The combined effect of promoting Zirconium (Zr) and Tungsten (W) na-nopowders on catalytic properties of pentasil type of zeolites in the conversion processes of natural gas and methanol to aromatic hydrocarbons (ArH) was studied. The addition of Zr to W-containing ZSM-5 leading to enhancement the activity and selectivity of the cat-alyst in the aromatic hydrocarbons formation processes were established. Modifying ZSM-5 with Zr and W nanopowders makes promoting effect on its catalytic properties in the conversion of methanol and natural gas to ArH. Maximum quantity of aromatic hy-drocarbons generated from the conversion of natural gas and methanol in the presence of catalysts was shown, where 1,5 wt.%Zr - 6,0 wt. % W/HZSM-5 and 3,0 wt.% Zr - 6,0wt.% W/HZSM-5, respectively.It is shown that to obtain an effective catalyst for the conversion of natural gas and methanol to aromatic hydrocarbons, a certain combination of weak and strong acid sites are necessary, which is achieved by controlling the amount of modifiers in the catalytic system.

In this paper, we discuss the comparative growth properties of composite entire functions and a special type of differential polynomial generated by one of the factor of the composite entire function on the basis of central index.

AMS Subject Classification (2010): 30D20, 30D35

A simple theoretical model has been used to study the thermodynamic properties of materials at nano scale. I have considered Copper (Cu), Platinum (Pt) and Nickel (Ni) for the study of size dependent thermodynamic properties i.e. cohesive energy, melting temperature, Debye temperature etc. In the present work, the thermodynamic properties have been studied for different shapes (i.e. for spherical and non-spherical) with different sizes. The thermodynamic properties change in different manner due to their shape factor. In present study it is found that there is a drastic change in the thermodynamic properties of nanomaterials below 20 nanometers. This study also shows that the shape of nanoparticles plays an important role to affect these properties

We have investigated Bianchi type-IX string cosmological model with cosmological term  in the presence of bulk viscous fluid with electromagnetic field. To obtain the deterministic solution we assume that bulk viscosity ξ is proportional to the expansion θ; proper energy density ρ is proportional to the string tension density λ and  Λ is proportional to R^-3, where R is scale factor. Various physical and geometrical aspects of the model are also discussed.