Tetrahydropyridines (THPDs) have recognized as a major constituent of naturally occurring alkaloids and exhibits various biological and pharmacological profiles. For their synthesis, MCRs are employed as an excellent tool to generate vast libraries.

Simple and mild one-pot protocols for the synthesis of diversely functionalized dihydro-2-oxypyrroles and tetrahydropyridines using catalytic amounts of 2,6-PDCA.

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We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as well as fractional integrals of a function with respect to another function. Finally, we apply our main result to multidimensional settings to obtain new results involving mixed Riemann-Liouville fractional integrals.

In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.

In this paper, we modify the (k, s) fractional integral operator involving k-Mittag-Leffler function and discuss its properties. We originate a new fractional operator named (k, s)-Prabhakar derivative and obtained some classical fractional operators as a special case of the newly proposed derivative. Some properties of the introduced operator are also part of the present work. The generalized Laplace transform is employed to study the characteristics of fractional operators. We modeled the free-electron laser (FEL) equation by involving the proposed derivative and can find the solution by using the said Laplace transform.

In childhood most common fractures are closed fracture of the distal third of the forearm in children, after closed reduction of the forearm fractures of distal third were immobilized with long arm cast and by some orthopedic surgeon with short arm cast. Objectives: To compare the result of above elbow cast with below elbow cast in the treatment of distal third forearm fractures in children. Study Design: Randomized study. Setting: Department of orthopedics, Allied Hospital, Faisalabad. Period: One year 14-Sep, 2015 to 15-Aug, 2016. Results: 180 Cases fulfilling the inclusion / exclusion criteria were included in the study. In group A38.89% (%35) in our study and group B 45.56% (n=41) were between 1-6 years of age while. In group A 61.11% (n=55) and group B 54.44% (n=49) were 7-12 years of age of the children mean + sd 7.66 + 2.54 and 7.38 + 2.46 years respectively, In group A 58.89 % (n=53) in group B 62.22% (n=56) were male while group –A 41-11% (N37) and in group B 37.78% were females below elbow cast compared with above elbow cast in treating distal one third forearm fracture in children shows that group A 23.33% (n+21) and group B 30% (n=27) and re displacement shows no significant difference between their two groups. Conclusion: We concluded there is no significant difference in outcome of above elbow cast with below elbow cast after reduction treating the fracture of children in distal on third forearm fractures.

A visible light-promoted, efficient, green, and sustainable strategy has been adopted to unlatch a new pathway toward the synthesis of a library of medicinally important 4,4′-(arylmethylene)bis(1H-pyrazol-5-ols) moieties using substituted aromatic aldehydes and sterically hindered 3-methyl-1-phenyl-2-pyrazoline-5-one in excellent yield. This reaction shows high functional group tolerance and provides a cost-effective and catalyst-free protocol for the quick synthesis of biologically active compounds from readily available substrates. Synthesized compounds were characterized by spectroscopic techniques such as IR, 1 HNMR, 13 CNMR, and single-crystal XRD analysis. All the synthesized compounds were evaluated for their antiproliferative activities against a panel of five different human cancer cell lines and compared with Tamoxifen using MTT assay. Compound 3m exhibited maximum antiproliferative activity and was found to be more active as compared to Tamoxifen against both the MCF-7 and MDA-MB-231 cell lines with an IC 50 of 5.45 and 9.47 μM, respectively. A molecular docking study with respect to COVID-19 main protease (M pro ) (PDB ID: 6LU7 ) has also been carried out which shows comparatively high binding affinity of compounds 3f and 3g (−8.3 and −8.8 Kcal/mole, respectively) than few reported drugs such as ritonavir, remdesivir, ribacvirin, favipiravir, hydroxychloroquine, chloroquine, and olsaltamivir. Hence, it reveals the possibility of these compounds to be used as effective COVID-19 inhibitors.