Some generating functions for the Jacobi polynomials

AbstractA certain family of generating functions for the classical Jacobi polynomials, given earlier by R.K. Saxena and Z. Hussain [1], are observed here to be derivable directly from some known (and readily available) results in the literature. An interesting generalization of the aforementioned generating functions emerges naturally in the process. Some relevant connections of these results with various known generating functions are also pointed out

Restricted Boolean group rings

summary:In this paper we study restricted Boolean rings and group rings. A ring $R$ is $\textit{restricted Boolean}$ if every proper homomorphic image of $R$ is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient

Mechanical Behavior of Zr-Based Metallic Glasses and Their Nanocomposites

In the present chapter, results of our recent investigations on the role of gallium (Ga) on the aluminum (Al) site in Zr69.5Al7.5-xGaxCu12Ni11 metallic glass (MG) composition have been discussed. The material tailoring and cooling rate effects on the mechanical behavior of Zr-based metallic glasses and their nanocomposites have been studied. The substitution of Ga on the Al site in Zr–Al–Cu–Ni alloy affects the nucleation and growth characteristics of quasicrystals (QCs) and consequently changes the morphology of nanoquasicrystals. The Zr69.5Al7.5-xGaxCu12Ni11 system displayed metallic glass formation in the range of x = 0–7.5. In this process, we have come out with a new glass composition; Zr-Ga-Cu-Ni with glass transition temperature (Tg)—614 K. The effect of cooling rate on the glass forming ability (GFA) and mechanical properties for this new metallic glass composition has been discussed and compared with some other Zr-based metallic glasses. The various indentation parameters such as microhardness, yield strength, strain hardening constant, nature of shear band formation, and so on for the alloys have been analyzed. The study is focused on investigations of these materials to understand the structure (microstructure) property correlations

On Generalized Fractional Kinetic Equations

In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized fractional kinetic equations. The results are obtained in a compact form in terms of generalized Mittag-Leffler functions. Their relation to fundamental laws of physics is briefly discussed.Comment: 10 pages, LaTe

To Study Analgesic, Hypoglycemic and Hepatoprotective Activity of Moringa olefera Leaf Extract in Albino Wistar Rats

Introduction: Moringa oleifera is widely found in Asian subcontinent and it has been used as an Analgesic, Hypoglycemic and hepatoprotective in Indian folklore medicine. In this study we compared the Analgesic, Hypoglycemic and hepatoprotective effects of Moringa oleifera ethanolic extracts with other standard drug in Albino Wistar Rats. Methods:  Male Wistar albino rats were divided into 5 groups and administered placebo (saline), diclofenac and 3 groups of Moringa Oleifera using 100mg/Kg, 200mg/Kg and 400mg/kg doses for Analgesic Activity.  On the other hand, 30 Albino Wistar rats were divided into 5 groups of six each and administered placebo (saline), Liv-52 (standard) and 3 groups of Moringa Oleifera using 100mg/Kg, 200mg/Kg and 400mg/kg doses for hepatoprotective activity. In addition, the test leaf extracts preparations of Moringa oleifera [100, 200 and 400 mg], were administered for 21 days orally to the rats of respective groups by using oral feeding tube for Hypoglycemic activity. Results: The highest Tail flick latency period was observed in Group 2 and Group 5 at 120 min. At all-time of point, the tail-flick latency period differed significantly between the extract and Aspirin treated Groups being greater in the Group 2. Comparing different doses of the extract revealed that there is positive relationship between reaction time and increase dose of the extract in which, protection against heat application with 400 mg /kg was significant compared to all doses of the extract. Whereas, Rats treated with ethanolic Leaf extract of Moringa Oleifera (100/200/400 mg/kg, orally once daily) for 21days, the SGOT values (242.66 ± 11.63 IU/L, 242.66 ± 11.63 IU/L, 242.66 ± 11.63 IU/L) were significantly lower (P<0.05), (P<0.05), (P<0.01) when compared to SGOT levels in control rats (265 ± 4.75 IU/dl). Rats treated with ethanolic Leaf extract of Moringa Oleifera (100/200/400 mg/kg, orally once daily) for 21days, Conclusion: Ethanolic extracts of Moringa Oleifera leaves exhibits significant Analgesic, Hypoglycemic and hepatoprotective activity in a dose dependent manner.  Keywords: Analgesic, Hypoglycemic, Hepatoprotective, Moringa oleifer

Contamination, enrichment and translocation of heavy metals in certain leafy vegetables grown in composite effluent irrigated soil

The present investigation was carried out to determine the contamination, enrichment and translocation of heavy metals in vegetables viz., spinach (Spinacia oleracea L.), fenugreek (Trigonella foenum-graecum L.) and coriander (Coriandrum sativum L.) grown in the composite effluent (mixture of industrial and domestic wastewater) irrigated soil. The composite effluent of Hindon River was significantly (P<0.05/P<0.01) loaded with different physical (TDS, EC), chemical (pH, BOD5, COD, Cl –, TKN, PO43-, SO42-, Na+, K+, Ca2+, Mg2+), heavy metals (Cd, Cr, Cu, Fe, Mn, Pb, Zn) and microbial  (total bacteria, total fungi, total coliform and yeast) parameters in comparison to the ground water. The composite effluent irrigation significantly (P<0.05) altered the soil characteristics like EC, pH, PO43-, K+, Cd, Cr, Cu, Fe, Mn and Pb in the soil used for the cultivation of S. oleracea, T. foenum-graecum and C. sativum. The composite effluent irrigation significantly increased the contents of Cd, Cr, Cu, Fe, Mn, Pb and Zn in the S. oleracea, T. foenum-graecum and C. sativum. The enrichment factor of Cd, Cr, Cu, Fe, Mn, Pb and Zn in vegetables was recorded to be plant part specific after irrigation with composite effluent. The enrichment factor of Cd, Cr, Cu, Fe, Mn, Pb and Zn were recorded in the order of Cd>Zn>Pb> Fe>Cr>Mn>Cu for S. oleracea, Cd>Zn>Fe>Mn>Pb>Cr>Cu for T. foenum-graecum and Cd>Zn>Pb>Fe>Cu>Mn>Cr for C. sativum after irrigation with composite effluent. Therefore, disposal of sewage and industrial effluents in the Hindon River must be strictly prohibited to save the existence of the Hindon River and irrigation practices using composite effluent should also be banned to prevent the possible health hazards due to consumption of contaminated vegetables

Heavy metals and microbial contamination of certain leafy vegetables grown in abattoir effluent disposal province of Saharanpur (Uttar Pradesh), India

The present investigation was carried out to study the heavy metals and microbial contamination of four selected leafy vegetables viz., cabbage, lettuce, coriander and spinach grown in abattoir effluent irrigated soil. The results revealed that the values of various parameters of abattoir effluent viz., TDS (2840 mg L-1), BOD (2480.50 mg L-1), COD (2890.00 mg L-1), total N (195.80 mg L-1), Fe (18.48 mg L-1), Mn (2.88 mg L-1), total bacteria (6.97×108 CFU ml -1), coliform bacteria (3.24×104 MPN 100 ml -1) and total fungi (7.78×105 CFU ml -1) were found beyond the prescribed limit of Indian irrigation standards. The abattoir effluent irrigation significantly (p<0.05/p<0.01) increased the EC, total N, available P, OC, Ca, Mg, K, Na, Fe, Cd, Cr, Cu, Mn, Zn, total bacteria, coliform bacteria of the soil used for the cultivation of cabbage, lettuce, coriander and spinach in comparison to their respective controls. The most numbers of bacteria (8.67×108 CFU ml-1), coliform bacteria (7.80×105 MPN 100 ml-1) and total fungi (9.85×105 CFU ml-1) were noted in the lettuce after abattoir effluent irrigation. Therefore, the higher contents of heavy metals and microbial population in cabbage, lettuce, coriander and spinach might be related to their contents in the soils irrigated with abattoir effluent. Therefore, the agronomical practices with abattoir effluent should be regularly monitored to avert environmental problems and attendant health hazards