Structural,electrical and optical studies on spray-deposited aluminium-doped ZnO thin films

Thin films of zinc oxide (ZnO) were deposited on cleaned glass substrates by chemical spray pyrolysis technique using Zn(CH₃COO)₂ as precursor solution. Also, aluminium-doped thin films of ZnO were prepared by using AlCl₃ as doping solution for aluminium. The dopant concentration [Al/Zn atomic percentage (at%)] was varied from 0 to 1.5 at% in thin films of ZnO prepared in different depositions. Structural characterization of the deposited films was performed with X-ray diffraction (XRD) studies. It confirmed that all the films were of zinc oxide having polycrystalline nature and possessing typical hexagonal wurtzite structure with crystallite size varying between 100.7 and 268.6 nm. The films exhibited changes in relative intensities and crystallite size with changes in the doping concentration of Al. The electrical studies established that 1 at% of Al-doping was the optimum for enhancing electrical conduction in ZnO thin films and beyond that the distortion caused in the lattice lowered the conductivity. The films also exhibited distinct changes in their optical properties at different doping concentrations, including a blue shift and slight widening of bandgap with increasing Al dopant concentration.     

Vibrational Spectroscopy of Stretching and Bending Modes of Nickel Tetraphenyl Porphyrin： an Algebraic Approach

We calculate the vibrational frequencies of nickel tetraphenyl porphyrin for 36 vibrational bands by using the U（2） algebraic approach. The algebraic parameters in the calculations are accurate with the experimental data.     

Harder–Narasimhan Filtrations which are not split by the Frobenius maps

We will produce a smooth projective scheme X over ?, a rank 2 vector bundle V on X with a line subbundle L having the following property. For a prime p, let F _p be the absolute Fobenius of X _p , and let L _p ???V _p be the restriction of L???V. Then for almost all primes p, and for all t?≥?0, $(F_p^*)^t L_P \subset (F_p^*)^t V_p$ is a non-split Harder-Narasimhan filtration. In particular, $(F_p^*)^t V_p$ is not a direct sum of strongly semistable bundles for any t. This construction works for any full flag veriety G/B, with semisimple rank of G?≥?2. For the construction, we will use Borel–Weil–Bott theorem in characteristic 0, and Frobenius splitting in characteristic p.     

Analysis of a malaria model with mosquito-dependent transmission coefficient for humans

In this paper, we discuss an ordinary differential equation mathematical model for the spread of malaria in human and mosquito population. We suppose the human population to act as a reservoir. Both the species follow a logistic population model. The transmission coefficient or the interaction coefficient of humans is considered to be dependent on the mosquito population. It is seen that as the factors governing the transmission coefficient of humans increase, so does the number of infected humans. Further, it is observed that as the immigration constant increases, it leads to a rise in infected humans, giving an endemic shape to the disease.     

Characteristic classes for GO(2n) in étale cohomology

Let $GO(2n)$ be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic $\ne 2$ . We determine the smooth-étale cohomology ring with $\mathbb F_2$ coefficients of the algebraic stack $BGO(2n)$ . In the topological category, Holla and Nitsure determined the singular cohomology ring of the classifying space $BGO(2n)$ of the complex Lie group $GO(2n)$ in terms of explicit generators and relations. We extend their results to the algebraic category. The chief ingredients in this are: (i) an extension to étale cohomology of an idea of Totaro, originally used in the context of Chow groups, which allows us to approximate the classifying stack by quasi projective schemes; and (ii) construction of a Gysin sequence for the ${\mathbb G_m}$ -fibration $BO(2n)\to BGO(2n)$ of algebraic stacks.     

Unpolarized coupled DGLAP evolution equation at small-x

In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small-x limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated t-evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-Q ² region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when Q ² increases for fixed values of x.