Some Remarks on Results Related to ∇-Convex Function

In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented

Efficacy of single dose dermatological 0.1% tacrolimus Ointment in the treatment of vernal keratoconjunctivitis

Objective: To assess the safety of dermatological 0.1% tacrolimus ointment when used topically and its efficacy in the treatment of vernal keratoconvinctivtis. Method: The quasi-experimental, multi-centre study was conducted at the Gujranwala Medical College/District Headquarters Teaching Hospital, Gujranwala, and the Gomal Medial College/Mufti Mehmood Teaching Hospital, Dera Ismail Khan, Pakistan, from July 2019 to March 2020, and comprised patients of severe vernal keratoconvinctivtis. Symptoms and clinical signs were graded on a pre-devised scale. Patients were given small amount of tacrolimus 0.1% ointment applied to the inferior conjunctival fornix before going to bed. The duration of treatment was 3 months and the patients were followed up for up to 6 months. Data was analysed using SPSS 20. Results: Of the 50 patients, 30(60%) were males and 20(40%) were females. The overall mean age was 10.64±3.199 years. Mean symptom score and clinical signs score gradually reduced on each follow-up (p<0.05). Mild recurrence was noted in 12(24%) patients who were managed with lubricants and anti-histamine topical drops. No complication was noted. Conclusion: Tacrolimus 0.1% was found to be effective and safe in the treatment of severe refractory vernal keratoconvinctivtis even when given once a day. Clinical Trial Registration: Chinese Clinical Trial Registry Id: ChiCTR2000031929 link: www.chictr.org.cn/hvshowproject.aspx?id=28053 Key Words: Allergic, Conjunctivitis, Tacrolimus, Topical administration, Anti-allergic agents, Dermatologic agents, Efficacy

The Role of Obesity in Breast Cancer Pathogenesis

Research has shown that obesity increases the risk for type 2 diabetes mellitus (Type 2 DM) by promoting insulin resistance, increases serum estrogen levels by the upregulation of aromatase, and promotes the release of reactive oxygen species (ROS) by macrophages. Increased circulating glucose has been shown to activate mammalian target of rapamycin (mTOR), a significant signaling pathway in breast cancer pathogenesis. Estrogen plays an instrumental role in estrogen-receptor-positive breast cancers. The role of ROS in breast cancer warrants continued investigation, in relation to both pathogenesis and treatment of breast cancer. We aim to review the role of obesity in breast cancer pathogenesis and novel therapies mediating obesity-associated breast cancer development. We explore the association between body mass index (BMI) and breast cancer incidence and the mechanisms by which oxidative stress modulates breast cancer pathogenesis. We discuss the role of glutathione, a ubiquitous antioxidant, in breast cancer therapy. Lastly, we review breast cancer therapies targeting mTOR signaling, leptin signaling, blood sugar reduction, and novel immunotherapy targets

Efficient Adsorption of Lead Ions from Synthetic Wastewater Using Agrowaste-Based Mixed Biomass (Potato Peels and Banana Peels)

The aquatic environment is continuously being polluted by heavy metals released from industrial, domestic, agricultural, and medical applications. It is difficult to remove heavy metals, as they are nonbiodegradable. Heavy metals cause genotoxicity and serious carcinogenic disorders. Various conventional methods have been used for the removal of heavy metals, but these are time-consuming and not economical, so green methods, being economical, are preferred over conventional methods. Adsorption, being effective, environmentally friendly, and cheap, is often preferred. The present investigation investigated the adsorption efficiency of agrowaste-based biosorbents for removal of Pb(II) ion from the synthetic wastewater. Mixed biomass of banana peel and potato peels was used to create biosorbents. The biosorbents were characterized in terms of structural and surface morphology by SEM, while functional groups were analyzed by FT-IR and XRD analysis. The adsorption of Pb(II) was studied by a batch method, and various experimental parameters were studied. Optimum conditions for the removal of lead were pH = 5, concentration = 10 ppm, adsorbent dosage = 1.0 g, and contact time = 2 h. Kinetic modelling studies showed that the adsorption of Pb(II) ions followed a pseudo-second-order mechanism, and the Langmuir isotherm model was found to fit well for this study. Highlights: Synthesis of biosorbents (mixed biomass of potato peel and banana peel, biochar, TiO2 nanocomposites). Characterization of prepared biosorbents (SEM, XRD, FT-IR). Optimized parameters (pH, initial concentration, adsorbent dosage, and contact time) for removal of pollutant