A Sturm-Liouville problem with n-potential functions in the second order differential equation and which contains spectral parameter depending on linearly in one boundary condition is considered. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the Prüfer's substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions are given. Finally, a numerical example is given.

In this research Ab initio and DFT calculations were used to investigate the substitutions groups electronic effects CF3, CCl3 and CBr3 on cheletropic reaction of 2,5-Dihydrothiophene sulfone. The rate and activation energy of cheletropic reactions were investigate. the trend of reactions electronic effects of trans state were studied with B3L YP/3-21 G levels of theory. The results of the electronegativity, the band length, Muliken charge and electronic occupancy data showed that in Steric effects and electronic effects are effective on reaction rate and activation energy of cheletropic reaction. These results are in good agreement with experimental data. Trans-2,5- three chloro metyl Sulfolen has the highest activation energy and the lowest rate of reaction.

In this study, a full-potential density functional theory was used to investigate the effects of Ti substitution by different cations. In both rutile and anatase, Ti atom was replaced by Ce, Au, Sn, Ag, Mo, Nb, Zr and Y. Phase stability, electronic structure and formation energy of oxygen vacancy were compared for rutile and anatase. The results indicated that substitution of Ce and Zr increases anatase stability through which photocatalytic activity is enhanced. It seems that the cationic capacity and size play a critical role in anatase to rutile phase transition, where with an equi- or higher valence than Ti, larger cations increase the stability of anatase phase. Oxygen vacancy concentration, as a second factor of photocatalytic activity, was also studied by calculating its stability due to the cationic substitution. The data revealed that Au, Ag, Y, Ce and Sn effectively reduce oxygen-vacancy formation energy. Of the studied cations, Au and Ag had maximum reduction in band gap, by creating defect states in the middle of the band gap resulting from the overlaps of d-orbitals of these elements and oxygen p-orbitals. Mo and Ce impurities did not have a significant effect on reducing gaps by creating defect states under the conduction band. Finally, Sn impurity also generated defect states in the middle of the gap merely with the lack of oxygen.

Horseradish peroxidase (HRP), has gained significant interests in biotechnology, especially in biosensor field and diagnostic test kits. Hence, its solvent-exposed lysine residues 174, 232, and 241 have been frequently modified with the aim of improving its stability and catalytic efficiency. In this computational study, we investigated the effects of Lys-to-Glu substitutions on HRP structure to model charge-reversal manipulations at the enzyme surface. Simulation results implied that upon these substitutions, the number of stable hydrogen bonds and a-helical content of HRP are increased and the proximal Ca2+binding pocket becomes more integrated. The results revealed that although Glu174-heme hydrogen bond is lost after mutation, formation of a new hydrogen bonding network contributes to the stability of heme-protein linkage. Together, it may be concluded that these substitutions enhance the stability of the protein moiety as well as the heme-protein non-covalent interactions. In the enzyme active site, we observed increased accessibility of peroxide binding site and heme prosthetic group to the peroxide and aromatic substrates, respectively. Results also demonstrated that the bottleneck entry of the peroxide-binding site has become wider and more flexible upon substitutions. Moreover, the hydrophobic patch functioning as a binding site or trap for reducing aromatic substrates is more extended in mutated enzyme. These observations suggest that the reactivity of the enzyme to its substrates has increased. Together, the results of this simulation study could provide possible structural clues to explain those experimental observations in which the protein stability achieved upon manipulation of charge distribution on protein surface.  

Since decades, Newcastle disease (ND) has become endemic in the poultry population of the Indian subcontinent. ND is a highly contagious disease of poultry and other avian species. However, the genetic nature of ND viruses circulating in the rock pigeons is unraveled. The present investigation is a part of Newcastle disease virus (NDV) surveillance in wild birds. Two velogenic NDV strains could be isolated from apparently healthy rock pigeons, thus establishing the status of carrier/reservoir host. The fusion protein cleavage site in the fusion protein has multiple basic amino acid (RRRKRF) motifs similar to velogenic isolates. Phylogenetic analysis based on complete fusion gene sequences confirmed that the isolates belong to NDV sub genotype XIII 2.2. Further analysis revealed several amino acid substitutions in the hypervariable region, heptad repeat regions and neutralizing epitopes of the fusion protein and heptad repeat regions and antigenic sites of the hemagglutinin-neuraminidase (HN) protein that are critical for fusion. A unique D170A substitution in the neutralizing epitope is identified that is critical for structure and function of the fusion protein. Mutations within the virulence determinants including fusion (F) and HN, elucidate continuous evolution of the viruses among the rock pigeons. Accidental spillover of these mutated viruses into commercial poultry operations may result in disease outbreaks with economic breakdown.

In this work, the structural, optical and photocatalytic properties of Cu1-3xNixZn2xFe2O4 ferrites prepared by citrate-nitrate method were investigated. The samples were characterized by X-ray diffraction (XRD) and UV-Vis spectrometer at room temperature. Examining the XRD patterns indicates the presence of a spinel structural phase transition from a tetragonal to cubic structure, which shows an increase in symmetry with the co-substitution of Ni and Zn in the copper ferrite. The bandgap values of the samples show a minimum value of 1.43 eV for x = 0.05. The highest catalytic activity of 95% in the degradation of methylene blue is obtained for the x = 0.05 sample due to its smaller energy gap.