Representations of Clifford Algebras on Function Spaces on the Cantor Set

We give a representation of the (infinite-dimensional) complex Clifford algebra on the Hilbert space of square-integrable complexvalued functions on the Cantor set.     

An analysis of the fourth‐order PDEs – ‘patterns’ and ‘di‐block polymers’

We analyze some fourth‐order partial differential equations that model the ‘propagation of hexagonal patterns’ and the ‘microphase separation of di‐block copolymers’. The underlying invariance properties and conservation laws of the models and related partial differential equations are studied. Copyright © 2017 John Wiley & Sons, Ltd.     

Separation and identification of different therapeutic pharmaceutical drugs on humic acid-based HPLC column: Method optimization using central composite design

Multimode chromatographic separations are highly desirable in pharmaceutical and environmental sciences. Current study deals with the application of newly developed mixed-mode end capped-immobilized humic acid onto an aminopropyl silica based chromatographic column for separation and identification of six drugs belonging to different therapeutic groups for its applicability in pharmaceutical industries. For this, central composite design was used to evaluate the separation and resolution by optimization of three most effective parameters (acetonitrile%, flow rate, and pH of mobile phase). Second-order quadratic model was used to evaluate their effect on resolution of peaks; the probability value (<0.05) obtained from analysis of variance suggested the best applicability of the model. Desirability function was applied to calculate optimum conditions (44.8% acetonitrile, 1.75 mL/min of flow rate, and 7.5 pH) required to achieve maximum separation with good resolution within 11 min. The method was validated for linearity, precision accuracy, selectivity, and sensitivity. The results revealed a highly precise (coefficient of variance > 1%), linear (R² = 0.99), and highly selective method. Moreover, the limit of detection/quantification values revealed acceptable sensitivity of the method. The developed column was compared for its efficiency with a commercially available column and found to be highly applicable for industrial applications.     

High performance capillary electrophoresis method for determination of ibuprofen enantiomers in human serum and urine

A direct and stereospecific capillary zone electrophoresis (CZE) method for quantification ibuprofen enantiomers in biological matrices: human serum and urine, has been developed. Chiral separation of the enantiomers of ibuprofen and (+)-S-indobufen [(+)-S-INDB, internal standard, IS] was obtained in an uncoated silica capillary filled with a background electrolyte (BGE), consisted of heptakis 2,3,6-tri-O-methyl-β-cyclodextrin (TM-β-CD) in buffer of pH 5.0. The complete enantioselective analysis of ibuprofen and its 1-hydroxy metabolite confirmed appropriate specificity of the method. The electrophoretic parameters: electroosmotic (μ_EOF) and electrophoretic (μ_ep) mobility and resolution factor (R_s) were determined. Extraction procedures with organic solvent and solid phase extraction (SPE) with C₁₈ stationary phase for isolation of enantiomers from biological fluids were compared. SPE method for further studies was chosen. Stereoselective extraction of IBP enantiomers from serum at basic pH has been discovered. Validation of the method was carried out. Calibration curves of ibuprofen enantiomers were linear in the range of 0.1-25.0 μg/ml in serum and of 0.5-250.0 μg/ml in urine. Recovery of both enantiomers from serum and urine amounted 74-86 and 90-98%, respectively. Intra- and inter-day measurement precision and accuracy were below 15%. Limits of detection for IBP enantiomers amounted 0.05 and 0.25 μg/ml in samples of serum and urine, respectively. Limit of quantitation was also estimated. IBP enantiomers proved to be stable following three freeze and thaw cycles and during storage in autosampler at ambient temperature. The validated methods enable pharmacokinetic studies of enantiomers in both media. The elaborated HPCE method can be alternative to HPLC.     

A linear variation of the thermal expansivity with frequency shifts for the translational mode in ammonia solid II near the melting point

We examine here our spectroscopic modification of the Pippard relation which is a linear variation of the thermal expansivity alpha(p) with the frequency shifts (1/nu)(partial differentialnu/partial differentialp)(T) close to the melting point in ammonia solid II. For this we use our calculated frequencies for the Raman mode of nu (51 cm(-1)) in ammonia solid II for the pressures of 3.65, 5.02 and 6.57 kbars. We establish this linearity between alpha(p) and (1/nu)(partial differentialnu/ partial differentialp)(T) for the pressures studied in ammonia solid II close to the melting point. The observed behaviour of ammonia solid II is explained in terms of our spectroscopic relation given here.     

Separability of wild automorphisms of a polynomial ring

For a large class (including the Nagata automorphism) of wild automorphisms F of k[x, y, z] (where k is a field of characteristic zero), we prove that we can find a weight w such that there exists no tame automorphism with the same w-weight multidegree.     

Two‐phase flow electrosynthesis: Comparing N‐octyl‐2‐pyrrolidone–aqueous and acetonitrile–aqueous three‐phase boundary reactions

A microfluidic double channel device is employed to study reactions at flowing liquid–liquid junctions in contact with a boron‐doped diamond (BDD) working electrode. The rectangular flow cell is calibrated for both single‐phase liquid flow and biphasic liquid–liquid flow for the case of (i) the immiscible N‐octyl‐2‐pyrrolidone (NOP)–aqueous electrolyte system and (ii) the immiscible acetonitrile–aqueous electrolyte system. The influence of flow speed and liquid viscosity on the position of the phase boundary and mass transport‐controlled limiting currents are examined. In contrast to the NOP–aqueous electrolyte case, the acetonitrile–aqueous electrolyte system is shown to behave close to ideal without ‘undercutting’ of the organic phase under the aqueous phase. The limiting current for three‐phase boundary reactions is only weakly dependent on flow rate but directly proportional to the concentration and the diffusion coefficient in the organic phase. Acetonitrile as a commonly employed synthetic solvent is shown here to allow effective three‐phase boundary processes to occur due to a lower viscosity enabling faster diffusion. N‐butylferrocene is shown to be oxidised at the acetonitrile–aqueous electrolyte interface about 12 times faster when compared with the same process at the NOP–aqueous electrolyte interface. Conditions suitable for clean two‐phase electrosynthetic processes without intentionally added supporting electrolyte in the organic phase are proposed. Copyright © 2008 John Wiley & Sons, Ltd.     

Preparation,characterization, and antibacterial activity of organo-sepiolite/chitosan/silver bionanocomposites

Bionanocomposites with different loadings of silver (Ag) were prepared via synthesis of Ag nanoparticles (AgNPs) using the wet chemical reduction method in the lamellar space layer of the organo-sepiolite/chitosan (O-SEP/CS). The prepared O-SEP/CS/Ag bionanocomposites were characterized using various analysis methods for their structure, morphology, and optical properties. The characteristic absorption bands from the UV–visible absorption spectrum confirmed the formation of AgNPs. The antibacterial activities of O-SEP/CS/Ag bionanocomposites were investigated against gram-positive and gram-negative bacteria using the disc diffusion method. The results suggest that O-SEP/CS/Ag bionanocomposites can be useful in wide range of bio-medical applications because of high antibacterial activity.