Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Tb3+-> Eu3+ Energy Transfer in Mixed-Lanthanide-Organic Frameworks

In this work, we report a theoretical and experimental investigation of the energy transfer mechanism in two isotypical 2D coordination polymers, (infinity)[(Tb1-xEux)(DPA)(HDPA)], where H(2)DPA is pyridine 2,6-dicarboxylic acid and x = 0.05 or 0.50. Emission spectra of (infinity)[(Tb0.95Eu0.05)(DPA)(HDPA)] and (infinity)[(Tb0.5Eu0.5)(DPA)(HDPA)], (I) and (2), show that the high quenching effect on Tb3+ emission caused by Eu3+ ion indicates an efficient Tb3+-> Eu3+ energy transfer (ET). The k(ET) of Tb3+-> Eu3+ ET and rise rates (k(r)) of Eu3+ as a function of temperature for (1) are on the same order of magnitude, indicating that the sensitization of the Eu3+5D0 level is highly fed by ET from the D-5(4) level of Tb3+ ion. The eta(ET) and R-0 values vary in the 67-79% and 7.15 to 7.93 angstrom ranges. Hence, Tb3+ is enabled to transfer efficiently to Eu3+ that can occupy the possible sites at 6.32 and 6.75 angstrom. For (2), the ET processes occur on average with eta(ET) and R-0 of 97% and 31 angstrom, respectively. Consequently, Tb3+ ion is enabled to transfer energy to Eu3+ localized at different layers. The theoretical model developed by Malta was implemented aiming to insert more insights about the dominant mechanisms involved in the ET between lanthanides ions. Calculated single Tb3+-> Eu3+ ETs are three orders of magnitude inferior to those experimentally; however, it can be explained by the theoretical model that does not consider the role of phonon assistance in the Ln(3+)-> Ln(3+) ET processes. In addition, the Tb3+-> Eu3+ ET processes are predominantly governed by dipole-dipole (d-d) and dipole-quadrupole (d-q) mechanisms.

Microcollinearity between autopolyploid sugarcane and diploid sorghum genomes

Abstract Background Sugarcane (Saccharum spp.) has become an increasingly important crop for its leading role in biofuel production. The high sugar content species S. officinarum is an octoploid without known diploid or tetraploid progenitors. Commercial sugarcane cultivars are hybrids between S. officinarum and wild species S. spontaneum with ploidy at ~12×. The complex autopolyploid sugarcane genome has not been characterized at the DNA sequence level. Results The microsynteny between sugarcane and sorghum was assessed by comparing 454 pyrosequences of 20 sugarcane bacterial artificial chromosomes (BACs) with sorghum sequences. These 20 BACs were selected by hybridization of 1961 single copy sorghum overgo probes to the sugarcane BAC library with one sugarcane BAC corresponding to each of the 20 sorghum chromosome arms. The genic regions of the sugarcane BACs shared an average of 95.2% sequence identity with sorghum, and the sorghum genome was used as a template to order sequence contigs covering 78.2% of the 20 BAC sequences. About 53.1% of the sugarcane BAC sequences are aligned with sorghum sequence. The unaligned regions contain non-coding and repetitive sequences. Within the aligned sequences, 209 genes were annotated in sugarcane and 202 in sorghum. Seventeen genes appeared to be sugarcane-specific and all validated by sugarcane ESTs, while 12 appeared sorghum-specific but only one validated by sorghum ESTs. Twelve of the 17 sugarcane-specific genes have no match in the non-redundant protein database in GenBank, perhaps encoding proteins for sugarcane-specific processes. The sorghum orthologous regions appeared to have expanded relative to sugarcane, mostly by the increase of retrotransposons. Conclusions The sugarcane and sorghum genomes are mostly collinear in the genic regions, and the sorghum genome can be used as a template for assembling much of the genic DNA of the autopolyploid sugarcane genome. The comparable gene density between sugarcane BACs and corresponding sorghum sequences defied the notion that polyploidy species might have faster pace of gene loss due to the redundancy of multiple alleles at each locus.