On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation

AbstractIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions

GIZA 11 AND GIZA 12; TWO NEW FLAX DUAL PURPOSE TYPE VARIETIES

Sixteen flax genotypes {13 promising lines and 3 check varieties viz., Giza 8 (oil type), Sakha 1 (dual purpose type) and Sakha 3 (fiber type)} were evaluated for straw, seed, oil yields and their related traits under twelve different environments; four locations (Sakha, Etay El-Baroud, Ismailia and Giza Exp. Stations through three successive seasons (2011/12, 2012/13 and 2013/14). These materials were evaluated in a randomized complete blocks design with three replications at the twelve above-mentioned environments. The analysis of variance revealed highly significant differences among genotypes (G), environments (E) and G x E interaction for all studied traits except straw weight per plant, indicating a wide range of variation among genotypes, environments and these genotypes exhibited differential response to environmental conditions. The significant variance due to residual for all characters except both straw weight per plant and oil yield per fad indicated that genotypes differed with respect to their stability suggesting that prediction would be difficult, which means that mean performance alone would not be appropriate. Interaction component of variance (σ2ge) was less than the genotypic variance (σ2g) for all characters, indicating that genotypes differ in their genetic potential for these traits. This was reflected in high heritability and low discrepancy between phenotypic (PCV) and genotypic (GCV) coefficients of variability values for these traits indicating the possibility of using each of long fiber percentage, plant height and technical stem length as selection indices for improving straw weight per plant, as well as, using 1000-seed weight and capsules number per plant as selection indices for improving seed weight per plant. Yield stability (YSi) statistic indicated that S.541-C/3 and S.541-D/10 gave high mean performance and stability for straw, fiber, seed and oil yields per fad in addition to oil percentage, capsules number per plant and 1000-seed weight. Therefore, the two genotypes well be released under the name Giza 11 and Giza 12, respectively. These newly released varieties are of dual purpose type for straw, fiber, seed and oil yield. They may replace the low yielding cultivars Giza 8, Sakha 1 and Sakha 3

Report on root rot and wilt diseases of sesame in Egypt

In IDL-704