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Jaiswal, J. P.
- Assessing Genetic Diversity in Bread Wheat using Inter Simple Sequence Repeat (ISSR) Markers
Authors
1 G. B. Pant University of Agriculture and Technology, Panthnagar (Uttarakhand), IN
Source
Asian Journal of Bio Science, Vol 11, No 1 (2016), Pagination: 141-145Abstract
A major effort of a plant breeder is the constant improvement of the best available genotypes for further enhancement in their yield potential either directly or through improvement of various factors which contribute indirectly to high yield. Genetic diversity of wheat cultivars is very important in reducing genetic vulnerability during plant breeding efforts. In order to estimate the genetic diversity, molecular markers provide excellent tools. The aim of this study was to molecularly characterize the fifty wheat accessions to assess phylogenetic relationship and mutual genetic distances through the use of 10 ISSR markers and 50 accessions of wheat. The dendrogram separated genotypes into two clusters I and II comprising of 49 and 1 accessions, respectively. The allelic polymorphism information content (PIC) value ranged from 0.147 to 0.467 with an average of 0.287. The similarity co-efficient ranged from .41 to .89. Significant correlation of microsatellite genetic distance was tested by mantel test (r= 0.77557). Results shows that high level of polymorphism among the wheat accessions. Cluster analysis suggested that ISSR markers were efficient tools for estimating intra-specific genetic diversity in wheat and this molecular marker could differentiate the accessions obtained from different locations. ISSRs have been successfully used to estimate the extent of genetic diversity at inter- and intra-specific level in a wide range of crops. The genetic relationships estimated by the polymorphism of ISSR markers revealed greater level of genetic variability in wheat accessions of wide adaptability and applicability.
Keywords
Bread Wheat, Genetic Diversity, ISSR Markers, Wheat Accessions.- Semilocal Convergence of a Seventh-Order Method in Banach Spaces Under HÖlder Continuity Condition
Authors
1 Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh - 462003, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 56–69Abstract
The motive of this article is to analyze the semilocal convergence of a well existing iterative method in the Banach spaces to get the solution of nonlinear equations. The condition, we assume that the nonlinear operator fulfills the Hölder continuity condition which is softer than the Lipschitz continuity and works on the problems in which either second order Frèchet derivative of the nonlinear operator is challenging to calculate or does not hold the Lipschitz condition. In the convergence theorem, the existence of the solution x* and its uniqueness along with prior error bound are established. Also, the R-order of convergence for this method is proved to be at least 4+3q. Two numerical examples are discussed to justify the included theoretical development followed by an error bound expression.Keywords
Banach Space, Nonlinear Operator, Semilocal Convergence, Hölder Condition, Frèchet Derivative, Recurrence Relation, Error Bound.References
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- Ball Convergence of Modified Homeier-Like's Method in Banach Spaces under Weak Continuity Condition
Authors
Source
The Journal of the Indian Mathematical Society, Vol 89, No 3-4 (2022), Pagination: 305-316Abstract
The aim of this study is to analyze the local convergence of the multi-step Homeier's-like method for solving nonlinear equations in Banach space. Furthermore, we avoid hypotheses on high order derivatives which limit the applicability of the method. Instead, we only use hypotheses on the first derivative. Thus the applicability of the method has been extended by preserving the order of convergence. The convergence of the solution is proved under the weak hypotheses i.e. $\omega$-continuity condition. Some numerical instances where earlier results cannot be applied to solve equations but our results can be applied are provided to validate the theoretical contribution.
Keywords
Banach Space, Lcal Cconvergence, Recurrence Relation, β-Continuity condition.References
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