Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.     

Electrorheological characteristics of polyaniline and its copolymer suspensions with ionic and nonionic substituents

Electrorheological (ER) characteristics of ER fluids, composed of suspensions of semiconducting polyaniline and two different copolyaniline particles in silicone oil, were determined experimentally. Ionic sodium diphenylamine sulfonate and nonionic o-ethoxyaniline were used to synthesize copolyanilines, i.e. N-substituted copolyaniline and poly(aniline-co-o-ethoxyaniline), respectively. ER fluids composed of these three different polymers were compared with respect to their rheological properties under an applied electric field. It was found that ER fluids containing a copolymer with an ionic group exhibited the highest ER performance among polyaniline and its copolymer systems in a shear-rate region above 1 s⁻¹. Received: 22 February 1999 /Accepted in revised form: 25 August 1999     

Determination of pyrrolizidine alkaloids in comfrey by liquid chromatography-electrospray ionization mass spectrometry

Symphytum officinale L. (comfrey) is a medicinal plant commonly used in decoctions and aliments. Besides therapeutic bioactive compounds present in the herb, it is found to contain hepatotoxic pyrrolizidine alkaloids (PAs), such as lycopsamine and others. In the present study, PAs such as lycopsamine, echimidine and lasiocarpine were determined using electrospray liquid chromatography-mass spectrometry (LC-MS) with the method precision (relative standard deviation, RSD) <10%. Detection of lycopsamine, symviridine and their N-oxides could be confirmed with a newly developed method based on HPLC ion-trap and orbitrap MS with electrospray ionization interface. With LC-MS, quantitative analysis of lycopsamine in the botanical extract was carried out. The effect of extraction solvent was optimized by sonication and methanol: H₂O (50:50) was selected. Then a rapid method based on pressurized hot water extraction (PHWE) was employed for the extraction of lycopsamine from comfrey followed by the comparison with heating under reflux with the RSD ranging from 2.49% to 19.32%. Our results showed a higher extraction efficiency for heating under reflux compared with PHWE. It was proposed that the lower extraction efficiency for PHWE was attributable to dissolved nitrogen from air which caused the reduction in the solubility of lycopsamine in the compressed hot solvent. In this study, quantitative analysis of PAs in comfrey was demonstrated. In addition, it was found that the use of subcritical water for extractions depended on the physical properties of the dissolved solutes and their tendency to degrade under the chosen extraction conditions.     

Validation and application of orientational order-based TMD prediction

Through our recent examination of four famous water models, we hypothesized that there should be common features of orientational order universally at the temperature for maximum density (TMD) of 1 g/cm³ whatever reasonable water model used. However, it was derived empirically rather than theoretically and it demands more severe tests eagerly to be a common law. In the present work, we tested two additional water models, TIP4P-2005 and TIP5P-Ew models developed recently. From this, we found the consistent common features of orientational order around reported values of TMD again. To demonstrate simple yet effective predictability of an unknown TMD for a certain water model using the method derived from our hypothesis, simulations of our method were carried out at several temperatures with intervals of 20 °C for TIP4P-ice model. In spite of its much less computational cost and temperature range that was chosen arbitrarily, TMD was predicted correctly with resolution of 20 °C at least. We propose that our method offers a useful guideline for TMD by narrowing down the choice of TMD candidates without heavy computational efforts, at least for point-charge water models.     

Dynamics of a finite harmonic oscillator chain with a surface impurity

A method is presented for constructing the normal modes and spectrum of a finite harmonic oscillator chain to which a polyatomic surface impurity is attached. This scheme is a generalization of an earlier theory due to Puszkarski. Special attention is devoted to localized surface modes and to the identification of the circumstances which cause them to occur. Diagnostic calculations have been performed in order to learn how an adsorbed diatomic molecule alters the normal modes and eigenfrequencies of the lattice. Examples are provided of cases where these effects are slight and of others where the perturbation generates localized optical and/or acoustic surface modes.     

Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Towards Bioprospection of Commercial Materials of Mentha spicata L. Using a Combined Strategy of Metabolomics and Biological Activity Analyses

Spearmint (Mentha spicata L.) has been widely studied for its diversity of compounds for product generation. However, studies describing the chemical and biological characteristics of commercial spearmint materials from different origins are scarce. For this reason, this research aimed to bioprospecting spearmint from three origins: Colombia (Col), Mexico (Mex), and Egypt (Eg). We performed a biological activity analysis, such as FRAP, DPPH, and ABTS, inhibition potential of S. pyogenes, K. pneumoniae, E. coli, P. aeuroginosa, S. aureus, S aureus Methicillin-Resistant, and E. faecalis. Furthermore, we performed chemical assays, such as total polyphenol and rosmarinic acid, and untargeted metabolomics via HPLC-MS/MS. Finally, we developed a causality analysis to integrate biological activities with chemical analyses. We found significant differences between the samples for the total polyphenol and rosmarinic acid contents, FRAP, and inhibition analyses for Methicillin-Resistant S. aureus and E. faecalis. Also, clear metabolic differentiation was observed among the three commercial materials evaluated. These results allow us to propose data-driven uses for the three spearmint materials available in current markets.     

Synthesis and electrorheological characterization of emulsion polymerized SAN‐clay nanocomposite suspensions

Styrene‐acrylonitrile (SAN) copolymer‐clay nanocomposite was synthesized by emulsion polymerization, which is the easiest method of intercalation (e.g., melt or solution intercalation). Existence of the intercalated polymer was verified by Fourier transform‐infrared spectroscopy and X‐ray diffraction (XRD) analysis. From XRD, we confirmed the insertion of styrene‐acrylonitrile copolymer between the interlayers of clay, whose separation consequently becomes larger than that of the polymer‐free clay. Thermogravimetric analysis showed that the thermal stability of the organic polymers was sustained. Using electrorheological (ER) fluids composed of intercalated particles and silicone oil, we observed typical ER behavior, such as higher shear stress in the presence of an electric field and increasing yield stress with particle concentration. We further observed the critical shear rate at which the ER fluids exhibit pseudo‐Newtonian behavior.