Numerical solution of the one phase 1D fractional Stefan problem using the front fixing method

In this paper, we present a novel numerical scheme to solve a 1D, one‐phase extended Stefan problem with fractional Caputo derivative with respect to time. The proposed method is based on a suitable choice of the new space coordinate for the subdiffusion equation and extends the front‐fixing method to the subdiffusion case. In the final part, examples of numerical results are discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Interval versions of Milne’s multistep methods

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski–Durbin–Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented.     

Lagrangean and Hamiltonian fractional sequential mechanics

The models described by fractional order derivatives of Riemann-Liouville type in sequential form are discussed in Lagrangean and Hamiltonian formalism. The Euler-Lagrange equations are derived using the minimum action principle. Then the methods of generalized mechanics are applied to obtain the Hamilton’s equations. As an example free motion in fractional picture is studied. The respective fractional differential equations are explicitly solved and it is shown that the limitα→1⁺ recovers classical model with linear trajectories and constant velocity. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Environmental Effects in Computational Spectroscopy: Accuracy and Interpretation

Spectroscopic techniques are valuable tools for understanding the structure and dynamics of complex systems, such as biomolecules or nanomaterials. Most of the current research is devoted to the development of new experimental techniques for improving the intrinsic resolution of different spectra. However, the subtle interplay of several different effects acting at different length and time scales still makes the interpretation and analysis of such spectra a very difficult task. In this respect, computational spectroscopy is becoming a needful and versatile tool for the assignment and interpretation of experimental spectra. It is in fact possible nowadays to model with relatively high accuracy the physical–chemical properties of complex molecules in different environments, and to link spectroscopic evidence directly to the structural and dynamical properties of optically or magnetically active solvated probes. In this Review, significant steps toward the simulation of entire spectra in condensed phases are presented together with some basic aspects of computational spectroscopy, which highlight how intramolecular and intermolecular degrees of freedom influence several spectroscopic parameters.     

Copolymers dispersions designed to shaping of ceramic materials

Journal of Thermal Analysis and Calorimetry - To study the effect of ionic liquids (ILs) of the microstructure on the surface of the coal, four ILs ([Emim][BF4], [Bmim][BF4], [Bmim][NO3], and...     

Alkali metal cation complexation by 1,3-alternate,mono-ionisable calix[4]arene-benzocrown-6 compounds

Alkali metal cation extraction behaviour for two series of 1,3-alternate, mono-ionisable calix[4]arene-benzocrown-6 compounds is examined. In Series 1, the proton-ionisable group (PIG) is a substituent on the benzo group of the polyether ring that directs it away from the crown ether cavity. In Series 2, the PIG is attached to one para position in the calixarene framework, thereby positioning it over the crown ether ring. Competitive solvent extraction of alkali metal cations from aqueous solutions into chloroform shows high Cs⁺ efficiency and selectivity. Single-species extraction pH profiles of Cs⁺ for Series 1 and 2 ligands with the same PIG are very similar. Thus, association of Cs⁺ with the calixcrown ring is more important than the position of the PIG relative to the crown ether cavity. Solid-state structures of two unionised ligands from Series 2 are presented. Also described is a crystal containing two different ionised ligand–Cs⁺ complexes.     

Characteristics of glucose electrode with enzyme immobilised on nylon net

Glucose oxidase was immobilised on nylon net by the method of O-alkylation using dimethyl sulfate and lysine as a spacer. The influence of alkylation conditions on the characteristics of the resulting glucose electrode was evaluated. The best electrode was then tested under batch and flow conditions, respectively. The influence of pH and temperature on electrode response were examined. The glucose oxidase immobilised on nylon net seemed to be inhibited by glucose in alkaline pH and at higher temperatures. Moreover, the shape of the electrode signal after addition of glucose was unusual. Glucose oxidase immobilised on nylon net was unstable and lost its activity rather quickly, especially when stored dry in the refrigerator. Also the operational stability of the electrode in the flow system was rather poor.     

Non-equivalent water molecules in [Ni(H2O)6](ClO4)2 and in [Ni(D2O)6](ClO4)2 in the thermogravimetric investigations

The thermal decomposition of [Ni(H₂O)₆](ClO₄)₂ and [Ni(D₂O)₆](ClO₄)₂ were studied by thermogravimetric analysis (TG) and simultaneous differential thermal analysis (SDTA) at a constant heating rate. The gaseous products of the decomposition were on-line identified by a quadrupole mass spectrometer (QMS). In both cases the process of decomposition starts at ca. 410 K and is connected with removal of water molecules in a stepwise way; at the beginning the first water molecule is lost, then the second and at higher temperature the third one. The rest of the water molecules are lost in the temperature region of ClO₄⁻ decomposition. The energy of activation of the process was calculated in both cases.     

DSC study of linolenic acid autoxidation inhibited by BHT,dehydrozingerone and olivetol

Non-isothermal oxidation of linolenic acid (LNA) in bulk phase was monitored by differential scanning calorimetry. The kinetic parameters E _a, Z and k (activation energies, pre-exponential factors, and rate constants, respectively) were calculated by Ozawa-Flynn-Wall method for the first detectable exothermic effect of uninhibited LNA oxidation. The kinetic parameters were also calculated for LNA oxidation inhibited by 2,6-di-tert-butyl-4-methylphenol (BHT), and two natural compounds, 1,3-dihydroxy-5-pentylbenzene (olivetol), and 4-(4’-hydroxy-3’-methoxyphenyl)-3-buten-2-one (DHZ, dehydrozingerone) at various concentrations. For oxidation processes at 25, 90 and 180°C the plots of logk values vs. concentration of phenolic compounds indicated that optimal concentration of inhibitor determined for one particular temperature cannot be extrapolated to other temperatures.     

Tungsten electrode for urea

Tungsten electrodes for urea were prepared via covalent linking of urease on oxidized metal surfaces in different ways. The most stable electrodes were obtained when tungsten was silanized and activated by glutaraldehyde or hexamethylene diisocyanate. The electrode with urease coupled via glutaraldehyde was tested for optimum conditions of use. The nature of the buffer and its concentration and ionic strength are particularly important.