Sonocatalytic epoxidation of alkenes by vanadium-containing polyphosphomolybdate immobilized on multi-wall carbon nanotubes

A Keggin type polyoxometalate (POM) has been immobilized in the unique network structure of multi-wall carbon nanotubes (CNTs). The vanadium-containing polyphosphomolybdate (PVMo) supported on CNTs, which was prepared by a one-step solid-state reaction, was characterized by FT-IR, XRD, SEM and elemental analyses. These uniform nanoparticles have an average size 20–30 nm. Furthermore, due to the chemical interaction between PVMo and carboxylic acid groups, PVMo nanoparticles were successfully immobilized on the CNTs. Moreover, the obtained composite was found as an efficient catalyst for oxidation of hydrocarbons under reflux and ultrasonic irradiation (US) conditions.     

Factorization Method and Special Orthogonal Functions

We present a general construction for ladder operators for the special orthogonal functions based on Nikiforov-Uvarov mathematical formalism. A list of creation and annihilation operators are provided for the well known special functions. Furthermore, we establish the dynamic group associated with these operators.     

On Dynamics of Brans–Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans–Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans–Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann–Robertson–Walker cosmological models.     

On differential modular forms and some analytic relations between Eisenstein series

In the present article we define the algebra of differential modular forms and we prove that it is generated by Eisenstein series of weight 2, 4 and 6. We define Hecke operators on them, find some analytic relations between these Eisenstein series and obtain them in a natural way as coefficients of a family of elliptic curves. The fact that a complex manifold over the moduli of polarized Hodge structures in the case h ¹⁰=h ⁰¹=1 has an algebraic structure with an action of an algebraic group plays a basic role in all of the proofs.      

The loop product for 3-manifolds

Let M be a connected, closed, oriented and smooth manifold of dimension d. Let LM be the space of loops in M. Chas and Sullivan introduced the loop product, an associative product of degree ?d on the homology of LM. In this Note we aim at identifying 3-manifolds with “non-trivial” loop products. To cite this article: H. Abbaspour, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

QUASI-PERMUTATION REPRESENTATIONS OF ALTERNATING AND SYMMETRIC GROUPS

The quantities c(G), q(G) and p(G) for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c(G) = q(G)=p(G) = n, when G = An or Sn.     

Determination of accurate surface tensions of maleimide copolymers containing fluorinated side chain from contact angle measurements

Surface energetics of two fluorinated maleimide copolymers containing fluorinated side chain, i.e., poly(ethene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ETMF) and poly(octadecene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ODMF), are studied by contact angle measurements with 10 liquids consisting of fairly bulky molecules. Because of the inertness of octamethylcyclotetrasiloxane (OMCTS) and decamethylcyclopentasiloxane (DMCPS) molecules, their contact angles are used to determine the surface tension of the two polymers. It is found that other liquids show specific interactions with the ETMF films, and their contact angles deviate from a smooth curve that represents the surface tension of ETMF, i.e., 11.00 mJ/m². On ODMF surfaces, only OMCTS and DMCPS yield useful contact angles. Other liquids either dissolve the polymer film or show a slip-stick pattern. This finding is discussed in terms of interactions between segments of the polymer chains and the test liquids. OMCTS and DMCPS are suggested as the appropriate probe liquids, meeting specific criteria necessary for the determination of accurate surface tension of fluoropolymers.     

An algorithm and upper bounds for the weighted maximal planar graph problem

In this paper, we investigate the weighted maximal planar graph (WMPG) problem. Given a complete, edge-weighted, simple graph, the WMPG problem involves finding a subgraph with the highest sum of edge weights that is maximal planar, namely, it can be embedded in the plane without any of its edges intersecting, and no additional edge can be added to the subgraph without violating its planarity. We present a new integer linear programming (ILP) model for this problem. We then develop a cutting-plane algorithm to solve the WMPG problem based on the proposed ILP model. This algorithm enables the problem to be solved more efficiently than previously reported algorithms. New upper bounds are also provided, which are useful in evaluating the quality of heuristic solutions or in generating initial solutions for meta-heuristics. Computational results are reported for a set of 417 test instances of size varying from 6 to 100 nodes including 105 instances from the literature and 312 randomly generated instances. The computational results indicate that instances with up to 24 nodes can be solved optimally in reasonable computational time and the new upper bounds for larger instances significantly improve existing upper bounds.     

Coupled cluster,MP2, and DFT study of structures,stabilities, vibrations,and bonding properties of XXeOH (X = F,Cl, Br,and I)

The optimized geometries, molecular properties, and stabilities of new noble gas molecules, XXeOH (X = F, Cl, Br, and I), were studied using CCSD, MP2, CAM-B3LYP, and WB97XD methods and large basis sets. All XXeOH molecules showed equilibrium structures with Cs symmetry. The results also showed that some bonds in XXeOH could be presented as a typical ionic bond. An alteration in ion-pair character was observed for IXeOH, showing two OH ^? and IXe ⁺ parts, while in other molecules, they could be presented as XeOH ⁺ and X ^? . Two decomposition routes were proposed for these molecules that showed high exothermic reactions. However, despite their low thermodynamic stabilities, their decomposition rate constants were small and all molecules (except BrXeOH) had high kinetic stabilities, indicating the possibility for identification and characterization of these molecules. However, in addition to the calculation of their vibrational frequencies, NBO atomic charges, and hybridizations, the bonding properties of XXeOH molecules were studied by AIM calculations (to calculate electron densities, bond elipticities, and Laplacian of electron densities) and second-order intramolecular perturbation energies using NBO calculations. Moreover, the ease of formations and relative stabilities of XXeOH molecules were compared using heats of formations, Gibbs free energies of formations and isodesmic reactions. These calculations showed that the stability of XXeOH molecules was decreased from F to I.