The variational iteration method for solving the Volterra integro-differential forms of the Lane–Emden equations of the first and the second kind

In this paper, we establish the Volterra integro-differential forms of the Lane–Emden equations. We use the variational iteration method (VIM) to effectively treat these forms. The Volterra integro-differential forms of the Lane–Emden equations overcome the singular behavior at the origin $x=0$ and do not use a variety of Lagrange multipliers. Several numerical examples are examined to show the validity of the integro-differential forms.     

An efficient method for solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions and error estimate

In this paper, we propose an efficient method for solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions. The target is to obtain approximations of coupled Lane–Emden boundary value problems via series representation. Convergence and an error estimate are presented. Finally, two BVPs are solved to illustrative high accuracy of our method. Furthermore, our algorithm is easy to implement.     

An effective modification of the Benedict–Webb–Rubin equation of state

A modification of the BWR equation of state is proposed, which is a simplified form of a previously proposed one. It applies to systems formed by hydrocarbons and related compounds, with particular attention to the critical conditions. The range of treatable compounds was extended to a value 0.9 of the acentric factor, corresponding to C₂₀ hydrocarbons. The critical compressibility factor Z_c was made independent of the acentric factor, for a more accurate prediction of pure-component properties (the previous equation did not give the same improvement). Mixing rules require one binary interaction constant for each component pair. Zero binary constants can be used for methane–alkane and alkane–alkane pairs. Examples of applications to pure hydrocarbons and their mixtures are given.     

The importance of Colle–Salvetti for computational density functional theory

The purpose of this presentation is to show the importance of the Colle–Salvetti (Theor Chim Acta 37:329, 1975) paper in the development of modern computational density functional theory. To do this we cover the following topics (1) the Bright Wilson understanding (2) the Kohn–Sham equations (3) local density exchange (4) the exchange-hole (5) generalised gradient approximation for exchange (Becke and Cohen) (6) left–right correlation and dynamic correlation (7) the development of the Lee–Yang–Parr dynamic correlation functional from the Colle–Salvetti paper (8) the early success of GGA DFT. Finally we observe that the the BLYP and OLYP exchange-correlation functionals are not semi-empirical; this may explain their great success.     

Position-dependent effective mass Schrödinger equations for PT-symmetric potentials

We use the method of point canonical transformations and choose the Rosen-Morse-type potential as the reference potential to study exact solutions of the position-dependent effective mass Schr?dinger equations. Choosing three position-dependent mass distributions, we construct seven exactly solvable target potentials with PT symmetry. The energy spectra of the bound states and corresponding wavefunctions for the PT-symmetric potentials are given in the exact closed forms. We also discuss the isospectrality of different Schr?dinger equations with the same mass distribution or different mass distributions for different PT-symmetric potentials.      

Discovery of a small-molecule inhibitor of Dvl–CXXC5 interaction by computational approaches

The Wnt/β-catenin signaling pathway plays a significant role in the control of osteoblastogenesis and bone formation. CXXC finger protein 5 (CXXC5) has been recently identified as a negative feedback regulator of osteoblast differentiation through a specific interaction with Dishevelled (Dvl) protein. It was reported that targeting the Dvl–CXXC5 interaction could be a novel anabolic therapeutic target for osteoporosis. In this study, complex structure of Dvl PDZ domain and CXXC5 peptide was simulated with molecular dynamics (MD). Based on the structural analysis of binding modes of MD-simulated Dvl PDZ domain with CXXC5 peptide and crystal Dvl PDZ domain with synthetic peptide–ligands, we generated two different pharmacophore models and applied pharmacophore-based virtual screening to discover potent inhibitors of the Dvl–CXXC5 interaction for the anabolic therapy of osteoporosis. Analysis of 16 compounds selected by means of a virtual screening protocol yielded four compounds that effectively disrupted the Dvl–CXXC5 interaction in the fluorescence polarization assay. Potential compounds were validated by fluorescence spectroscopy and nuclear magnetic resonance. We successfully identified a highly potent inhibitor, BMD4722, which directly binds to the Dvl PDZ domain and disrupts the Dvl–CXXC5 interaction. Overall, CXXC5–Dvl PDZ domain complex based pharmacophore combined with various traditional and simple computational methods is a promising approach for the development of modulators targeting the Dvl–CXXC5 interaction, and the potent inhibitor BMD4722 could serve as a starting point to discover or design more potent and specific the Dvl–CXXC5 interaction disruptors.     

Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method

In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the decomposition series solutions. The numerical results display that the Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.     

Multiple solutions of coupled-cluster doubles equations for the Pariser–Parr–Pople model of benzene

To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser–Parr–Pople model of cyclic polyenes, complete solutions to the CCD equations for the ¹A _1g ^- states of benzene are obtained by means of the homotopy method. By varying the value of the resonance integral ß from –5.0 to –0.5 eV, we cover the so-called weakly, moderately, and strongly correlated regimes of the model. For each value of ß, 230 CCD solutions are obtained. It turned out, however, that only for a few solutions a correspondence with some physical states can be established. It has also been demonstrated that, unlike for the standard methods of solving CCD equations, some of the multiple solutions to the CCD equations can be attained by means of the iterative process based on Pulay's direct inversion in the iterative subspace approach.     

Example of a technique for evaluation of interferences caused by complicated sample matrix elements in ICP–AES determination

An example of a useful and rapid procedure for the evaluation of interferences caused by complicated sample matrices in inductively coupled plasma atomic emission spectrometry (ICP–AES) is described. Using simple acid–base standards, all the elements investigated were determined separately in complicated matrices with satisfactory results. Multiple linear regression was used to calculate the linear correction coefficients for each matrix element analyzed. Good analytical results improved still further when this correction method was used.     

Development of a certified reference material for cachaça: an effective material for quality assurance

Cachaça is the typical and genuine denomination for the sugar cane beverage produced in Brazil. It has an alcoholic content between 38 and 48 % by volume, at 20 °C, and is obtained from the distillation of fermented sugar cane juice with the possible addition of up to 6 g/L of sugar, expressed by sucrose. This paper aims to outline the approach taken for the certification of the mass fraction of individual alcohols and their associated uncertainties in a cachaça certified reference material (CRM) produced by the Organic Analysis Laboratory of the Chemical Metrology Division of Inmetro. The requirements of ISO Guide 31, ISO Guide 34 and ISO Guide 35 were followed for the certification. This included the assessment of the degree of homogeneity of the material, the short-term stability study to determine the transport conditions, the long-term stability study to establish the shelf life and storage conditions of the CRM and the characterization process. The certified values were determined by two analytical techniques: gas chromatography coupled to mass spectrometry and gas chromatography with flame ionization detection. In order to support the routine testing of cachaça, in helping analytical laboratories validate and standardize their methods, the certified reference material (CRM 02.1/10.003b) was developed and certified for the mass fractions of methanol (9.18 mg/100 g ± 0.82 mg/100 g), 2-butanol (4.15 mg/100 g ± 0.40 mg/100 g), 1-butanol (1.30 mg/100 g ± 0.18 mg/100 g), isobutanol (24.0 mg/100 g ± 1.0 mg/100 g) and 1-propanol (29.4 mg/100 g ± 1.3 mg/100 g) in a spiked cachaça.     

Analytic solutions to a family of Lotka–Volterra related differential equations

An initial formal analysis of the analytic solution (C.M. Evans and G.L. Findley, J. Math. Chem. 25 (1999) 105–110.) to the Lotka–Volterra (LV) dynamical system is presented. A family of firstorder autonomous ordinary differential equations related to the LV system is derived, and the analytic solutions to these systems are given. Invariants for the latter systems are introduced, and a simple transformation which allows these systems to be reduced to Hamiltonian form is provided.     

Kinetics of fiber impregnation by a binder. Gradient generalization of Navier–Stokes–Darcy equations

A model of polymer composition material that is composed of a unidirectional fiber and binder has been considered. The space between two neighboring filaments of fibers is considered as a capillary along which the binder propagates during impregnation. In order to describe the flow process, a gradient generalization of the Navier–Stokes equation has been suggested. A corrected model of the flow of binder in the capillary-porous space of a unidirectional fiber material is developed on its basis. In particular cases, the found solution coincides with the Navier–Stokes–Darcy equations and conventional Navier–Stokes equation. The model that has been developed allows the refinement of the nonclassical effect of the existence of two boundary layers that appear during flow and may prevent it.     

Combination of computational methods,adsorption isotherms and selectivity tests for the conception of a mixed non-covalent–semi-covalent molecularly imprinted polymer of vanillin

A novel molecularly imprinted polymer (MIP) for vanillin was prepared by photo initiated polymerization in dichloromethane using a mixed semi-covalent and non-covalent imprinting strategy. Taking polymerisable syringaldehyde as “dummy” template, acrylamide was chosen as functional monomer on B3LYP/6-31+G(d,p) density functional theory computational method basis with counterpoise. The binding parameters for the recognition of vanillin on imprinted polymers were studied with three different isotherm models (Langmuir, bi-Langmuir and Langmuir–Freundlich) and compared. The results indicate an heterogeneity of binding sites. It was found and proved by DFT calculations that the specific binding of vanillin in the cavities is due to non-covalent interactions of the template with the hydroxyphenyl- and the amide-moieties. The binding geometry of vanillin in the MIP cavity was also modelled. The obtained MIP is highly specific for vanillin (with an imprinting factor of 7.4) and was successfully applied to the extraction of vanillin from vanilla pods, red wine spike with vanillin, natural and artificial vanilla sugar with a recovery of 80%.     

Development of an SdFFF–ETAAS hyphenated technique for dimensional and elemental characterization of colloids

Direct hyphenation of electrothermal atomic-absorption spectroscopy (ETAAS) to sedimentation field-flow fractionation (SdFFF) has been developed to enable elemental characterization of submicron particles as a function of size. This hyphenation is particularly suitable for characterizing colloidal particles of environmental interest, for example water-borne particles. The interface is an automatic capillary injection device (CID) which enables direct introduction of large and variable volumes of colloidal particle suspensions into a hot graphite furnace, thus preconcentrating the colloidal particles on the furnace walls. The method was validated by determination of Fe in certified submicron Fe₂O₃. The procedure was set up by first optimizing the SdFFF fractionation under programmed field conditions, thus enabling optimum fractionation of particle size. The ETAAS procedure was then tested to determine whether it could be used for direct analysis of Fe₂O₃ slurries without the need for a mineralization step. CID coupled to ETAAS was subsequently exploited for its ability to enhance the sensitivity, because of the increased injection volume. Statistical tests and data handling were conducted to prove the suitability of the ETAAS-CID module. Finally, off-line and on-line ETAAS-CID-SdFFF hyphenation were investigated. These experiments emphasized the advantages of the on-line coupling, because it enables synchronized sampling, enrichment, and elemental analysis of the flowing eluate. The benefits of the proposed hyphenation are the high specificity of analytical detection, increased sensitivity, reduction of analysis time, and minimum sample handling and contamination.      

Protein–protein recognition: a computational mutagenesis study of the MDM2–P53 complex

Protein P53 is involved in more than 50% of the human cancers and the P53–MDM2 complex is a target for anticancer drug design. It is possible to engineer small P53 mimics that would be expected to disrupt the P53–MDM2 complex, and release P53 to initiate cell-cycle arrest or apoptosis. These small peptides should bind to the functional epitopes of the protein–protein interface, and prevent the interaction between P53 and MDM2. Here, we apply an improved computational alanine scanning mutagenesis method, which allows the determination of the hot spots present in both monomers, P53 and MDM2, of three protein complexes (the P53-binding domain of human MDM2, its analogue from Xenopus laevis, and the structure of human MDM2 in complex with an optimized P53 peptide). The importance of the hydrogen bonds formed by the protein backbone has been neglected due to the difficulty of measuring experimentally their contribution to the binding free energy. In this study we present a computational approach that allows the estimation of the contribution to the binding free energy of the C=O and N–H groups in the backbone of the P53 and MDM2 proteins. We have noticed that the hydrogen bond between the HE1 atom of the hot spot Trp23 and the O atom of the residue Leu54, as well as the NH-pi hydrogen bond between the Ile57 and Met58 were observed in the Molecular dynamics simulation, and their contribution to the binding free energy measured. This study not only shows the reliability of the computational mutagenesis method to detect hot spots but also demonstrates an excellent correlation between the quantitative calculated binding free energy contribution of the C=O and N–H backbone groups of the interfacial residues and the qualitative values expected for this kind of interaction. The study also increases our understanding of the P53–MDM2 interaction.     

An effective lactic acid-modified Hβ zeolite for synthesis of bis(indolyl)methanes

Excellent activity and stability have been observed for a lactic acid-modified Hβ (LA-Hβ) zeolite in the synthesis of bis(indolyl)methanes by Friedel–Crafts alkylation of indole with aldehydes. It is proposed that lactic acid treatment is appropriate for dealumination of Hβ zeolite, and results in a LA-Hβ zeolite with greater surface area, fewer weak acid sites, and more moderately-strong acid sites, as confirmed by the Brunauer–Emmett–Teller method, inductively coupled plasma emission spectrometry, and temperature-programmed desorption of NH₃. Moreover, both electronic and steric effects of substituents on the aromatic ring of the aldehydes were found to be important in this reaction.     

Pre-ashing of biological samples — a sample preparation technique for solid sampling ZAAS

Summary A pre-ashing method by a conventional electrothermal furnace was used as a concentration technique for powdered biological samples in the solid sampling technique with GF-ZAAS. A relationship equation between the concentration factors and the concentrations of main inorganic components in biological samples has been established, and it has become possible to calculate the concentration factors, if the total concentration of K, Na, Mg and Ca, or total concentration of K and Mg, or the concentration of K only are known. The proposed method has been successfully applied to the direct determination of Co, Ni, Mn and Pb at the g/kg levels in biological samples.Presented at the 5th International Colloquium on Solid Sampling, with Atomic Spectroscopy, May 18–20, 1992; Geel, Belgium. Papers edited by R.F.M. Herber, Amsterdam