Optimal timing of regime switching in optimal growth models: A Sobolev space approach

This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. We derive the appropriate necessary conditions for such problems by means of standard techniques from the calculus of variations and some basic properties of Sobolev spaces.     

Influence of the pore size of reversed phase materials on peptide purification processes

The influence of the pore size of a chromatographic reversed phase material on the adsorption equilibria and diffusion of two industrially relevant peptides (i.e. a small synthetic peptide and insulin) has been studied using seven different reversed phase HPLC materials having pore sizes ranging from 90 Å to 300 Å. The stationary phase pore size distribution was obtained by inverse size exclusion measurement (iSEC). The effect of the pore size on the mass transfer properties of the materials was evaluated from Van Deemter experiments. It has been shown that the lumped mass transfer coefficient increases linearly with the average pore size. The Henry coefficient and the impurity selectivity were determined in diluted conditions. The saturation capacity of the main peptides was determined in overloaded conditions using the inverse method (i.e. peak fitting). It was shown that the adsorption equilibria of the peptides on the seven materials is well described by a surface-specific adsorption isotherm. Based on this a lumped kinetic model has been developed to model the elution profile of the two peptides in overloaded conditions and to simulate the purification of the peptide from its crude mixture. It has been found that the separation of insulin from its main impurity (i.e. desamido-insulin) was not affected by the pore size. On the other hand, in the case of the synthetic peptide, it was found that the adsorption of the most significant impurity decreases with the pore size. This decrease is probably due to an increase in silanol activity with decreasing pore size.     

Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation

This paper focuses on the Logarithmic High Dimensional Model Representation (Logarithmic HDMR) method which is a divide–and–conquer algorithm developed for multivariate function representation in terms of less-variate functions to reduce both the mathematical and the computational complexities. The main purpose of this work is to bypass the evaluation of N–tuple integrations appearing in Logarithmic HDMR by using the features of a new theorem named as Fluctuationlessness Approximation Theorem. This theorem can be used to evaluate the complicated integral structures of any scientific problem whose values can not be easily obtained analytically and it brings an approximation to the values of these integrals with the help of the matrix representation of functions. The Fluctuation Free Multivariate Integration Based Logarithmic HDMR method gives us the ability of reducing the complexity of the scientific problems of chemistry, physics, mathematics and engineering. A number of numerical implementations are also given at the end of the paper to show the performance of this new method.     

Quantitative mineralogical properties (morphology-chemistry-structure) of pharmaceutical grade kaolinites and recommendations to regulatory agencies

The physical and chemical characteristics of kaolinite (kaolin) may be variable, and minor amounts of other clay minerals, nonclay minerals, and other impurities may affect the properties of kaolinites. Thus specific technical properties of pharmaceutical grade kaolinites become very important because these clays are used in medical applications, e.g., as pharmaceutical excipients, and will be consumed by humans. Seven pharmaceutical grade kaolinite specimens were used in this study: K1004, KA105, 2242-01, K2-500, Acros, Acros-mono, and KX0007-1. In addition, two kaolinites from the Clay Minerals Society Source Clays, KGa-1b and KGa-2, were used for comparison purposes. The Acros-mono and 2242-01 kaolinites contained minor amounts of illite, which was demonstrated both compositionally and structurally by using inductively coupled plasma spectroscopy and powder X-ray diffraction. The KX0007-1 kaolinite powder was found to be heavily contaminated with quartz, cristobalite, and alunite. Crystal structure computations also showed excess Si in its tetrahedral site, and the mineral no longer has the typical kaolinite crystal structure. These widely-used industrial standards should be quantitatively characterized morphologically, compositionally, and structurally. Results of the mineralogical characteristics should be clearly labeled on the pharmaceutical grade kaolinites and reported to the relevant regulatory agencies.     

Microphase Separation of Phenylene Oligomers with Polymeric Side Chains: A Dissipative Particle Dynamics Study

The microphase‐separated morphologies of p‐phenylene oligomers with POx, PCL, PS, and PEO side chains are studied using DPD simulations. It is shown that the microphase‐separated morphologies depend significantly on the degree of chemical incompatibility between the components as indicated by the Flory‐Huggins interaction parameters. The good agreement of the microphase separated morphologies as simulated by DPD with the experimentally determined thin film morphologies suggests that DPD can produce convincing morphological information at the nanoscale. The results show that grafting of polymeric side chains can be an important tool to control the morphology of polymers with a rigid backbone.

     

An Infinitesimal Deformation Approach to the Crystallographic Theory of the Martensite Phase Transformation: Application to Au-Cd,Fe-Ni AND In-Tl Alloys

Using the infinitesimal deformation approach, a crystallographic analysis of the austenite-martensite transformation from the cubic to orthorhombic phase - which predicts crystallographic parameters such as habit plane, orientation relationship between austenite and martensite, rotation matrix and total shape deformation matrix - is derived from a knowledge of the crystal structures of the initial and final phase only. The numerical values coming from orientation relationships obtained for Au-47.5 Cd Fe-Ni and In--Tl alloys are compared with predictions of the phenomenological crystallographic theory, infinitesimal deformation approach and experimental data.     

A novel method for quantification of ethanol and methanol in distilled alcoholic beverages using Raman spectroscopy

In this study, direct quantification of ethanol and methanol in distilled alcoholic beverages using Raman spectroscopy was performed. Raman spectra of varying ethanol–methanol mixtures were obtained, baseline corrections were made, and the data were normalized using Raman scattering intensity of an internal standard (acetonitrile, 921 cm^–1). Then, calibration graphs were produced for ethanol and methanol concentrations in the ranges of 0–7 M and 0–10 M, respectively. Accurate R² values of the calibration graphs proved the notable linear correlations (0.998 for ethanol and 0.998 for methanol). The method was validated based on linearity, sensitivity, intraday and interday repeatability, and recovery tests. The limit of detection and limit of quantification values of the validated method were determined for ethanol concentration as 1.2 and 3.7 mM, and for methanol concentration as 3.4 and 10.3 mM, respectively. The ability of the developed method to detect ethanol and methanol concentrations in real samples was also investigated. The results of the developed method were compared with the experimental results from traditional method and high correlation value (R² = 0.926) was obtained. Besides being sensitive and cheap, the developed method is rapid with the analysis time of less than 30 s. Furthermore, it eliminates labor‐consuming operations, chromatographic separation, and measurement error due to the high number of experiment steps in the standard method. Copyright © 2012 John Wiley & Sons, Ltd.     

Noncovalently galactose imprinted polymer for the recognition of different saccharides

Molecularly imprinted polymers (MIPs) represent a new class of materials possessing high selectivity and affinity for the target molecule. The main goal of this study was to prepare a galactose imprinted polymer and its potential application for the recognition of different saccharides. The selectivity of galactose imprinted polymer for several saccharides; glucose, mannose, fructose, maltose, lactose, sucrose and raffinose was investigated. Macroporous polymer was prepared utilizing ethyleneglycoldimethacrylate as a crosslinking agent, in the presence of galactose as a template molecule with acrylamide as a functional monomer. After the synthesis of polymer, galactose was removed by methanol:acetic acid washing. The selectivity of galactose imprinted polymer for other saccharides was utilized by batch rebinding assay. The arrangement of functional groups within cavities versus shape selectivity is discussed. The results showed that, the orientation of the functional groups was the dominating factor for the selectivity of galactose imprinted polymer. The dissociation constants of polymer were determined by Scatchard analysis.     

Exact Solutions for Fractional Differential-Difference Equations by (G′/G)-Expansion Method with Modified Riemann-Liouville Derivative

In this paper, the ($G′/G$)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.