importance of the parent scaffold. In the current study, various new substituted pyridine and substituted pyrimidine thioglycosides were synthesized via the reaction of substituted pyridine and pyrimidine thiols with 2,3,4,6-tetra-O-acetyl-α-D-glucopyranosyl bromide in presence of sodium acetate and ethanol .The chemical structures of the synthesized compounds were confirmed by elemental and spectral techniques including FT-IR, 1 H NMR In addition to 13 C NMR and mass spectroscopy for some of them. Alternatively, some of the synthesized compounds revealed significant antibacterial and antifungal activates. Also, most of these compounds exhibited highly promising anti-inflammatory activities compared with indomethacin.
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