Supersoluble crossed product criterion for division algebras

LetD be a finite-dimensionalF-central division algebra. A criterion is given forD to be a supersoluble (nilpotent) crossed product division algebra in terms of subgroups of the multiplicative groupD* ofD. More precisely, it is shown thatD is a supersoluble (nilpotent) crossed product if and only ifD* contains an abelian-by-supersoluble (abelian-by-nilpotent) generating subgroup.     

Equation of state and P-V-T properties of polymer melts based on glass transition data

This paper addresses a method for predicting the participating constants in equation of state (EOS) for compressed polymeric fluids using two scaling constants. The theoretical EOS undertaken is Ihm-Song-Mason (ISM), which is based on the Weeks-Chandler-Anderson (WCA), and the two constants are the surface tension γ_g and the molar density ρ_g, both at the glass transition point. There are three temperature-dependent quantities that are required to use the EOS: the second virial coefficients B₂(T), an effective van der Waals co-volume, b(T) and a correction factor, α(T). The second virial coefficients are calculated from a two-parameter corresponding states correlation, which is constructed with two constants as scaling parameters, i.e., the surface tension γ_g and molar density ρ_g. This new correlation has been applied to the ISM EOS to predict the volumetric behavior of polymer melts including polypropylene (PP), poly(ethylene oxide) (PEO), polystyrene (PS), poly(vinyl methyl ether) (PVME), and polycarbonate bisphenol-A (PC) at compressed states. The operating temperature range is from 311.5 to 603.4 K and pressures up to 200.0 MPa. Other two-temperature-dependent parameters α(T) and b(T) appearing in the ISM EOS, are calculated by scaling rules. It was found that the calculated volumes agree well with the experimental values. A collection of 421 data points has been examined for the aforementioned polymers. The average absolute deviation between the calculated densities and the experimental densities is of the order of 0.6%. The newly obtained correlation has been further assessed through a detailed comparison against previous correlations proposed by other researchers.     

Multispectroscopic studies of the interaction of calf thymus DNA with the anti-viral drug, valacyclovir

The present study investigated the binding interaction between an antiviral drug, valacyclovir and calf thymus DNA (CT-DNA) using emission, absorption, circular dichroism, viscosity and DNA melting studies. In fluorimetric studies, thermodynamic enhancement constant (K(D)) and bimolecular enhancement constant (K(B)) were calculated at different temperatures and demonstrated that fluorescence enhancement is not initiated by a dynamic process, but instead by a static process that involves complex DNA formation in the ground state. Further, the enthalpy and entropy of the reaction between the drug and CT-DNA showed that the reaction is exothermic and enthalpy-favored. In addition, detectable changes in the circular dichroism spectrum of CT-DNA in the presence of valacyclovir indicated conformational changes in the DNA double helix following interaction with the drug. All these results prove that this antiviral drug interacts with CT-DNA via an intercalative mode of binding.     

Highly Efficient Etherification and Oxidation of Aromatic Alcohols Using Supported and Unsupported Phosphorus Pentoxide as a Heterogeneous Reagent

A highly efficient procedure for etherification and oxidation of aromatic alcohol is described using unsupported and supported P₂O₅ on alumina and/or silica gel. The silica gel and alumina proved to be the most suitable support among the supports examined in our experiments. It was illustrated that the etherification and oxidative performance in reactions depend largely upon variables including reaction temperature, the nature of the P₂O₅ used (supported or unsupported P₂O₅), and whether solvent-free conditions are applied. It was shown that P₂O₅ not only can convert the aromatic alcohols into corresponding ethers and/or aldehyde and ketone but also can convert aromatic ethers into aldehyde or ketone via oxidative cleavage. Finally, quantum mechanical calculations were performed to rationalized these events, and it was indicated that aldehyde and ketone are more favorable products on the basis of the heat of formation (ΔH_f).

Some Cohen–Macaulay and Unmixed Binomial Edge Ideals

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some classes of graphs. We compute the depth of the binomial edge ideal of a generalized block graph. We also characterize all generalized block graphs whose binomial edge ideals are Cohen–Macaulay and unmixed. So that we generalize the results of Ene, Herzog, and Hibi on block graphs. Moreover, we study unmixedness and Cohen–Macaulayness of the binomial edge ideal of some graph products such as the join and corona of two graphs with respect to the original graphs.     

Energy of unitary Cayley graphs and gcd-graphs

This work is based on ideas of Ili? [A. Ili?, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881-1889] on the energy of unitary Cayley graph. For a finite commutative ring R with unity , the unitary Cayley graph of R is the Cayley graph whose vertex set is R and the edge set is {{a,b}:a,b∈Randa-b∈R^×}, where R^× is the group of units of R. We study the eigenvalues of the unitary Cayley graph of a finite commutative ring and some gcd-graphs and compute their energy. Moreover, we obtain the energy for the complement of unitary Cayley graphs.