Lie group classifications and exact solutions for time-fractional Burgers equation

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.Comment: 9 pp, accepte

A field-theoretical approach to the extended Hubbard model

We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard-Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge-charge and spin-spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity

A Comparative Study of fBf_B within QCD Sum Rules with Two Typical Correlators up to Next-to-Leading Order

The B-decay constant $f_B$ is an important component for studying $B$-meson decays, which can be studied through QCD sum rules. We make a detailed discussion on $f_B$ from two sum rules, i.e. sum rules I and II, which are derived from the conventional correlator and the correlator with chiral currents respectively. It is found that these two sum rules are consistent with each other. However, the sum rules II has less uncertainty sources than that of sum rules I, and then it can be more accurate if we know the dimension-four gluon condensate well. It is found that $f_B$ decreases with the increment of $m_b$, and to compare with the Belle experimental data on $f_B$, both sum rules prefer smaller pole $b$-quark mass, $m_b=4.68\pm0.07$ GeV. By varying all the input parameters in their reasonable region and adding all the uncertainties together in quadrature, we obtain $f_B=172^{+23}_{-25}$ MeV for sum rules I and $f_B=214_{-34}^{+26}$ MeV for sum rules II.Comment: 11 pages, 4 figures, 2 tables. To match the printed version. To be published in Communications in Theoretical Physic

Effects of biofertilizer containing N-fixer, P and K solubilizers and AM fungi on maize growth: a greenhouse trial

Biofertilizer has been identified as an alternative to chemical fertilizer to increase soil fertility and crop production in sustainable farming. The objective of this greenhouse study was to evaluate the effects of four biofertilizers containing an arbuscular mycorrhizal fungus (Glomus mosseae or Glomus intraradices) with or without N-fixer (Azotobacter chroococcum), P solubilizer (Bacillus megaterium) and K solubilizer (Bacillus mucilaginous) on soil properties and the growth of Zea mays. The application treatments included control (no fertilizer), chemical fertilizer, organic fertilizer and two types of biofertilizer. The application of biofertilizer containing mycorrhizal fungus and three species of bacteria significantly increased the growth of Z. mays. The use of biofertilizer (G. mosseae and three bacterial species) resulted in the highest biomass and seedling height. This greenhouse study also indicated that half the amount of biofertilizer application had similar effects when compared with organic fertilizer or chemical fertilizer treatments. Microbial inoculum not only increased the nutritional assimilation of plant (total N, P and K), but also improved soil properties, such as organic matter content and total N in soil. The arbuscular mycorrhizal fungi (AMF) had a higher root infection rate in the presence of bacterial inoculation. By contrast, the AMF seemed to have an inhibiting effect on the P-solubilizing bacteria. The nutrient deficiency in soil resulted in a larger population of Nfixing bacteria and higher colonization of AMF

Dynamical study on polaron formation in a metal/polymer/metal structure

By considering a metal/polymer/metal structure within a tight-binding one-dimensional model, we have investigated the polaron formation in the presence of an electric field. When a sufficient voltage bias is applied to one of the metal electrodes, an electron is injected into the polymer chain, then a self-trapped polaron is formed at a few hundreds of femtoseconds while it moves slowly under a weak electric field (not larger than $$ V/cm). At an electric field between $1.0\times 10^4$ V/cm and $$ V/cm, the polaron is still formed, since the injected electron is bounded between the interface barriers for quite a long time. It is shown that the electric field applied at the polymer chain reduces effectively the potential barrier in the metal/polymer interface

Hierarchical Neutrino Mass Matrices, CP violation and Leptogenesis

In this work we study examples of hierarchical neutrino mass matrices inspired by family symmetries, compatible with experiments on neutrino oscillations, and for which there is a connection among the low energy CP violation phase associated to neutrino oscillations, the phases appearing in the amplitude of neutrinoless double beta decay, and the phases relevant for leptogenesis. In particular, we determine the predictions from a texture based on an underlying SU(3) family symmetry together with a GUT symmetry, and a strong hierarchy for the masses of the heavy right handed Majorana masses. We also give some examples of inverted hierarchies of neutrino masses, which may be motivated in the context of U(1) family symmetries.Comment: 34 pages. Replaced with published version -typos, corrections and references adde