Hyperbolic Geometry with Clifford Algebra

The Clifford algebra in D. Hestenes formulation is used to study hyperbolic geometry and some interesting theorems are obtained. The computational power of this formulation is fully revealed by the ease of extending old results and discovering new ones. An important new result is the formulas on the area and perimeter of a convex polygon, based on extending Gauss equalities.     

Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings

Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases, ₂ (the Virasoro string) and ₃ (the string).     

On the Varieties of Parabolic Subgroups, their Generalizations and Combinatorial Applications

Investigations of homogeneous varieties T=(G:P) of all cosets of finite Coxeter or Chevalley groups G by their maximal parabolic subgroups P had been conducted at the Kalunin seminar at Kiev State University since the 1970s, as were investigations of their corresponding permutation groups, geometries and association schemes.In I. A. Faradev et al. (eds), Investigations in Algebraic Theory of Combinatorial Objects (Kluwer Acad. Publ., 1994), one can find some results on the investigation of noncomplete Galois correspondence between fusion schemes of the orbital scheme for (G,T) and overgroups of (G,T), as well as calculations of the intersectional indices of the Hecke algebra of (G,T). We will discuss additional results on this topic and consider questions related to the following problems: embeddings of varieties (G:P) into the Lie algebra corresponding to Chevalley group G; interpretations of Lie geometries, small Schubert cells, connections between the geometry of G and its associated Weyl geometry in terms of linear algebra, and applications of these problems to calculations performed in Lie geometries and association schemes; constructions of geometric objects arising from Kac–Moody Lie algebras and superalgebras, and applications of these constructions to investigations of graphs of large girth and large size.     

A Characterization of Monotone and Regular Divergences

In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by encov, using the invariant properties of Amari's -connections.     

Galois rigidity of pro- pure braid groups of algebraic curves

In this paper, Grothendieck's anabelian conjecture on the pro- fundamental groups of configuration spaces of hyperbolic curves is reduced to the conjecture on those of single hyperbolic curves. This is done by estimating effectively the Galois equivariant automorphism group of the pro- braid group on the curve. The process of the proof involves the complete determination of the groups of graded automorphisms of the graded Lie algebras associated to the weight filtration of the braid groups on Riemann surfaces.

     

Simultaneous determination of 15 marker constituents in various radix Astragali preparations by solid-phase extraction and high-performance liquid chromatography

An improved quality control method was developed to simultaneously determine 15 major constituents (eight flavonoids and seven saponins) in various radix Astragali preparations, using SPE for pretreatment of samples, HPLC with diode-array and evaporative light scattering detectors (DAD-ELSD) for quantification in one run, and HPLC-ESI-TOF/MS for definite identification of compounds in preparations. Optimum separations were obtained with a ZORBAX C(18) column, using a gradient elution with 0.3% aqueous formic acid and ACN. This established method was fully validated with respect to linearity, precision, repeatability, and accuracy, and was successfully applied to quantify the 15 compounds in 19 commercial samples, including 3 dosage forms, i. e., oral solution, injection, concentrated granule, and its processed products of radix Astragali. The results demonstrated that many factors might result in significant differences in quality of the final preparations, including crude drugs, pretreatment processes, manufacturing procedure, storage conditions, etc. Then the developed method provided a reasonable and powerful manner to ensure the efficacy, safety, and batch-to-batch uniformity of radix Astragali products by standardizing each procedure, and thus should be proposed as quality control for the clinical use and modernization of herbal preparations.     

Electrodeposited polyaniline as a fiber coating for solid-phase microextraction of organochlorine pesticides from water

The study on the performance of polyaniline as a fiber coating for solid-phase microextraction (SPME) purposes has been reported. Polyaniline coatings were directly electrodeposited on the surface of a stainless steel wire and applied for the extraction of some organochlorine pesticides (OCPs) from water samples. Analyses were performed using GC-electron capture detection (GC-ECD). The results obtained show that polyaniline fiber coating is suitable for the successful extraction of organochlorine compounds. This behavior is most probably due to the porous surface structure of polyaniline film, which provides large surface areas and allowed for high extraction efficiency. Experimental parameters such as adsorption and desorption conditions were studied and optimized. The optimized method has an acceptable linearity, with a concentration range of 1-5000 ng/L. Single fiber repeatability and fiber-to-fiber reproducibility were less than 12 and 17%, respectively. High environmental resistance and lower cost are among the advantages of polyaniline fibers over commercially available SPME fibers. The developed method was applied to the analysis of real water samples from Yangtse River and Tianmu Lake.     

Solid-phase microextraction for the determination of benzoylureas in orange juice using liquid chromatography combined with post-column photochemically induced fluorimetry derivatization and fluorescence detection

A solid-phase microextraction (SPME) method has been developed for the determination of six benzoylureas (diflubenzuron, triflumuron, hexaflumuron, teflubenzuron, lufenuron, and flufenoxuron) in natural orange juice based on the direct immersion mode of a 60 microm polydimethylsiloxane/divinylbenzene fiber. An orange juice was obtained from blended, homogenized, and diluted ecological natural orange juice samples. An aliquot of 3 mL of a spiked sample was extracted under optimum SPME conditions. The determination of benzoylureas was carried out using HPLC combined with post-column photochemically induced fluorimetry derivatization and fluorescence detection. The limits of quantification obtained in matrix were within the range of 0.02 to 0.04 mg/kg and these limits are lower than the maximum residue levels established in Spanish regulations for all pesticides in this study. Recoveries in juice samples ranged between 85 and 110% and relative standard deviations between 1.8 and 7.4%.     

Analysis of volatile components of drugs and explosives by solid phase microextraction-ion mobility spectrometry

Current ion mobility spectrometry (IMS) devices are used to detect drugs and explosives in the form of particles and, in cases where the vapor pressure of the drugs or explosives is sufficiently high, the gas can be sampled and detected directly. The aim of this study is to demonstrate the use of solid phase microextraction (SPME) as a preconcentration technique coupled to an IMS for the detection of odor signature compounds of drugs and explosives. The reduced mobilities (K(o)) and IMS operating conditions for the odor signature compounds of cocaine, marijuana, and 3,4-methylenedioxy-N-methylamphetamine (MDMA) are reported for the first time. LODs, linear dynamic ranges (LDRs), and the precision of the analysis of these odor signature compounds, and the explosive taggant 2,3-dimethyl-2,3-dinitrobutane (DMNB) were obtained by SPME-IMS and normal IMS conditions. The systematic optimization of the IMS operating parameters for the detection of these odor compounds is also reported incorporating the use of genetic algorithms (GAs) for finding the optimal settings for the detection of these compounds of interest. These results support the case for targeting volatile components as a presumptive detection for the presence of the parent compounds of drugs and explosives. Furthermore, the IMS-specific GA developed can be used as an optimization tool for the detection of other compounds of interest in future work.