A comparison study between sodium dodecyl sulfate and sodium dodecyl sulfonate with respect to the thermodynamic properties,micellization, and interaction with poly(ethylene glycol) in aqueous solutions

The density, sound velocity, and conductivity measurements were performed on aqueous solutions of sodium dodecyl sulfate (C₁₂H₂₅SO₄Na) or sodium dodecyl sulfonate (C₁₂H₂₅SO₃Na) in the absence and presence of poly(ethylene glycol) (PEG) at different temperatures. Changes in the apparent molar volumes and isentropic compressibilities upon micellization were derived using a pseudophase-transition approach and the infinite dilution apparent molar properties of the monomer and micellar form of C₁₂H₂₅SO₄Na and C₁₂H₂₅SO₃Na were determined. Variations of the critical micelle concentrations (CMCs) of both surfactants in the solutions investigated with temperature were obtained from which thermodynamic parameters of micellization were estimated. It was found that at low temperature the micelle formation process is endothermic and therefore, this process must be entropically driven. However, upon increasing the temperature, the enthalpic factor becomes more significant and, at temperatures higher than 303.15 K the micellization is enthalpy driven. The interactions between C₁₂H₂₅SO₄Na/C₁₂H₂₅SO₃Na and PEG were studied and it was found that sodium alkyl sulfonates were seen to interact more weakly than their sulfate analogues.     

Superalgebras for three interacting particles in an external magnetic field

In this paper we discuss interacting particles in an external magnetic field. By comparing the Schr?dinger equation of three interacting particles with the associated Laguerre differential equation, we obtain the energy spectrum which corresponds to indices n_i and m_i. Finally by using the so called factorization method we obtain the raising and lowering operators. These operators are supersymmetric structures related to the Hamiltonian partner. Also these operators lead to the realization of Heisenberg Lie superalgebras with two, four and six supercharges.     

From inflation to acceleration,with phantom and canonical scalar fields in non-flat universe

Motivated by the recent work of Elizalde et al. [E. Elizalde, S. Nojiri, S.D. Odintsov, D. Saez–Gomez, V. Faraoni, Phys. Rev. D 77 (2008) 106005], we generalize their work to the non-flat case. We consider a universe filled with matter and show that it is possible to obtain both inflation and accelerated expansion at late times by using a single scalar field. Realistic examples are worked out in order to illustrate this fact. Then we extend the problem to the interacting case.     

A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula

Acta Mathematica Sinica, English Series - In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and...     

Copper/Graphene/Clay Nanohybrid: A Highly Efficient Heterogeneous Nanocatalyst for the Synthesis of Novel 1,2,3‐Triazolyl Carboacyclic Nucleosides via ‘Click’ Huisgen 1,3‐Dipolar Cycloaddition

A very mild and highly efficient synthesis of some novel 1H‐1,2,3‐triazolyl carboacyclic nucleosides via a ‘Click’ Huisgen cycloaddition of N‐propargyl nucleobases and azido alcohols using Cu/aminoclay/reduced graphene oxide nanohybrid (Cu/AC/r‐GO nanohybrid) as nanocatalyst is described. The preparation and characterization of Cu/AC/r‐GO nanohybrid are discussed. This catalyst was characterized by X‐ray diffraction, FT‐IR, TEM, and energy‐dispersive analysis of X‐ray techniques. Cu/AC/r‐GO nanohybrid is a stable and highly efficient heterogeneous nanocatalyst that can be easily prepared, used, and restored from the reaction mixture by simple filtration, and reused for many consecutive trials without significant decrease in activity.     

A New Trinuclear Zn(II) Complex {[Zn(μ-ONN)(μ<Subscript>2</Subscript>-O)(μ-OO)]<Subscript>2</Subscript>Zn}: Synthesis,Characterization, Thermal Decomposition and Antibacterial Activity

New centrosymmetric trinuclear zinc(II) complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} has been synthesized by the reaction of a potentially ONN tridentate Schiff base ligand, and N,N-dimethylethylendiamin, with Zn(OAc)₂·2H₂O in methanol, in the refluxed conditions and characterized by elemental analysis, FT-IR and UV–Vis spectroscopy. Single crystal X-ray structure analysis reveals a trinuclear complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} with zinc(II) ions connected by three different bridges, (μ-ONN) of the Schiff base ligand, μ₂-O and μ-OO of the acetate. The complex is centrosymmetric, with one of the Zn atoms located at the inversion center. While the central Zn(II) ion is six-coordinated, the coordination number of the other Zn(II) ions is five. Finally, the {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} complex was thermally decomposed in air at 700 °C resulted in ZnO nano crystalites with the average size of 42 nm. The antibacterial activity of ligand and its zinc(II) complex were tested against gram-positive and gram-negative bacteria. The ligand showed higher activity than its zinc(II) complex.     

Cofiniteness and finiteness of local cohomology modules over regular local rings

Let (R,m) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss _R (R/I) = Assh _R (_I). It is shown that the R- module H^ht(I) _I (R) is I-cofinite if and only if cd(I,R) = ht(I). Also we present a sufficient condition under which this condition the R-module H ⁱ _I (R) is finitely generated if and only if it vanishes.