In this paper, we use the properties of Chebyshev polynomials, elementary methods, and combinational techniques to study the computational problem of one kind of convolution sums involving second kind Chebyshev polynomials, and we give an exact computational method, which expresses the sums as second kind Chebyshev polynomials. As some applications of our results, we also obtain several new identities and congruences involving the second kind Chebyshev polynomials, Fibonacci numbers, and Lucas numbers.
MSC: 11B39
Because of the complex etiology, the treatment of gastric cancer is a formidable challenge for contemporary medical. The current treatment method focuses on traditional surgical procedures, supplemented by other treatments. Among these other treatments, Traditional Chinese Medicine (TCM) plays an important role. Here, we used the systems pharmacology approach to reveal the potential molecular mechanism of PRGRC on gastric cancer which composes of Pinellia ternata(Thunb.) Breit., Rheum palmatumL., Gentiana scabraBunge, Radix Aucklandiae and Citrus aurantium L. This approach combines pharmacokinetics analysis with pharmacodynamics evaluation for the active compounds screening, targets prediction and pathways assessing. Firstly, through pharmacokinetic evaluation and target prediction models, 83 potential compounds and 184 gastric cancer-related targets were screened out. Then, the results of network analysis suggested that the targets of PRGRC were mainly involved two aspects: apoptosis and inflammation. Finally, we verified the reliability of the above analysis at the cellular level by using naringenin and luteolin with good pharmacokinetic activity as representative compounds. Overall, we found that PRGRC could influence the development of gastric cancer from a multi-scale perspective. This study provided a new direction for analyzing the mechanism of TCM.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.