Quasi-Permutation Representations of p-Groups of Class 2

If G is a finite linear group of degree n, that is, a finitegroup of automorphisms of an n-dimensional complex vector space(or, equivalently, a finite group of non-singular matrices oforder n with complex coefficients), we shall say that G is aquasi-permutation group if the trace of every element of G isa non-negative rational integer. The reason for this terminologyis that, if G is a permutation group of degree n, its elements,considered as acting on the elements of a basis of an n-dimensionalcomplex vector space V, induce automorphisms of V forming agroup isomorphic to G. The trace of the automorphism correspondingto an element x of G is equal to the number of letters leftfixed by x, and so is a non-negative integer. Thus, a permutationgroup of degree n has a representation as a quasi-permutationgroup of degree n. See [8].     

Gas chromatographic determination of some phenolic compounds in fuels and engine oil after simultaneous derivatization and microextraction

In this study, a simultaneous derivatization/air‐assisted liquid–liquid microextraction method has been developed for sample preparation of some phenolic compounds in fuels and engine oil. Analytes are transferred by back liquid–liquid extraction into NaOH solution and then are derivatized with butyl chloroformate and extracted simultaneously into carbon tetrachloride. The extracted derivatized analytes are analyzed using gas chromatography with flame ionization detection. The effect of extracting solvent type, derivatization agent and extraction solvent volumes, ionic strength of the aqueous solution, number of extraction cycles, etc., on the extraction efficiency is investigated. The calibration graphs are linear in the range of 3–10 000 μg/L. Enhancement factors, enrichment factors, and extraction recoveries are in the ranges of 497 to 1471, 571 to 991, and 60 to 109%, respectively. Detection limits are obtained in the range of 0.8 to 2.0 μg/L. Relative standard deviations for the extraction of each selected phenols are in the ranges of 2–4% for intraday (n = 6) and 3–6% (n = 5) for interday precisions for 200 μg/L. This technique is successfully applied for the extraction, preconcentration, and determination of the selected phenols in gasoline, kerosene, gas oil, and engine oil.     

Limq → ∞ \frac{c(G)}{r(G)} for Simple Groups

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let c(G) denote the minimal degree of a faithful representation of G by complex quasi-permutation matrices and let r(G) denote the minimal degree of a faithful rational valued character of G. Also let G denote one of the symbols A_l, B_l, C_l, D_l, E₆, E₇, E₈, G₂, F₄, ²B₂, ²E₄, ²G₂, and ³D₄. Let G(q) denote simple group of type G over GF(q). Let c(q) = c(G(q)) and r(q) = r(G(q)). Then we will show that lim Lim_q = 1.     

Quasi-Permutation Representations of Metacyclic p-Groups With Non-Cyclic Center

By a quasi-permutation matrix we mean a square matrix over the complex field with non-negative integral trace. Thus every permutation matrix over is a quasi-permutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q (G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field , and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. In this paper we will calculate c(G), q(G), and p(G), where G is a metacyclic p-group with non-cyclic center and p is either 2 or an odd prime number.AMS Subject Classification (2000) 20C15     

Magnetic Solid Phase Extraction Coupled with HPLC Towards Removal of Pigments and Impurities from Leaf-derived Paclitaxel Extractions of Taxus baccata and Optimization via Response Surface Methodology

A reusable and cost-effective magnetic graphite oxide (Fe₃O₄NPs@GO) nanocomposite was fabricated and applied for pre-purification of paclitaxel from leaf-derived crude extract of Taxus baccata. Furthermore, the potential roles of three crucial criteria (i.e., adsorbent dosage, sorption temperature and agitation/shaking power) on the two responses [i.e., efficiency of plant pigments removal (EPPR) and efficiency of taxol purity (ETP)] were examined and simultaneously optimized through response surface methodology. The nanocomposite was accurately characterized using TEM, AFM, BET, FT-IR, Raman and VSM. Moreover, for both proposed second-degree polynomial regression models, highly significant correlations were achieved between the experimental and predicted data (p < 0.0001). Meanwhile, the optimum conditions to simultaneously acquire the maximum EPPR (94.0 %) and ETP (11.4 %) were recorded as adsorbent dosage of 37.7 g L⁻¹, sorption temperature of 30.7 °C and agitation power of 153.1 rpm; and the predictive results were confirmed using experimental rechecking survey. Interestingly, upon five consecutive treatments, the nanocomposite still exhibited substantial potency in eliminating large amounts of plant pigments and impurities (up to 90 %), without significant reduction on sorption capacity and magnetism thereof. Our results demonstrated that the current nanocomposite, as SPE sorbent for MSPE, could be a simple, fast and reusable approach for HPLC-based purification studies of paclitaxel, and probably other plant secondary metabolites.

     

Raman active jagged-shaped gold-coated magnetic particles as a novel multimodal nanoprobe

The creation of novel engineered multimodal nanoparticles (NPs) is a key focus in bionanotechnology and can lead to deep understanding of biological processes at the molecular level. Here, we present a multi-component system made of gold-coupled core-shell SPIONs, as a new nanoprobe with signal enhancement in surface Raman spectroscopy, due to its jagged-shaped gold shell coating.     

A note on quasi-permutation representations of groups with two character degrees

In Behravesh (J. Lond. Math. Soc. (2) 55:251–260, 1997), we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper we will show that in groups with two character degrees we may have c(G)=q(G)≠p(G).     

Rayleigh and Lamb waves at liquid-solid boundaries

The equations governing Rayleigh and Lamb mode propagation are examined for free and for liquid-loaded solids. Examples are given to show under what conditions the free-solid approach yields acceptable solutions for the velocities and under what conditions the more involved liquid-loaded solid formulism must be used.     

Quasi-permutation representations of 2-groups satisfying the Hasse principle

In Behravesh (J Lond Math Soc 55(2):251–260, 1997), c(G), q(G) and p(G) are defined for a finite group G. In this paper, we will calculate c(G), q(G) and p(G) for some 2-groups G satisfying the Hasse principle in Fuma and Ninomiya (Math J Okayama Univ 46:31–38, 2004). We will consider

$G=\langle x, y, z: x^{2^{m-2}}=y^{2}=z^2=1, [x, y]=[y, z]=1, x^{z}=xy \rangle$

where m ≥ 4. By comparing the character tables and Galois conjugacy classes of Irr(G) and Irr(Z(G)), we will show that

$c(G)=q(G)=p(G)= 2c(Z(G))=2^{m-2}+4.$