Haar Wavelet Method for the System of Integral Equations

We employed the Haar wavelet method to find numerical solution of the system of Fredholm integral equations (SFIEs) and the system of Volterra integral equations (SVIEs). Five test problems, for which the exact solution is known, are considered. Comparison of the results is obtained by the Haar wavelet method with the exact solution

Haar wavelet method for the system of integral equations

We employed the Haar wavelet method to find numerical solution of the system of Fredholm integral equations (SFIEs) and the system of Volterra integral equations (SVIEs). Five test problems, for which the exact solution is known, are considered. Comparison of the results is obtained by the Haar wavelet method with the exact solution

New Solutions for System of Fractional Integro-Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method

Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro-differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro-differential equations and Abel’s integral equations

Q

We study in this paper the Q-symmetry and conditional Q-symmetries of Boussinesq equation. The solutions which we obtain, in this case, are in the form of convergent power series with easily computable components

Description of the Magnetic Field and Divergence of Multisolenoid Aharonov-Bohm Potential

Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential are very singular generalized functions concentrated at a finite number of thin solenoids. Deficiency index is found for the minimal operator generated by the Aharonov-Bohm differential expression

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

Symmetry analysis of an integrable Ito coupled system

AbstractIn this paper, we study the invariance analysis, integrability properties and P-property of the Ito coupled nonlinear partial differential equations. We explore several new solutions for the Ito system through the Lie symmetry analysis. Moreover, this work has been devoted to study the integrability aspects of the Ito system through higher order symmetries. We are also investigating the existence of higher order symmetries for the Ito system. Interestingly our investigations reveal a rich variety of particular solutions, which have not been reported in the literature, for this model