22 research outputs found
Iterative Solution of Fractional Diffusion Equation Modelling Anomalous Diffusion
In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior
Semianalytic Solution of Space-Time Fractional Diffusion Equation
We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior
Genetic Diversity and Population Structure of F3:6 Nebraska Winter Wheat Genotypes Using Genotyping-By-Sequencing
The availability of information on the genetic diversity and population structure in wheat (Triticum aestivum L.) breeding lines will help wheat breeders to better use their genetic resources and manage genetic variation in their breeding program. The recent advances in sequencing technology provide the opportunity to identify tens or hundreds of thousands of single nucleotide polymorphism (SNPs) in large genome species (e.g., wheat). These SNPs can be utilized for understanding genetic diversity and performing genome wide association studies (GWAS) for complex traits. In this study, the genetic diversity and population structure were investigated in a set of 230 genotypes (F3:6) derived from various crosses as a prerequisite for GWAS and genomic selection. Genotyping-by-sequencing provided 25,566 high-quality SNPs. The polymorphism information content (PIC) across chromosomes ranged from 0.09 to 0.37 with an average of 0.23. The distribution of SNPs markers on the 21 chromosomes ranged from 319 on chromosome 3D to 2,370 on chromosome 3B. The analysis of population structure revealed three subpopulations (G1, G2, and G3). Analysis of molecular variance identified 8% variance among and 92% within subpopulations. Of the three subpopulations, G2 had the highest level of genetic diversity based on three genetic diversity indices: Shannon’s information index (I) = 0.494, diversity index (h) = 0.328 and unbiased diversity index (uh) = 0.331, while G3 had lowest level of genetic diversity (I = 0.348, h = 0.226 and uh = 0.236). This high genetic diversity identified among the subpopulations can be used to develop new wheat cultivars
Front transition in higher order diffusion equations with a general reaction nonlinearity
New doubly-periodic solutions for the new integrable non local modified KdV equation
In this paper, new doubly-periodic solutions will be found for a new integrable nonlocal modified Korteweg-de Vries equation (mKdV). We adopt a technique using a travelling wave transformation which results in different solutions represented in Jacobi elliptic functions
Genetic Diversity and Population Structure of F3:6 Nebraska Winter Wheat Genotypes Using Genotyping-By-Sequencing
The availability of information on the genetic diversity and population structure in wheat (Triticum aestivum L.) breeding lines will help wheat breeders to better use their genetic resources and manage genetic variation in their breeding program. The recent advances in sequencing technology provide the opportunity to identify tens or hundreds of thousands of single nucleotide polymorphism (SNPs) in large genome species (e.g., wheat). These SNPs can be utilized for understanding genetic diversity and performing genome wide association studies (GWAS) for complex traits. In this study, the genetic diversity and population structure were investigated in a set of 230 genotypes (F3:6) derived from various crosses as a prerequisite for GWAS and genomic selection. Genotyping-by-sequencing provided 25,566 high-quality SNPs. The polymorphism information content (PIC) across chromosomes ranged from 0.09 to 0.37 with an average of 0.23. The distribution of SNPs markers on the 21 chromosomes ranged from 319 on chromosome 3D to 2,370 on chromosome 3B. The analysis of population structure revealed three subpopulations (G1, G2, and G3). Analysis of molecular variance identified 8% variance among and 92% within subpopulations. Of the three subpopulations, G2 had the highest level of genetic diversity based on three genetic diversity indices: Shannon’s information index (I) = 0.494, diversity index (h) = 0.328 and unbiased diversity index (uh) = 0.331, while G3 had lowest level of genetic diversity (I = 0.348, h = 0.226 and uh = 0.236). This high genetic diversity identified among the subpopulations can be used to develop new wheat cultivars
Genetic Diversity and Population Structure of F3:6 Nebraska Winter Wheat Genotypes Using Genotyping-By-Sequencing
The availability of information on the genetic diversity and population structure in wheat (Triticum aestivum L.) breeding lines will help wheat breeders to better use their genetic resources and manage genetic variation in their breeding program. The recent advances in sequencing technology provide the opportunity to identify tens or hundreds of thousands of single nucleotide polymorphism (SNPs) in large genome species (e.g., wheat). These SNPs can be utilized for understanding genetic diversity and performing genome wide association studies (GWAS) for complex traits. In this study, the genetic diversity and population structure were investigated in a set of 230 genotypes (F3:6) derived from various crosses as a prerequisite for GWAS and genomic selection. Genotyping-by-sequencing provided 25,566 high-quality SNPs. The polymorphism information content (PIC) across chromosomes ranged from 0.09 to 0.37 with an average of 0.23. The distribution of SNPs markers on the 21 chromosomes ranged from 319 on chromosome 3D to 2,370 on chromosome 3B. The analysis of population structure revealed three subpopulations (G1, G2, and G3). Analysis of molecular variance identified 8% variance among and 92% within subpopulations. Of the three subpopulations, G2 had the highest level of genetic diversity based on three genetic diversity indices: Shannon’s information index (I) = 0.494, diversity index (h) = 0.328 and unbiased diversity index (uh) = 0.331, while G3 had lowest level of genetic diversity (I = 0.348, h = 0.226 and uh = 0.236). This high genetic diversity identified among the subpopulations can be used to develop new wheat cultivars