Synthesis of highly branched perfluoroethers by direct fluorination,promising new materials based on the hexafluoroacetone–ethylene copolymer

Direct fluorination of the hexafluoroacetone-ethylene copolymer, [CH₂CH₂OC(CF₃)₂]_n, under conditions designed to promote fragmentation of the polymer chain has led to the synthesis of a number of structurally unusual branched perfluoropolyethers [? CF₂? CF₂? O-C(CF₃)₂? ]_n. These new perfluoropolyethers have been characterized by ¹⁹F-NMR, and their physical properties are reported. Direct fluorination under milder conditions yields a high-molecular-weight perfluoropolyether.     

The investigation of soliton solutions and conservation laws to the coupled generalized Schrödinger–Boussinesq system

This paper employed the principle of undetermined coefficients and Bernoulli sub-ODE methods to acquire the topological, non-topological, periodic wave and algebraic solutions of the coupled generalized Schrödinger–Boussinesq system (CGSBs). The concept of Lie point symmetry is applied to derive the point symmetries of the CSGE. The problem on nonlinear self-adjointness of the CSGE has not been solved in previous time. In the present paper, we solve this problem and find an explicit form of the differential substitution providing the nonlinear self-adjointness. Then we use this fact to construct a set of conserved vectors using the classical symmetries admitted by the equation and the general conservation laws (Cls) theorem presented by Ibragimov. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.     

A uniqueness criterion for fractional differential equations with Caputo derivative

We investigate the uniqueness of solutions to an initial value problem associated with a nonlinear fractional differential equation of order α∈(0,1). The differential operator is of Caputo type whereas the nonlinearity cannot be expressed as a Lipschitz function. Instead, the Riemann–Liouville derivative of this nonlinearity verifies a special inequality.     

Hydrodynamic models for heavy-ion collisions and beyond

A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the “mixed phase”. A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies ≈ 40 A GeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.     

A simple method for desymmetrizing 1,1′-ferrocenedicarboxaldehyde

A simple chromatography-free method for desymmetrizing ferrocene is described starting from the readily available dialdehyde. Oxidation of 1,1′-ferrocenedicarboxaldehyde in a water/acetonitrile mixture with KMnO₄ produced 1′-formyl-ferrocenecarboxylic acid. The same reaction carried out in a water/acetone mixture produced 1′-[(E)-3-oxo-but-1-enyl]-ferrocenecarboxylic acid.     

Multiple summability properties for Cohen ‐summing operators

We prove that Cohen p‐summing operators satisfy multiple summability properties. Some of these multiple summability properties are new even in the linear case. For example, we prove that the multilinear functional associated to a Cohen p‐summing n‐linear operator is multiple ‐summing.     

Analysis of the Effect of Potential Cycles on the Reflective Infrared Signals of Nitro Groups in Nanofilms: Application of the Fractional Moments Statistics

The effect of the potential cycles on the reflective IR signals of nitro‐groups in nanofilms was studied for the statistical characterization of nitrobenzene (NB) and nitroazobenzene (NAB)‐modified glassy carbon (GC) surfaces. Both NB and NAB nanofilms were obtained by the electrochemical reduction of the diazonium tetrafluoroborate salts in acetonitrile using cyclic voltammetry (CV). The modified surfaces were denoted as GC‐(NB)_n and GC‐(NAB)_n, respectively, where n indicates the number of CV cycles performed during modification. Reflective IR signals of the normalized NB and NAB nanofilms and GC were used for the quantitative evaluation of the effect of the potential cycles on the reflective IR signals of nitro‐groups in nanofilms. The detection and quantitative ‘reading’ of the influence of number of CV cycles were realized in the frame of a new error controllable approach that was applied for analysis of all available set of data. This approach includes in itself the following basic steps: (a) the procedure of the division (normalization) on the GC spectra, (b) the comparison of the smoothed spectra for their statistical proximity in the frame of the statistics of the fractional moments, (c) extraction of possible calibration parameters for possible calibration of the normalized spectra with respect to the number of CV cycles. These three basic steps are becoming effective for detection of the influence of some external factors. In our case it is important to detect the influence of the factor n characterizing CV cycles.