Symmetry analysis of wave equation on sphere

The symmetry classification problem for wave equation on sphere is considered. Symmetry algebra is found and a classification of its subalgebras, up to conjugacy, is obtained. Similarity reductions are performed for each class, and some examples of exact invariant solutions are given.     

Luciferin‐Regenerating Enzyme Mediates Firefly Luciferase Activation Through Direct Effects of D‐Cysteine on Luciferase Structure and Activity

Luciferin‐regenerating enzyme (LRE) contributes to in vitro recycling of D‐luciferin. In this study, reinvestigation of the luciferase‐based LRE assay is reported. Here, using quick change site‐directed mutagenesis seven T‐LRE (Lampyris turkestanicusLRE) mutants were constructed and the most functional mutant of T‐LRE (T⁶⁹R) was selected for this research and the effects of D‐ and L‐cysteine on T⁶⁹R T‐LRE‐luciferase‐coupled assay are examined. Our results demonstrate that bioluminescent signal of T⁶⁹R T‐LRE‐luciferase‐coupled assay increases and then reach equilibrium state in the presence of 5 mm D‐cysteine. In addition, results reveal that 5 mm D‐ and L‐cysteine in the absence of T⁶⁹R T‐LRE cause a significant increase in bioluminescence intensity of luciferase over a long time as well as decrease in decay rate. Based on activity measurements, far‐UV CD analysis, ANS fluorescence and DLS (Dynamic light scattering) results, D‐cysteine increases the activity of luciferase due to weak redox potential, antiaggregatory effects, induction of changes in conformational structure and kinetics properties. In conclusion, in spite of previous reports on the effect of LRE on luciferase bioluminescent intensity, the majority of increase in luciferase light output and time‐course originate from the direct effects of D‐cysteine on structure and activity of firefly luciferase.     

Microwave‐Assisted Catalyst Free Three Component Synthesis of Mono and Bis Spiro Pyrazolopyridines in Solvent Free Reaction

Multicomponent synthesis of mono and bis‐spiro pyrazolopyridines from isatin derivatives, indanedione, and 3‐methyl‐5‐aminopyrazole under microwave irradiation in the absence of any catalyst or solvent with high yield and short reaction time is reported.     

Genetic diversity and haplotype structure of 21 Y‐STRs,including nine noncore loci,in South Tunisian Population: Forensic relevance

Y chromosome STRs (Y‐STRs) are being used frequently in forensic laboratories. Previous studies of Y‐STR polymorphisms in different groups of the Tunisian population identified low levels of diversity and discrimination capacity (DC) using various commercial marker sets. This definitely limits the use of such systems for Y‐STRs genotyping in Tunisia. In our investigation on South Tunisia, 200 unrelated males were typed for the 12 conventional Y‐STRs included in the PowerPlex® Y System. Additional set of nine noncore Y‐STRs including DYS446, DYS456, DYS458, DYS388, DYS444, DYS445, DYS449, DYS710, and DYS464 markers were genotyped and evaluated for their potential in improving DC. Allele frequency, gene diversity, haplotype diversity (HD), and DC calculation revealed that DYS464 was the most diverse marker followed by DYS710 and DYS449 markers. The standard panel of 12 Y‐STRs (DC = 80.5%) and the nine markers were combined to obtain DC of 99%. Among the 198 different haplotypes observed, 196 haplotypes were unique (HD = 99.999). Out of the nine noncore set, six Y‐STRs (DYS458, DYS456, DYS449, DYS710, DYS444, and DYS464) had the greatest impact on enhancing DC. Our data provided putative Y‐STRs combination to be used for genetic and forensic applications.     

Magnetic,Electrical and Thermal Studies of Polypyrrole-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> Nanocomposites

This research paper comprises of the synthesis of polypyrrole (PPy)-Fe₂O₃ nanocomposites by employing the in situ chemical oxidative polymerization method. The concentration of the filler material was adjusted between 10–50 wt % of PPy. The synthesized nanocomposites were characterized by using X-ray diffraction (XRD). Magnetic analysis and DC electrical conductivity of the samples were carried out using vibrating sample magnetometer (VSM) and two probe DC conductivity method, point towards magnetically active and electrically conductive samples. The magnetic parameters under applied magnetic field demonstrated that the values of coercivity (H _c ), saturation magnetization (M _s ) and remanence (M _r ) can be tailored by carefully controlling the amount of dopant material into the nanocomposites indicating their suitability for controllable switching devices and microwave absorption applications. The DC electrical conductivity showed an increase up to 20 wt % of filler material and thereafter a decrease in the conductivity of nanocomposites with increase in filler content is observed. Thermogravimetric analysis (TGA) showed an increase in thermal stability with an increase in ferrite content in nanocomposites.     

On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.