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Melatonin, a pleiotropic hormone, has many regulatory effects on the circadian and seasonal rhythms, sleep and body immune system. It is used in the treatment of blind circadian rhythm sleep disorders, delayed sleep phase and insomnia. It is a potent antioxidant, anti-inflammatory, free radical scavenger, helpful in fighting infectious disease and cancer treatment. Decreased level of circulating melatonin was associated with an increased blood glucose level, losing the anti-oxidant protection and anti-inflammatory responses. We aimed to evaluate the effect of melatonin administration, in streptozotocin (STZ) induced diabetic rats, on blood glucose level and pancreatic beta (β) cells. Diabetes mellitus was induced in Sprague dawley male rats by the intravenous (i.v) injection of 65 mg/kg of STZ. Diabetic rats received melatonin at a dose of 10 mg/kg daily for 8 weeks by oral routes. The results showed, after 8 weeks of melatonin administration, a reduction in: 1- fasting blood glucose (FBG) and fructosamine (FTA) levels, 2- kidney and liver function parameters, 3- levels of serum triglycerides, cholesterol and LDL-C, 4- malondialdehyde (MDA), 5- NF-κB expression in treated group, 6- pro-inflammatory cytokines (IL-1β and IL-12) and immunoglobulins (IgA, IgE and IgG). Furthermore, an elevation in insulin secretion was noticed in melatonin treated group that indicated β cells regeneration. Therefore, melatonin administration, in STZ induced diabetic rats; reduced hyperglycemia, hyperlipidemia and oxidative stress. Melatonin acted as an anti-inflammatory agent that reduced pro-inflammatory cytokines (IL-1β and IL-12) and oxidative stress biomarkers (MDA). Melatonin succeeded in protecting β cells under severe inflammatory situations, which was apparent by the regeneration of islets of Langerhans in treated diabetic rats. Moreover, these results can open a gate for diabetes management and treatment.

In [32], A. Najati and S.-M. Jung obtained the Hyers-Ulam stability of the generalized quadratic functional equation $f(rx+sy)+rsf(x-y)=rf(x)+sf(y)$ with $r+s=1$, $r\neq0$, $s\neq0$, provided that $f$ is an even mapping. The purpose of this paper is to remove this restriction.

In the present paper, we apply a fixed point theorem to prove the Hyers–Ulam–Rassias stability of the quadratic functional equation $$f(kx+ y)+f\bigl(kx+\sigma(y)\bigr)=2k^{2}f(x)+2f(y),\quad x,y\in E_{1} $$ from a normed space E 1 into a complete β-normed space E 2, where σ:E 1⟶E 1 is an involution and k is a fixed positive integer larger than 2. Furthermore, we investigate the Hyers–Ulam–Rassias stability for the functional equation in question on restricted domains.

Cyclisation of diethyl 3-allyloxy-1-propynylphosphonates with Mo(CO)6 under PK conditions to give 3-substituted-5-oxo-3,5,6,6a-tetrahydro-1H-cyclopenta[c]furan-4-ylphosphonate, 2a−h, in 45−88% isol...

Cyclisation of diethyl 3-allyloxy-1-propynylphosphonates with Mo(CO)(6) under PK conditions to give 3-substituted-5-oxo-3,5,6,6a-tetrahydro-1H-cyclopenta[c]furan-4-ylphosphonate, 2a-h, in 45-88% isolated yields was done. The R groups are always syn with H(b) (where applicable). The stereochemistry was determined via both NMR and crystal X-ray analysis.