Nova egzaktna rješenja poopćene nelinearne Schrodingerove jednadžbe

Using the modified mapping method and the extended mapping method, we derive some new exact solutions of the generalized nonlinear Schrödinger equation, which are linear combinations of two different Jacobi elliptic functions and we also consider the solutions in the limiting cases.Izvodimo neka nova egzaktna rješenja poopćene nelinearne Schrodingerove jednadžbe primjenom izmijenjene i proširene pridružne metode. Rješenja su linearni sastavci dviju Jacobijevih eliptičkih funkcija. Razmatramo također granična rješenja

Analyticity of the Cauchy Problem for a Three-Component Generalization of Camassa–Holm Equation

In this paper, we investigate the Cauchy problem for a three-component generalization of Camassa–Holm equation (G3CH equation henceforth) with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time

Boundary Stabilization of a Nonlinear Viscoelastic Equation with Interior Time-Varying Delay and Nonlinear Dissipative Boundary Feedback

We investigate a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback. Under suitable assumptions on the relaxation function and time-varying delay effect together with nonlinear dissipative boundary feedback, we prove the global existence of weak solutions and asymptotic behavior of the energy by using the Faedo-Galerkin method and the perturbed energy method, respectively. This result improves earlier ones in the literature, such as Kirane and Said-Houari (2011) and Ammari et al. (2010). Moreover, we give an positive answer to the open problem given by Kirane and Said-Houari (2011)

Genomic change, retrotransposon mobilization and extensive cytosine methylation alteration in Brassica napus introgressions from two intertribal hybridizations

Publisher's Version/PDFHybridization and introgression represent important means for the transfer and/or de novo origination of traits and play an important role in facilitating speciation and plant breeding. Two sets of introgression lines in Brassica napus L. were previously established by its intertribal hybridizations with two wild species and long-term selection. In this study, the methods of amplified fragment length polymorphisms (AFLP), sequence-specific amplification polymorphism (SSAP) and methylation-sensitive amplified polymorphism (MSAP) were used to determine their genomic change, retrotransposon mobilization and cytosine methylation alteration in these lines. The genomic change revealed by the loss or gain of AFLP bands occurred for ~10% of the total bands amplified in the two sets of introgressions, while no bands specific for wild species were detected. The new and absent SSAP bands appeared for 9 out of 11 retrotransposons analyzed, with low frequency of new bands and their total percentage of about 5% in both sets. MSAP analysis indicated that methylation changes were common in these lines (33.4&ndash;39.8%) and the hypermethylation was more frequent than hypomethylation. Our results suggested that certain extents of genetic and epigenetic alterations were induced by hybridization and alien DNA introgression. The cryptic mechanism of these changes and potential application of these lines in breeding were also discussed.</p

A new blow-up criterion for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion

In this paper, we investigate the Cauchy problem for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion. Furthermore, we establish the blow-up result of the positive solutions in finite time under certain conditions on the initial datum. This result complements the early one in the literature, such as [E. Novruzov, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation, J. Math. Phys. 54 (2013), no. 9, 092703, DOI 10.1063/1.4820786] and [Z.Y. Zhang, J.H. Huang, and M.B. Sun, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited, J. Math. Phys. 56 (2015), no. 9, 092701, DOI 10.1063/1.4930198]

Genome-wide gene expressions respond differently to A-subgenome origins in Brassica napus synthetic hybrids and natural allotetraploid

The young allotetraploid Brassica napus (2n=38, AACC) is one of models to study the genomic responses to allopolyploidization. The extraction of AA component from natural B. napus should provide a unique opportunity to reveal the genome interplay for gene expressions during the evolution. Herein, B. napus hybrids (2n=19, AC) between the extracted and extant B. rapa (2n=20, AA) and the same B. oleracea genotype (2n=18, CC) were studied by RNA-seq and compared with natural B. napus donor, to reveal the gene expression changes from hybridization and domestication and the effects of A genome with different origins. Upon the initial merger of two diploid genomes, additive gene expression was prevalent in these two hybrids, for nonadditively expressed genes only represented a small portion of total expressed genes. A high proportion of genes exhibited expression level dominance, with no preference to either of the parental genomes. Comparison of homoeolog expressions also showed no bias toward any genomes and the parental expression patterns were often maintained in the hybrids and natural allotetraploids. Although the overall patterns of gene expression were highly conserved between two hybrids, the extracted B. rapa responded less and appeared more compatible for hybridization than the extant B. rapa. Our results suggested that expression level dominance and homoeolog expressions bias were balanced at the initial stage of genome merger, and such balance were largely maintained during the domestication of B. napus, despite the increased extent over time